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A reaction force perspective of a model amide bond formation reaction
Accepted Manuscript A reaction force perspective of a model amide bond formation reaction V. Suresh Kumar Neelamraju, Tanashree Jaganade PII: DOI: Reference:
S2210-271X(19)30043-X https://doi.org/10.1016/j.comptc.2019.02.003 COMPTC 12422
To appear in:
Computational & Theoretical Chemistry
Received Date: Revised Date: Accepted Date:
27 October 2018 13 January 2019 6 February 2019
Please cite this article as: V.S. Kumar Neelamraju, T. Jaganade, A reaction force perspective of a model amide bond formation reaction, Computational & Theoretical Chemistry (2019), doi: https://doi.org/10.1016/j.comptc. 2019.02.003
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A reaction force perspective of a model amide bond formation reaction V Suresh Kumar Neelamraju1 , Tanashree Jaganade Center for Computational Natural Sciences and Bioinformatics (CCNSB), International Institute of Information Technology, Hyderabad - 500 032, India.
Abstract A reaction force approach of amide bond formation between ammonia and formic acid is demonstrated along with each atom’s contribution to structural changes and electronic reordering of the chemical reaction. The B3LYP/631G(d,p) level of density functional theory based calculations were carried out to explore transition states (TSs) of stepwise and concerted amide bond formation reaction pathways. Various stages that characterize structural and electronic properties in the progress of reaction are identified from reaction force calculations on energetics of geometries obtained from intrinsic reaction coordinate (IRC) pathways. The reaction works in preparative region of the pathway are less than that in relaxation stage, reflecting favorable formation of product geometries (Formamide and water). More than 80% of the activation energy comes from structural changes in preparative region. A comparison of reaction force profiles and reaction works in preparative region of TS1 and TS2 of stepwise path and TS3 of concerted path discloses that both the stepwise and concerted mechanisms are equally competent in terms of kinetic feasibility. The atomic resolution of pathways unveils that, hydrogen and oxygen forming the water molecule contribute significantly to the negative reaction energy of product geometries. The preferential contribution of the atoms comes from enhanced ∗V
Suresh Kumar Neelamraju for Computational Natural Sciences and Bioinformatics (CCNSB), International Institute of Information Technology, Hyderabad - 500 032 India and on lien from Department of Physics, Koneru Lakshmaiah Education Foundation, Green fields, Vaddeswaram, Guntur 522 502, India, Email: [email protected], Tel.: +91 9848985146 1 Center
Preprint submitted to Journal of LATEX Templates
January 13, 2019
negative charge of the oxygen and positive charge on hydrogen in the progress of reaction. Keywords: Potential energy, Reaction force, Amide bond, Atomic contribution, Electronic reordering
1. Introduction Description of a chemical or physical processes in terms of derivatives of potential energy with respect to reaction coordinate, i.e., reaction force, is advantageous over analysis of the energy change with the reaction coordinate. The 5
reaction force provides a realistic analysis of chemical reactions by separating a reaction path into three stages. The preparative stage changes reactants to reactive species, transition region converts the reactive species to perturbed form of products and the relaxation stage shows how the perturbed products relaxed to stable product geometries [1, 2]. Also, it allows to estimate atomic contribu-
10
tion to the structural changes and electronic activity in all the three stages of reaction path. This analysis helps to identify reactive center of the molecular system that is responsible for change in potential energy along the reaction path [1, 3, 4]. The intrinsic reaction coordinate (IRC)[5, 6] approach introduced by Fukui
15
is popularly used quantum chemical method for exploring the minimum energy path that connects transition state to both the reactants and products. Analysis of such reaction paths using the concepts like reaction force, reaction force constant and reaction electronic flux and make use of procedure developed by Toro-Labb´e et al. provide an in depth atomic and electronic level understanding
20
of chemical reactions [1, 2, 7, 8, 9, 10, 11, 12]. Several reactions are studied using the concept, reaction force. V¨ohringerMart´inez et al. reported the dominant role of proton in activation energy barrier of proton transfer reactions, ONSH → HONS and the reactions of neutral to zwitterionic form of tryptophan [1]. Also, Jedrzejewski et al. highlighted elec-
25
tronic and atomic contribution in reactions HONS → ONSH and CO + HF →
2
HCOF [3]. Studies on relationship between reaction force and reaction force constant in reaction, OH-N=S → O=N-SH by Jaque et al. summarized that reaction force constant carries information on chemical bonding, rigidity and electronic population [13]. The effects of aqueous solution in reducing the ac30
tivation energy barrier of reaction, H3 C-Cl + H-OH → H3 C-OH + H-Cl was reported by Bruda al. [14]. In line with above mentioned reactions, amide bond formation mechanisms suggested by Oie et al.[15] also come under proton transfer reactions. The stepwise and concerted mechanisms for the amide bond formation reaction, NH3 +
35
HCOOH → H2 N-CHO + H2 O are shown in Fig. 1. Jensen et al. used total electron densities and localized molecular orbital to study energetics of the reaction and summarized that the reaction is a good model to study a dipeptide system [16]. A series of quantum chemical studies on model amide bond formation reactions involving amine and Mg cation as catalysts were also reported
40
by Oie et al.[17, 18, 19]. The mechanisms were also used to justify experimental observations in preferential cyclic dimerization reaction of tripeptides containing tetrahydrofuran amino acids and cyclic trimerization of furan based amino acids [20, 21]. Also, experimental evidence for water assisted hydrolysis of formamide[22, 23] was studied using a mechanism reverse to that suggested
45
by Oie et al. and pathways were modeled using ab into calculations [24, 25]. Even though, the reaction is thoroughly studied, partition of the pathways into structural changes and electronic rearrangements; and role of each atom in driving the reaction are not reported. The present work sheds light on these aspects of the reaction, NH3 + HCOOH → H2 N-CHO + H2 O, using the reaction force
50
approach. We explored the inherent contribution of each atom on the activation energy barrier of the reaction using both stepwise and concerted mechanisms. The article reports that more than 80% of activation energy of reaction in preparative stage is invested to disturb hybridization of carbon and perturb the trigonal
55
pyramidal structure around nitrogen. The electronic rearrangements in transition region are associated with the hydrogen atom. The role of oxygen and 3
hydrogen of water molecule is significant in making the reaction energetically favorable.
2. Methodology 60
The initial geometries[26] were subjected to optimization in gas phase using B3LYP[27] functional of DFT and 6-31G(d,p)[28] basis set. The B3LYP functional is appropriate for the study as it mixes Hartree-Fock exchange and cancels certain delocalization error which is important in modeling transition state geometries associated with stretched bonds [29]. Also, B3LYP/6-31G(d,p)
65
level of theory is used in similar studies involving, alanine, phenylalanine and tryptophan [1, 30]. All the optimized geometries were further subjected to Hessian calculations. Observed real frequencies confirm that the geometries except transitions states were at local minima. The transition states were characterized by presence of one imaginary frequency. The thermodynamic properties were
70
calculated at 298.15 K and 1 atm. The schematic representation of the reaction pathways for amide bond formation are shown in Fig. 1. The uncatalyzed stepwise pathway (Fig. 1) involves transfer of a hydrogen atom from ammonia to carbonyl oxygen of formic acid leading to the formation of a diolic intermediate. Transfer of a proton from one
75
of the OH groups to another OH of diol and further breaking of H-O-H molecule from the intermediate yields formamide and water as the products of reaction. The concerted pathway eliminates water molecule using -OH from the carboxyl terminal and -H from the amine group. The difference between two mechanisms is that while the stepwise mechanism is initiated by transfer of hydrogen from
80
ammonia to carbonyl oxygen of formic acid, the concerted mechanism begins with transfer of hydrogen from ammonia to hydroxyl oxygen of the formic acid. Equations shown below were used to calculate change in free energy, (∆G), and change in electronic energy (∆E) for formation of species in the pathways. ∆X = (XI/TS ) − (XR1 + XR2 )
(1)
∆X = (XP + XW ) − (XR1 + XR2 )
(2)
4
Figure 1: Schematic representation of stepwise and concerted reaction pathways for uncatalyzed amide bond formation, as suggested by Oie et al.[15]. Note: Number notation shown for an atom of a geometry is used in the discussion.
where X stands for free energy (G) or electronic energy (E), I: intermediate, TS: transition state, P: formamide, W: water, R1: ammonia and R2: formic acid. While equation (1) is used for all geometries except the products, the (2) 85
is used for product structure. 2.1. Reaction path, reaction force and atomic resolution of reaction force and reaction work The transition states as obtained from the mechanisms shown in Fig. 1 were used to explore intrinsic reaction paths using the IRC procedure as implemented
90
in Gaussian09[31] package. The paths are explored using Gonzalez and Schlegel algorithm[32] in mass weighted internal coordinates for 300 points with a step size of 0.01 a0 amu1/2 . The paths for 500 points were also obtained using
5
the same method to gain additional insights. Details of the algorithm and procedure used to obtain a new geometry on pathway from the known geometry 95
is explained elsewhere [1]. The reaction force on each step of the IRC is negative derivative of the molecular energy, Emol , with respect to the reaction coordinate, (ξ): dEmol (ξ) (3) dξ We obtained reaction force profiles corresponding to each of the TS1, TS2 F (ξ) = −
and TS3 IRC pathways (see Fig. 1) by calculating the negative ratio between 100
difference in electronic energies of adjacent geometries on the pathways and difference in their respective reaction coordinates. Importance of reaction force profile comes from its additional features compared to system’s potential energy surface. They are, 1) the force is zero at maximum and minimum of the energy and 2) it is either maximum or minimum
105
at inflection point of the potential energy. The minimum, zero and maximum divide the reaction force profile into several stages [4]. These stages provide insights into effects of external forces, structural and electronic rearrangements on the reaction mechanism. The bond lengths and bond angles of atoms involved in proton transfer pathways of TS1, TS2 and TS3 were used to analyze
110
structural changes in various stages of the reaction pathways. Atomic resolution of reaction force is understood from the Hellmann-Feynman (HF) theorem[33] represented as, hΨ | ∂H dE ∂λ | Ψi = dλ hΨ | Ψi
(4)
The theorem is a key ingredient for quantum mechanical treatment of forces acting on nuclei in a molecule [34]. The quantity, -dE/dλ represents classical force on a nucleus of system, if λ is position vector of that nucleus [34]. The force uniquely identifies a nucleus in a molecule[3] and is known as Hellmann115
Feynman (HF) force. By using the magnitudes of the HF force on a nucleus at each step of the IRC pathway and displacement of the nucleus while moving to the next step in 6
advancement of reaction, the reaction work of an atom is calculated. Following is the procedure used to estimate the reaction work. 120
The atomic contribution of each atom to move on the intrinsic reaction path is quantified from work (W ) required to move an atom (i) from a position (say k1 : (x1 ,y1 ,z1 )) in the current structure (α) to its position (say k2 : (x2 ,y2 ,z2 )) in the next structure (α + 1) on the path. It is the product of gradient, gi,α,k of atom, i, in the structure characterized by value of α, which corresponds to a
125
structure of intrinsic reaction coordinate, ξ, calculated along the three coordinates and displacement, di,α,k , required to move atom i along the coordinate k from the actual structure α to the next structure, α+1. It is represented by the equation:
Wi,ξ =
ξ x,y,z X X α=0
gi,α,k .di,α,k
(5)
k
In line with above equation, we calculate the work (Wi,n ) done on atom i, 130
in n steps of IRC pathway using the following equation:
Wi,n =
n X
(Fxji )(x(j+1)i − xji ) + (Fyji )(y(j+1)i − yji ) + (Fzji )(z(j+1)i − zji ) (6)
j=1
Here, Fxji , Fyji and Fzji are force components of atom i, at a step, j; (xji , yji , zji ) and (x(j+1)i , y(j+1)i , z(j+1)i ) are coordinates of ith atom at jth and (j + 1)th steps respectively. 2.2. Wiberg bond indices The Wiberg bond indices[35] that measure the electron population overlap between two atoms were estimated for the bonds involved in bond breaking and forming processes. The indices were obtained from: WAB =
XX
2 Pab
(7)
a∈A b∈B 135
where a and b are atomic orbitals of atoms A and B respectively. Pab is density matrix element. The indices were calculated from natural bond orbital 7
(NBO)[36] program. Also, the natural charges on atoms as obtained from NBO calculations are used to identify localization of charge around the atoms. All the quantum chemical calculations are carried out using Gaussian09[31] 140
suite of quantum chemical programs.
3. Results and discussion Coordinates of all the geometries in study are shown in Table S1. Absolute energies of the species are shown in Tables S2. First, free energy profiles and potential energy surfaces obtained from IRC pathways are analyzed for kinetic 145
and energetic aspects in the formation of product geometries. Next, the reaction force curves of TS1, TS2 and TS3 pathways are presented to gain insights into structure, electronic activities in progress of the reaction and kinetic aspects of the pathways. Subsequently, the atomic contribution to activation energy barrier is described to determine the atomic sites that play major role in fixing
150
barrier heights and reaction energies of the pathways. The Wiberg bond index profiles and natural charges on atoms are used to substantiate electronic activity in bond breaking and forming processes. 3.1. Energetics of optimized geometries and IRC pathways Optimized geometries on stepwise and concerted pathways of amide bond
155
formation reactions along with magnitudes for change in free energy, ∆G, and electronic energy ∆E of formation; and the geometries and relative energetics obtained from IRC calculations are shown in Fig. 2. The potential energy (PE) pathways of TS1, TS2 (both are of stepwise mechanism) and TS3 (concerted mechanism), generated by IRC calculations are shown in Figs. 3 and S1. Abso-
160
lute energies of fully optimized species and geometries obtained IRC pathways are shown in Tables S2(a) and S2(b) respectively. The formation of formamide from ammonia and formic acid is thermodynamically favored by 4.1 kcal/mol. Change in free energy for formation of intermediate in stepwise pathway is 12.2 kcal/mol. The free energies of activation of
8
Figure 2: Left: Optimized geometries on stepwise and concerted reaction pathways of amide bond formation between ammonia and formic acid obtained from B3LYP/6-31G(d,p) level of theory in gas phase. Change in free energy of formation, ∆G, and change in electronic energy of formation, ∆E, are given in kcal/mol. Right: Geometries on (A) TS1, (B) TS2 and (C) TS3 reaction pathways obtained from IRC calculations carried out at B3LYP/6-31G(d.p) level of theory in gas phase. The electronic energy of activation, ∆E ‡ , and reaction energy, ∆E 0 are calculated relative to electronic energy, E of initial geometry in pathways. The magnitudes are in kcal/mol. Notations: TSX:R - Reactant on TSX pathway, TSX:TS - Transition state on TSX pathway, TSX:I, Intermediate on TSX pathway, TSX:P - Product on TSX pathway. X: 1, 2, or 3.
9
165
TS1, TS2 and TS3 are 43.4, 41.9 and 44.7 kcal/mol respectively, indicating that both the stepwise and concerted mechanisms are equally competent in terms of kinetic feasibility as difference in the energies of activation is minimal. The results agree with trends of earlier computational studies by Oie et al., based on MP2/3-21G(d,p) level of theory (Free energy of activation, ∆G‡ , of TS1,
170
TS2 and TS3 are 50.0, 35.6 and 52.6 kcal/mol respectively and change in free energy of intermediate and product are 16.7 and -0.4 kcal/mol respectively) [15]. Kinetic feasibility of the pathways is also on par with the reports of ab initio studies on uncatalyzed amide bond formation of the model reaction carried out by Oie et al.[19]. Also, the QM/MM calculations on the model reaction revealed
175
that the free activation energies of TS1, TS2 and TS3 are 44.3, 41.6 and 43.6 kcal/mol respectively[37]. This confirms that TS geometries explored in the study are appropriate for subsequent calculations. Further analysis on the barrier heights comes from the potential energy plots as given by IRC calculations on TS1, TS2 and TS3 geometries (Figs. 3 and S1).
180
We caution here that the IRC calculations do not always converge to full optimized geometries [30]. Also, we make a note that discussion on the IRC pathway in the current study is limited to the range of reaction coordinates -3.0 to +3.0 a0 amu1/2 about the transition state of respective pathway, unless specified. Relative energies of transitions states TSX-TS (X=1-3) and products (TS1-I,
185
I: Intermediate, TS1-P, TS2-P, P: Product) on PE plots of TSX-TS (X=1,2,3) are measured with respect to initial geometries on respective pathways (TS1R, TS2-I and TS3-R, R: Reactant). Electronic energy of activation, (∆E ‡ ) of transition states TS1-TS, TS2-TS and TS3-TS are 26.6, 27.4 and 22.2 kcal/mol respectively. The relative electronic energies of product geometries (also re-
190
ferred to as reaction energies, ∆E 0 ), TS1-I, TS2-P and TS3-P are -6.0, -5.6 and -7.8 kcal/mol respectively. In case of extended IRC pathways (ξ = -5.0 +5.0 a0 amu1/2 ), the ∆E ‡ of TS1-TS, TS2-TS and TS3-TS are 36.1, 32.3, and 34.3 kcal/mol respectively and ∆E 0 of TS1-I, TS2-P and TS3-P are 2.2, -6.6 and -4.3 kcal/mol respectively (see Fig. S1). Equal kinetic preference of both
195
the mechanisms is observed from the extended IRC pathways. We compare the 10
energetics with change in electronic energy of formation (∆E) of fully optimized geometries and seek agreement with trends (The ∆E of TS1, TS2, TS3, INT and Products are 33.1, 32.3, 34.9, -1.3 and -3.1 kcal/mol respectively). 3.2. Reaction force profiles and reaction works 200
To gain insights into structural and electronic effects on the reaction barrier heights, the reaction force plots corresponding to TS1, TS2 and TS3 pathways shown in Figs. 4 and S1 are analyzed. The minimum, zero and maximum points of the reaction force, divide the reaction path into four zones. The reaction coordinate, ξ, corresponding to the minimum, zero and maximum reaction force
205
are represented by α, β and γ respectively. The reaction works of individual atoms summed over total number steps of a zone are calculated using the equation 6. The sum of contributions from each atom of the system in a zone is the total reaction work of the zone, which is shown as Wn (n = 1,2,3,4) in Fig. 4. Magnitudes of bond lengths and bond angles of atoms involved in bond breaking
210
and formation process of the TS1, TS2 and TS3 reaction pathways are shown in Tables S3, S4 and S5 respectively. TS1 pathway: Amplitude of reaction force curve in preparative stage (TS1R → α) is less deep and wider than that in relaxation stage (γ → TS1-I) and W1 < W4 , indicating that formation of diolic intermediate (TS1-I) from ammonia
215
and formic acid (TS1-R) is favorable. The preparative stage brings the reactants, ammonia and formic acid close to each other such that distance between ◦
C1 and N1 reduced by 0.37 A (Table S3). Also, the stretching of bonds, N1-H2 ◦
and C1=O1 by 0.05 and 0.09 A respectively, disturb the trigonal pyramidal structure of ammonia and sp2 hybridization of carbon atom. The work invested 220
for these changes is W1 : 21.9 kcal/mol (82.6% of the total electronic energy of activation ∆E ‡ : 26.6 kcal/mol), corresponds to potential energy required to reach the reaction force minimum from the reactant. The work W2 = 4.61 kcal/mol spent in the region ξ = α to β corresponds to potential energy difference between transition state and reaction force minimum. The energy is invested for
225
rearrangement of electron density due to stretching of the bonds N1-H2 and 11
Figure 3: Potential energy surfaces of TS1, TS2 and TS3 pathways as given by IRC calculations of amide bond formation between ammonia and formic acid.
12
Figure 4: Reaction force plots of TS1, TS2 and TS3 as given by IRC calculations of amide bond formation between ammonia and formic acid. Magnitudes of reaction works, W1 to W4 are in kcal/mol.
13
C1= O1. Beyond β, the reaction force increases and becomes maximum at ξ = γ, indicating completion of rearrangement of electron density, with potential energy difference between reaction force maximum and transition state, W3 = -8.0 kcal/mol. Finally, the system relaxes with structural changes (formation of ◦ 230
O1-H2 and C1-N1 bonds with 0.97 and 1.46 A respectively and increase of N1C1-O1 angle from 95.3◦ to 108.9◦ , confirms sp3 carbon) that involve the work, W4 = -24.6 kcal/mol, corresponding to potential energy difference between the TS1-I and geometry at γ. The reaction energy is the sum of all contributions, W1 to W4 , gives -6.06 kcal/mol, representing preferential formation of TS1-I
235
(diol intermediate) from ammonia and formic acid. This is in contrast to the result obtained from the free energy data. But, we seek agreement with inferences obtained from the reaction force profile of extended reaction path (ξ = -5.0 to 5.0 a0 amu1/2 , See Fig. S1). It shows that formation of TS1-I is not favorable as W1 (31.4 kcal/mol) > W4 (25.9 kcal/mol). Comparison of the reac-
240
tion works with that in reaction force profile of ξ = -3.0 to 3.0 a0 amu1/2 infers that while W1 is increased by 10 kcal/mol, W4 remains same. The extension to the reaction coordinate takes account of the additional work in the preparative region of the pathway and explored a comparatively stable reactant geometry. The study recognizes the importance of range considered for reaction coordinate
245
of the pathway. TS2 pathway: It describes the reaction that transforms diol intermediate (TS2-I) to formamide and water (TS2-P). It involves breaking of O2-H1 and C1-O1 bonds and formation of H1-O1 bond and simultaneous release of water as the reaction progresses. The reaction is favorable as amplitude of reaction
250
force curve in relaxation stage (γ → TS2-P) is larger than that in preparative stage (TS2-I → α). In the first stage, the TS2-I is activated by elongation of the bonds O2-H1 and C1-O1 that disturb sp3 hybridization around the carbon. It utilizes the work, W1 = 23.2 kcal/mol, that corresponds to potential energy difference between the reactive species (geometry at α) and reactant. The work
255
is 84.7% of total electronic energy of activation, 27.4 kcal/mol. Beyond, α, negative reaction force decreases to zero at ξ = β, that costs the work, W2 = 14
4.26 kcal/mol, invested for reordering of electron density due to stretching of the bonds. Further, reaction force increases to positive maximum at ξ = γ, where rearrangement of electron density due to breaking of bonds, O2-H1 and C1-O1 260
completes within the Born-Oppenheimer approximation. This involve the work W3 = -6.29 kcal/mol, which corresponds to potential energy difference between geometry at reaction force maximum and transition state. In the last stage, the structure at reaction force maximum, relaxes with formation of formamide and water, using the work, W4 = -26.75 kcal/mol. Summing up all the works W1
265
to W4 , yield the reaction energy of -5.59 kcal/mol. This indicates formation of formamide and water (TS2-P) from TS2-I is favorable reaction. Increase in range of reaction coordinate to ± 5.0 a0 amu1/2 enhances the magnitudes of W1 and W4 to 28.4 and 32.4 kcal/mol (See Fig. S1) and retains the trends discussed above.
270
TS3 pathways: The path delineates transformation of ammonia and formic acid (TS3-R) into formamide and water (TS3-P) in a single step. Comparison of reaction force amplitudes in preparative stage (TS3-R → α) and relaxation stage (γ → TS3-P) of the path infers that formation of TS3-P from TS3-R is energetically favorable reaction. Preparative stage involves elongation of bonds ◦
275
◦
N1-H2 (0.04 A), C1-O2 (0.29 A) and brings both the reactants close to each ◦
other so that distance between N1 and C1 reduces by 0.24 A. These changes requires the work W1 = 19.0 kcal/mol, corresponding to the potential energy difference between reactive species and reactants. The energy is 85.1% of total electronic energy of activation 22.31 kcal/mol. Between α and β, the negative 280
reaction force decreases to zero, indicating electronic reordering due to the structural changes, that cost the work, W2 = 3.33 kcal/mol. The rise of reaction force from β to γ includes the work W3 : -4.71 kcal/mol. This is equivalent energy involved in completion of rearrangement of electron density due to breaking of the bonds, N1-H2 and C1-O2. Beyond, ξ = γ, the structure relaxes involving
285
the work, W4 : -25.43 kcal/mol with formation of water and formamide. The reaction energy -7.83 kcal/mol which is the sum of all the works W1 to W4 substantiates the favorable formation of formamide. 15
Table 1: Magnitudes of atomic contributions to reaction energy, activation energy and reaction works of TS1 reaction pathway explored at B3LYP/6-31G(d,p) level of theory in gas phase. All the values of in kcal/mol.
Atom
∆E 0
∆E ‡
W1
W2
W3
W4
H1
0.10
0.15
0.15
0.00
-0.00
-0.04
H2
-12.00
8.72
5.18
3.53
-7.12
-13.56
H3
-0.02
0.59
0.57
0.02
-0.04
-0.57
H4
-0.78
0.74
0.70
0.04
-0.08
-1.44
H5
-0.20
0.06
0.04
0.02
-0.03
-0.24
O1
0.76
2.79
2.53
0.25
-0.18
-1.84
O2
-0.23
0.10
0.09
0.00
-0.00
-0.33
N1
5.94
7.61
7.47
0.14
-0.06
-1.61
C1 Patoms
0.33
5.84
5.24
0.61
-0.50
-5.01
-6.06
26.60
21.98
4.61
-8.02
-24.64
i
Favorable formation of TS3-P is also observed from reaction force profile of extended reaction coordinate (ξ = ± 5.0 a0 amu1/2 ) with reaction works W1 = 290
31.0 and W4 = 33.9 kcal/mol. Reaction force plots of the pathways reflected favorable formation of amide bond in the model reaction. Significant contribution to the activation energy of the pathways comes from structural changes in preparative stage. Magnitudes of W1 of TS1, TS2 and TS3 pathways calculated from reaction force profiles
295
obtained in the reaction coordinate range of ± 5.0 a0 amu1/2 are 31.4, 28.0 and 31.0 respectively, indicating that kinetic feasibility of both stepwise and concerted mechanisms is equal. Transition stage of the pathways α → β, is characterized for electronic activity. The evidence for electronic reordering in the region comes from Wiberg bond index profiles (See Fig. S2). Major changes
300
in the bond orders are observed in transition state region of all the pathways. The bond order profiles are further discussed in the following section.
16
Figure 5: Atomic contributions to the total potential energies for TS1, TS1 and TS3 pathways explored at B3LYP/6-31G(d,p) level of theory in gas phase.
17
Table 2: Magnitudes of atomic contributions to reaction energy, activation energy and reaction works of TS2 reaction pathway explored at B3LYP/6-31G(d,p) level of theory in gas phase. All the values of in kcal/mol.
Atom
∆E 0
∆E ‡
W1
W2
W3
W4
H1
-4.64
6.35
3.78
2.57
-5.17
-5.82
H2
0.03
0.57
0.50
0.07
-0.03
-0.51
H3
0.39
0.43
0.43
0.00
-0.00
-0.04
H4
0.25
0.37
0.35
0.02
-0.00
-0.11
H5
-0.03
0.16
0.14
0.01
-0.01
-0.17
O1
-2.80
7.32
7.01
0.31
-0.17
-9.95
O2
-0.88
1.53
1.39
0.15
-0.16
-2.26
N1
0.81
0.94
0.93
0.01
-0.01
-0.12
C1 Patoms
1.28
9.79
8.67
1.12
-0.74
-7.73
-5.59
27.44
23.19
4.26
-6.29
-26.75
i
3.3. Atomic contributions to energetics of reaction pathways The reaction energy, the electronic energy of activation and works invested in each stage of the pathways are further separated into atomic contributions. 305
Potential energies of TS1, TS2 and TS3 pathways as recovered from atomic contribution are shown in Fig. 5. Magnitudes of atomic contributions to reaction works, activation energies and total reaction energies of TS1, TS2 and TS3 pathways are shown in Tables 1, 2 and 3 respectively. The Wiberg bond index profiles of atoms, involved in bond forming and breaking processes of the
310
pathways shown in Fig. S2 are used to gain insights into change in electron population between atoms. Magnitudes of the bond indices and natural charges of a few atoms involved in bond breaking and formation processes of the reaction pathways are shown in Tables S6 and S7 respectively. Atomic contributions to reaction works of pathways explored in reaction coordinate range ± 5.0 a0
315
amu1/2 are shown in Tables S8 to S10. TS1 pathway: Largest preferential contribution to the reaction energy (∆E 0 = Σ4i=1 Wi ) comes from H2 (-12.0 kcal/mol). While N1 shares positive 18
reaction energy (5.94 kcal/mol) other atoms contribute reaction energies less than 1 kcal/mol. Also, atomic contribution to the the activation energy (∆E ‡ 320
= Σ2i=1 Wi ) is significant from H2 (8.72 kcal/mol), N1 (7.61 kcal/mol), C1 (5.84 kcal/mol) and O1 (2.79 kcal/mol). The dependence of the energy contributions on the regions defined by reaction force is as follows: In the first region, the atoms, H2, N1, C1 and O1 contribute to the potential energy with works W1 : 5.18, 7.47, 5.24 and 2.79 kcal/mol respectively. Larger contribution from H2,
325
N1 and C1 compared to O1 is reflected in mode of activation associated to the ◦
atoms. While decrease of distance between C1 and N1 by 0.37 A involves translation of both the reactants, activation of N1-H1 bond is by elongation of the ◦
bond (0.05 A) along with enhancement of
6
H3-N1-H2 by 8.1◦ (causes devia-
tion from trigonal pyramidal structure of ammonia), the atom O1 is activated 330
only by stretch of the bond C1-O1. The works of second and third regions are significantly from H2, by 3.53 and -7.12 kcal/mol respectively. The change in Wiberg bond indices of bonds N1-H2 and O1-H2 from ξ = α to γ (see Fig. S2) and decrease of distance between H2 and O1 primarily by translation of light atom H2, support the major contribution of H2 in both the regions. Finally,
335
in the fourth region, preferential contribution comes from H2 (-13.56 kcal/mol), C1 (-5.01 kcal/mol) as H2 is involved significantly in both the structural change ◦
(shrink of H2-O1 distance by 0.17 A) and electronic reordering (Wiberg bond index of bond H2-O1 increases from 0.43 to 0.72 a.u.); and atom C1 changes its hybridization from sp2 to sp3 . 340
Also, increase of positive charge of H2 (0.42 to 0.49 C) and negative charge on O1 (-0.70 to -0.78 C) from reactant to product state reflects significant localization of charge along the covalent bond between O1-H2, and reveals negative contribution of H2 to the reaction energy of proton transfer reaction pathway, TS1: TS1-R → TS1-I.
345
Magnitudes of atomic contributions to the potential energy curve of TS1TS pathway explored in the reaction coordinate range ± 5.0 a0 amu1/2 follow the trends discussed above. A significant increase of total activation energy from 27.6 kcal/mol (Table 1) to 36.1 kcal/mol (Table S8) is due to the rise 19
in energy share atoms N1 (12.4 kcal/mol) and C1 (7.4 kcal/mol). The data 350
summarizes that a major amount of energy in the pathway is invested to decrease the distance between N1 and C1. TS2 pathway: The atoms, H1 and O1 show significant favorable contribution to the total reaction energy -5.59 kcal/mol. A notable share of total activation energy (27.4 kcal/mol) comes from C1 (9.79 kcal/mol), H1 (6.35
355
kcal/mol) and O1 (7.32 kcal/mol). The region based division of these energies is as follows: In the preparative region, activation of the atoms C1, H1, O1, O2 and N1 by elongation of bonds, C1-O1, and O2-H1; shortening bond, C1-O2 and N1-C1, used the works 8.67, 3.78, 7.01, 1.39 and 0.93 kcal/mol respectively. Significant share of C1 and O1 is due to distortion in sp3 hybridization of carbon
360
caused by C1-O1 bond stretch and decreased electron population between the atoms, evidenced from reduced Wiberg bond index (See Fig. S2). Also, elongation of O2-H1 bond, particularly by translation of H1 reveals its contribution. A noteworthy work share in second and third regions is from H1 i.e, 2.57 and -5.17 kcal/mol respectively. The energies reflect the electronic activity in disso-
365
ciation of bond O2-H1 and formation of the bond O1-H1, supported by Wiberg bond index profiles. The energy of product region is based on work share of atoms, O1 (-9.95 kcal/mol), C1 (-7.73 kcal/mol), H1 (-5.82 kcal/mol) and O2 (-2.26 kcal/mol). While the contribution of O1 and H1 is due to their role in formation of water molecule, the energy contribution of C1 and O2 comes from
370
emergence of double bond between them (causes to sp2 hybridization state of C). The contribution of atoms H1 and O1 (atoms of water molecule) with reaction energies, -4.64 and -2.80 kcal/mol, drives the reaction towards favorable with total reaction energy -5.59 kcal/mol. The preferential contribution of the
375
atoms is supported by significant increase of negative charge on O1 by -0.15 C in the progress of reaction. It reveals localization of charge around O1 and strength of covalent bonds associated to it. The data unveils that preferential formation of water is prime cause for evolution of formamide in the reaction. The agreement between atomic resolution to energetic trends of pathway mod20
Table 3: Magnitudes of atomic contributions to reaction energy, activation energy and reaction works of TS3 reaction pathway explored at B3LYP/6-31G(d,p) level of theory. All the values of in kcal/mol.
Atom
∆E 0
∆E ‡
W1
W2
W3
W4
H1
0.16
0.41
0.33
0.08
-0.04
-0.22
H2
-4.20
4.49
2.87
1.62
-3.78
-4.19
H3
0.18
0.44
0.42
0.03
-0.03
-0.23
H4
-0.05
0.18
0.17
0.01
-0.03
-0.21
H5
-0.08
0.06
0.05
0.01
-0.02
-0.12
O1
0.65
0.74
0.74
0.00
-0.01
-0.09
O2
-4.01
5.13
4.76
0.37
-0.15
-9.00
N1
1.23
4.30
4.07
0.23
-0.07
-2.99
C1 Patoms
-1.72
6.54
5.58
0.97
-0.59
-7.67
-7.83
22.31
18.98
3.33
-4.71
-25.43
i
380
elled in the reaction coordinate range ± 5.0 a0 amu1/2 (see Table S9) and those discussed above, further confirms the appreciable role of water in the formation of formamide. TS3 pathway: The total reaction energy, ∆E 0 , (-7.83 kcal/mol) is shared significantly among H2 (-4.20 kcal/mol), O2 (-4.01 kcal/mol), C1 (-1.72 kcal/mol)
385
and N1 (1.23 kcal/mol). The total activation energy ∆E ‡ , 22.31 kcal/mol comes mainly from H2, O2, N1 and C1 with the energies, 4.49, 5.13, 4.30 and 6.54 kcal/mol respectively. The atomic level separation of these energies among the regions defined by reaction force revealed the following insights. The major activation energy share of the preparative region, i.e., 18.98 kcal/mol is contributed
390
by C1, O2, N1 and H2 with the works, 5.58, 4.76, 4.07 and 2.87 kcal/mol respectively. Work share of C1 and N1 is attributed to translation of both the reactants particularly by movement of atoms C1 and N1, which reduces the ◦
distance between them by 0.24 A. Apart from that, energy contribution of O2 and H2 is due to displacement of the atoms in stretching of the bonds C1-O2 ◦ 395
◦
(0.29 A) and N1-H2 (0.04 A) respectively. The stretching of bond N1-H2 also 21
deviates the trigonal pyramidal structure of ammonia. The work share of atoms in second and third regions (transition state region) is primarily by H2 with energies of 1.62 and -3.78 kcal/mol respectively. The support for involvement of atom in electronic reordering comes from Wiberg bond index profile (Fig. 400
S2). Finally, the total work of relaxation region -25.43 kcal/mol is shared significantly on O2 (-9.00 kcal/mol), C1 (-7.67 kcal/mol), N1 (-2.99 kcal/mol) and H2 (-4.19 kcal/mol). While the energy share of O2 and H2 is justified by their role in formation of water molecule, the energy contribution from C1 and N1 is involved in formation of partial double bond. The preferential energy share of O2 (-4.01 kcal/mol) and H2 (-4.01 kcal/mol)
405
to the total reaction energy (-7.83 kcal/mol), is justified by localization of charge around the atoms, which is evidenced from increase of negative charge on O2 (by 0.12 C) and positive charge on H2 (by 0.07 C). The data concludes that preferential amide bond formation between ammonia and formic acid is driven 410
by favorable formation of water molecule. Further verification to the results mentioned above comes from the atomic resolution to the energetic trends of the reaction pathway explored in reaction coordinate range ± 5.0 a0 amu1/2 .
4.
Conclusions We carried out B3LYP/6-31G(d,p) level of density functional theory calcu-
415
lations in gas phase to explore atomic contribution in amide bond formation between ammonia and formic acid using the concept of reaction force. Straight forward uncatalyzed stepwise and concerted reaction mechanisms are used to locate the transition states and intermediates on the reaction pathways. The data on relative free energy of optimized geometries and reaction energy cal-
420
culations on IRC pathways favor the formation of formamide and water. The reaction force profiles confirm that work invested in preparative region is less than that involved in relaxation region of the pathways and justifies the favorable formation of the product geometries. The profiles show that structural reorganization in preparative stage contributes significantly to activation energy
22
425
barrier of the pathways. The extension in range of reaction coordinate from ± 3.0 to ± 5.0 increased the reaction work in preparative region of TS3, close to that of TS1 and TS2 paths and supports equal competence between stepwise and concerted reaction mechanism of amide bond formation. The study reveals that structural changes that disturb the hybridization state of carbon, deviate
430
ammonia from its trigonal pyramidal structure are notable in determination of activation energy. Significant contribution from C1, N1, O1 or O2, H1 or H2 to activation energy is due to their involvement in changing the hybridization state of carbon and the pyramidal structure of ammonia. The Wiberg bond index profiles confirm the bond breaking and forming process along the pathways and
435
electronic activity in transition region (α to γ). Preferential contributions from hydrogen and oxygen atoms forming the water molecule are responsible for negative reaction energy of product geometries. Data on natural charges on atoms reveal that progress of reaction localizes more charge on hydrogen and oxygen atoms of water molecule and causes for favorable contribution from these atoms
440
to the total reaction energy. The atomic level inferences gained in the study help to characterize the pathways leading to amide bond formation between amino acids.
Acknowledgement We gratefully acknowledge Center for Computational Natural Science and 445
Bioinformatics (CCNSB), IIIT-Hyderabad for providing HPC resources. NVSK thanks Dr. U. Deva Priyakumar, Prof. Harjinder Singh and Dr. Punnagai Munusami of CCNSB, IIIT-Hyderabad for useful discussion in improving the work.
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HIGHLIGHTS OF THE ARTICLE Title: A reaction force perspective of a model amide bond formation reaction Ms. Ref. No.: COMPTC-D-18-00632R1 Authors: V Suresh Kumar Neelamraju , Tanashree Jaganade Affiliation: Center for Computational Natural Sciences and Bioinformatics (CCNSB), International Institute of Information Technology, Hyderabad - 500 032, India. Email: [email protected] 1. The reaction force profiles of amide bond formation between ammonia and formic acid show that structural reorganization in preparative stage contributes significantly to activation energy barrier of the pathways. 2. Significant contribution from carbon, nitrogen, oxygen and hydrogen to activation energy is due to their involvement in changing the hybridization state of carbon and the pyramidal structure of ammonia. 3. A comparison of reaction force profiles and reaction works in preparative region of TS1 and TS2 of stepwise path and TS3 of concerted path discloses that both the stepwise andconcerted mechanisms are equally competent in terms of kinetic feasibility. 4. Preferential contributions from hydrogen and oxygen atoms forming the water molecule are responsible for negative reaction energy of product geometries. 5. Data on natural charges on atoms reveal that progress of reaction localizes more charge on hydrogen and oxygen atoms of water molecule and causes for favorable contribution from these atoms to the total reaction energy.
S2210-271X(19)30043-X https://doi.org/10.1016/j.comptc.2019.02.003 COMPTC 12422
To appear in:
Computational & Theoretical Chemistry
Received Date: Revised Date: Accepted Date:
27 October 2018 13 January 2019 6 February 2019
Please cite this article as: V.S. Kumar Neelamraju, T. Jaganade, A reaction force perspective of a model amide bond formation reaction, Computational & Theoretical Chemistry (2019), doi: https://doi.org/10.1016/j.comptc. 2019.02.003
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A reaction force perspective of a model amide bond formation reaction V Suresh Kumar Neelamraju1 , Tanashree Jaganade Center for Computational Natural Sciences and Bioinformatics (CCNSB), International Institute of Information Technology, Hyderabad - 500 032, India.
Abstract A reaction force approach of amide bond formation between ammonia and formic acid is demonstrated along with each atom’s contribution to structural changes and electronic reordering of the chemical reaction. The B3LYP/631G(d,p) level of density functional theory based calculations were carried out to explore transition states (TSs) of stepwise and concerted amide bond formation reaction pathways. Various stages that characterize structural and electronic properties in the progress of reaction are identified from reaction force calculations on energetics of geometries obtained from intrinsic reaction coordinate (IRC) pathways. The reaction works in preparative region of the pathway are less than that in relaxation stage, reflecting favorable formation of product geometries (Formamide and water). More than 80% of the activation energy comes from structural changes in preparative region. A comparison of reaction force profiles and reaction works in preparative region of TS1 and TS2 of stepwise path and TS3 of concerted path discloses that both the stepwise and concerted mechanisms are equally competent in terms of kinetic feasibility. The atomic resolution of pathways unveils that, hydrogen and oxygen forming the water molecule contribute significantly to the negative reaction energy of product geometries. The preferential contribution of the atoms comes from enhanced ∗V
Suresh Kumar Neelamraju for Computational Natural Sciences and Bioinformatics (CCNSB), International Institute of Information Technology, Hyderabad - 500 032 India and on lien from Department of Physics, Koneru Lakshmaiah Education Foundation, Green fields, Vaddeswaram, Guntur 522 502, India, Email: [email protected], Tel.: +91 9848985146 1 Center
Preprint submitted to Journal of LATEX Templates
January 13, 2019
negative charge of the oxygen and positive charge on hydrogen in the progress of reaction. Keywords: Potential energy, Reaction force, Amide bond, Atomic contribution, Electronic reordering
1. Introduction Description of a chemical or physical processes in terms of derivatives of potential energy with respect to reaction coordinate, i.e., reaction force, is advantageous over analysis of the energy change with the reaction coordinate. The 5
reaction force provides a realistic analysis of chemical reactions by separating a reaction path into three stages. The preparative stage changes reactants to reactive species, transition region converts the reactive species to perturbed form of products and the relaxation stage shows how the perturbed products relaxed to stable product geometries [1, 2]. Also, it allows to estimate atomic contribu-
10
tion to the structural changes and electronic activity in all the three stages of reaction path. This analysis helps to identify reactive center of the molecular system that is responsible for change in potential energy along the reaction path [1, 3, 4]. The intrinsic reaction coordinate (IRC)[5, 6] approach introduced by Fukui
15
is popularly used quantum chemical method for exploring the minimum energy path that connects transition state to both the reactants and products. Analysis of such reaction paths using the concepts like reaction force, reaction force constant and reaction electronic flux and make use of procedure developed by Toro-Labb´e et al. provide an in depth atomic and electronic level understanding
20
of chemical reactions [1, 2, 7, 8, 9, 10, 11, 12]. Several reactions are studied using the concept, reaction force. V¨ohringerMart´inez et al. reported the dominant role of proton in activation energy barrier of proton transfer reactions, ONSH → HONS and the reactions of neutral to zwitterionic form of tryptophan [1]. Also, Jedrzejewski et al. highlighted elec-
25
tronic and atomic contribution in reactions HONS → ONSH and CO + HF →
2
HCOF [3]. Studies on relationship between reaction force and reaction force constant in reaction, OH-N=S → O=N-SH by Jaque et al. summarized that reaction force constant carries information on chemical bonding, rigidity and electronic population [13]. The effects of aqueous solution in reducing the ac30
tivation energy barrier of reaction, H3 C-Cl + H-OH → H3 C-OH + H-Cl was reported by Bruda al. [14]. In line with above mentioned reactions, amide bond formation mechanisms suggested by Oie et al.[15] also come under proton transfer reactions. The stepwise and concerted mechanisms for the amide bond formation reaction, NH3 +
35
HCOOH → H2 N-CHO + H2 O are shown in Fig. 1. Jensen et al. used total electron densities and localized molecular orbital to study energetics of the reaction and summarized that the reaction is a good model to study a dipeptide system [16]. A series of quantum chemical studies on model amide bond formation reactions involving amine and Mg cation as catalysts were also reported
40
by Oie et al.[17, 18, 19]. The mechanisms were also used to justify experimental observations in preferential cyclic dimerization reaction of tripeptides containing tetrahydrofuran amino acids and cyclic trimerization of furan based amino acids [20, 21]. Also, experimental evidence for water assisted hydrolysis of formamide[22, 23] was studied using a mechanism reverse to that suggested
45
by Oie et al. and pathways were modeled using ab into calculations [24, 25]. Even though, the reaction is thoroughly studied, partition of the pathways into structural changes and electronic rearrangements; and role of each atom in driving the reaction are not reported. The present work sheds light on these aspects of the reaction, NH3 + HCOOH → H2 N-CHO + H2 O, using the reaction force
50
approach. We explored the inherent contribution of each atom on the activation energy barrier of the reaction using both stepwise and concerted mechanisms. The article reports that more than 80% of activation energy of reaction in preparative stage is invested to disturb hybridization of carbon and perturb the trigonal
55
pyramidal structure around nitrogen. The electronic rearrangements in transition region are associated with the hydrogen atom. The role of oxygen and 3
hydrogen of water molecule is significant in making the reaction energetically favorable.
2. Methodology 60
The initial geometries[26] were subjected to optimization in gas phase using B3LYP[27] functional of DFT and 6-31G(d,p)[28] basis set. The B3LYP functional is appropriate for the study as it mixes Hartree-Fock exchange and cancels certain delocalization error which is important in modeling transition state geometries associated with stretched bonds [29]. Also, B3LYP/6-31G(d,p)
65
level of theory is used in similar studies involving, alanine, phenylalanine and tryptophan [1, 30]. All the optimized geometries were further subjected to Hessian calculations. Observed real frequencies confirm that the geometries except transitions states were at local minima. The transition states were characterized by presence of one imaginary frequency. The thermodynamic properties were
70
calculated at 298.15 K and 1 atm. The schematic representation of the reaction pathways for amide bond formation are shown in Fig. 1. The uncatalyzed stepwise pathway (Fig. 1) involves transfer of a hydrogen atom from ammonia to carbonyl oxygen of formic acid leading to the formation of a diolic intermediate. Transfer of a proton from one
75
of the OH groups to another OH of diol and further breaking of H-O-H molecule from the intermediate yields formamide and water as the products of reaction. The concerted pathway eliminates water molecule using -OH from the carboxyl terminal and -H from the amine group. The difference between two mechanisms is that while the stepwise mechanism is initiated by transfer of hydrogen from
80
ammonia to carbonyl oxygen of formic acid, the concerted mechanism begins with transfer of hydrogen from ammonia to hydroxyl oxygen of the formic acid. Equations shown below were used to calculate change in free energy, (∆G), and change in electronic energy (∆E) for formation of species in the pathways. ∆X = (XI/TS ) − (XR1 + XR2 )
(1)
∆X = (XP + XW ) − (XR1 + XR2 )
(2)
4
Figure 1: Schematic representation of stepwise and concerted reaction pathways for uncatalyzed amide bond formation, as suggested by Oie et al.[15]. Note: Number notation shown for an atom of a geometry is used in the discussion.
where X stands for free energy (G) or electronic energy (E), I: intermediate, TS: transition state, P: formamide, W: water, R1: ammonia and R2: formic acid. While equation (1) is used for all geometries except the products, the (2) 85
is used for product structure. 2.1. Reaction path, reaction force and atomic resolution of reaction force and reaction work The transition states as obtained from the mechanisms shown in Fig. 1 were used to explore intrinsic reaction paths using the IRC procedure as implemented
90
in Gaussian09[31] package. The paths are explored using Gonzalez and Schlegel algorithm[32] in mass weighted internal coordinates for 300 points with a step size of 0.01 a0 amu1/2 . The paths for 500 points were also obtained using
5
the same method to gain additional insights. Details of the algorithm and procedure used to obtain a new geometry on pathway from the known geometry 95
is explained elsewhere [1]. The reaction force on each step of the IRC is negative derivative of the molecular energy, Emol , with respect to the reaction coordinate, (ξ): dEmol (ξ) (3) dξ We obtained reaction force profiles corresponding to each of the TS1, TS2 F (ξ) = −
and TS3 IRC pathways (see Fig. 1) by calculating the negative ratio between 100
difference in electronic energies of adjacent geometries on the pathways and difference in their respective reaction coordinates. Importance of reaction force profile comes from its additional features compared to system’s potential energy surface. They are, 1) the force is zero at maximum and minimum of the energy and 2) it is either maximum or minimum
105
at inflection point of the potential energy. The minimum, zero and maximum divide the reaction force profile into several stages [4]. These stages provide insights into effects of external forces, structural and electronic rearrangements on the reaction mechanism. The bond lengths and bond angles of atoms involved in proton transfer pathways of TS1, TS2 and TS3 were used to analyze
110
structural changes in various stages of the reaction pathways. Atomic resolution of reaction force is understood from the Hellmann-Feynman (HF) theorem[33] represented as, hΨ | ∂H dE ∂λ | Ψi = dλ hΨ | Ψi
(4)
The theorem is a key ingredient for quantum mechanical treatment of forces acting on nuclei in a molecule [34]. The quantity, -dE/dλ represents classical force on a nucleus of system, if λ is position vector of that nucleus [34]. The force uniquely identifies a nucleus in a molecule[3] and is known as Hellmann115
Feynman (HF) force. By using the magnitudes of the HF force on a nucleus at each step of the IRC pathway and displacement of the nucleus while moving to the next step in 6
advancement of reaction, the reaction work of an atom is calculated. Following is the procedure used to estimate the reaction work. 120
The atomic contribution of each atom to move on the intrinsic reaction path is quantified from work (W ) required to move an atom (i) from a position (say k1 : (x1 ,y1 ,z1 )) in the current structure (α) to its position (say k2 : (x2 ,y2 ,z2 )) in the next structure (α + 1) on the path. It is the product of gradient, gi,α,k of atom, i, in the structure characterized by value of α, which corresponds to a
125
structure of intrinsic reaction coordinate, ξ, calculated along the three coordinates and displacement, di,α,k , required to move atom i along the coordinate k from the actual structure α to the next structure, α+1. It is represented by the equation:
Wi,ξ =
ξ x,y,z X X α=0
gi,α,k .di,α,k
(5)
k
In line with above equation, we calculate the work (Wi,n ) done on atom i, 130
in n steps of IRC pathway using the following equation:
Wi,n =
n X
(Fxji )(x(j+1)i − xji ) + (Fyji )(y(j+1)i − yji ) + (Fzji )(z(j+1)i − zji ) (6)
j=1
Here, Fxji , Fyji and Fzji are force components of atom i, at a step, j; (xji , yji , zji ) and (x(j+1)i , y(j+1)i , z(j+1)i ) are coordinates of ith atom at jth and (j + 1)th steps respectively. 2.2. Wiberg bond indices The Wiberg bond indices[35] that measure the electron population overlap between two atoms were estimated for the bonds involved in bond breaking and forming processes. The indices were obtained from: WAB =
XX
2 Pab
(7)
a∈A b∈B 135
where a and b are atomic orbitals of atoms A and B respectively. Pab is density matrix element. The indices were calculated from natural bond orbital 7
(NBO)[36] program. Also, the natural charges on atoms as obtained from NBO calculations are used to identify localization of charge around the atoms. All the quantum chemical calculations are carried out using Gaussian09[31] 140
suite of quantum chemical programs.
3. Results and discussion Coordinates of all the geometries in study are shown in Table S1. Absolute energies of the species are shown in Tables S2. First, free energy profiles and potential energy surfaces obtained from IRC pathways are analyzed for kinetic 145
and energetic aspects in the formation of product geometries. Next, the reaction force curves of TS1, TS2 and TS3 pathways are presented to gain insights into structure, electronic activities in progress of the reaction and kinetic aspects of the pathways. Subsequently, the atomic contribution to activation energy barrier is described to determine the atomic sites that play major role in fixing
150
barrier heights and reaction energies of the pathways. The Wiberg bond index profiles and natural charges on atoms are used to substantiate electronic activity in bond breaking and forming processes. 3.1. Energetics of optimized geometries and IRC pathways Optimized geometries on stepwise and concerted pathways of amide bond
155
formation reactions along with magnitudes for change in free energy, ∆G, and electronic energy ∆E of formation; and the geometries and relative energetics obtained from IRC calculations are shown in Fig. 2. The potential energy (PE) pathways of TS1, TS2 (both are of stepwise mechanism) and TS3 (concerted mechanism), generated by IRC calculations are shown in Figs. 3 and S1. Abso-
160
lute energies of fully optimized species and geometries obtained IRC pathways are shown in Tables S2(a) and S2(b) respectively. The formation of formamide from ammonia and formic acid is thermodynamically favored by 4.1 kcal/mol. Change in free energy for formation of intermediate in stepwise pathway is 12.2 kcal/mol. The free energies of activation of
8
Figure 2: Left: Optimized geometries on stepwise and concerted reaction pathways of amide bond formation between ammonia and formic acid obtained from B3LYP/6-31G(d,p) level of theory in gas phase. Change in free energy of formation, ∆G, and change in electronic energy of formation, ∆E, are given in kcal/mol. Right: Geometries on (A) TS1, (B) TS2 and (C) TS3 reaction pathways obtained from IRC calculations carried out at B3LYP/6-31G(d.p) level of theory in gas phase. The electronic energy of activation, ∆E ‡ , and reaction energy, ∆E 0 are calculated relative to electronic energy, E of initial geometry in pathways. The magnitudes are in kcal/mol. Notations: TSX:R - Reactant on TSX pathway, TSX:TS - Transition state on TSX pathway, TSX:I, Intermediate on TSX pathway, TSX:P - Product on TSX pathway. X: 1, 2, or 3.
9
165
TS1, TS2 and TS3 are 43.4, 41.9 and 44.7 kcal/mol respectively, indicating that both the stepwise and concerted mechanisms are equally competent in terms of kinetic feasibility as difference in the energies of activation is minimal. The results agree with trends of earlier computational studies by Oie et al., based on MP2/3-21G(d,p) level of theory (Free energy of activation, ∆G‡ , of TS1,
170
TS2 and TS3 are 50.0, 35.6 and 52.6 kcal/mol respectively and change in free energy of intermediate and product are 16.7 and -0.4 kcal/mol respectively) [15]. Kinetic feasibility of the pathways is also on par with the reports of ab initio studies on uncatalyzed amide bond formation of the model reaction carried out by Oie et al.[19]. Also, the QM/MM calculations on the model reaction revealed
175
that the free activation energies of TS1, TS2 and TS3 are 44.3, 41.6 and 43.6 kcal/mol respectively[37]. This confirms that TS geometries explored in the study are appropriate for subsequent calculations. Further analysis on the barrier heights comes from the potential energy plots as given by IRC calculations on TS1, TS2 and TS3 geometries (Figs. 3 and S1).
180
We caution here that the IRC calculations do not always converge to full optimized geometries [30]. Also, we make a note that discussion on the IRC pathway in the current study is limited to the range of reaction coordinates -3.0 to +3.0 a0 amu1/2 about the transition state of respective pathway, unless specified. Relative energies of transitions states TSX-TS (X=1-3) and products (TS1-I,
185
I: Intermediate, TS1-P, TS2-P, P: Product) on PE plots of TSX-TS (X=1,2,3) are measured with respect to initial geometries on respective pathways (TS1R, TS2-I and TS3-R, R: Reactant). Electronic energy of activation, (∆E ‡ ) of transition states TS1-TS, TS2-TS and TS3-TS are 26.6, 27.4 and 22.2 kcal/mol respectively. The relative electronic energies of product geometries (also re-
190
ferred to as reaction energies, ∆E 0 ), TS1-I, TS2-P and TS3-P are -6.0, -5.6 and -7.8 kcal/mol respectively. In case of extended IRC pathways (ξ = -5.0 +5.0 a0 amu1/2 ), the ∆E ‡ of TS1-TS, TS2-TS and TS3-TS are 36.1, 32.3, and 34.3 kcal/mol respectively and ∆E 0 of TS1-I, TS2-P and TS3-P are 2.2, -6.6 and -4.3 kcal/mol respectively (see Fig. S1). Equal kinetic preference of both
195
the mechanisms is observed from the extended IRC pathways. We compare the 10
energetics with change in electronic energy of formation (∆E) of fully optimized geometries and seek agreement with trends (The ∆E of TS1, TS2, TS3, INT and Products are 33.1, 32.3, 34.9, -1.3 and -3.1 kcal/mol respectively). 3.2. Reaction force profiles and reaction works 200
To gain insights into structural and electronic effects on the reaction barrier heights, the reaction force plots corresponding to TS1, TS2 and TS3 pathways shown in Figs. 4 and S1 are analyzed. The minimum, zero and maximum points of the reaction force, divide the reaction path into four zones. The reaction coordinate, ξ, corresponding to the minimum, zero and maximum reaction force
205
are represented by α, β and γ respectively. The reaction works of individual atoms summed over total number steps of a zone are calculated using the equation 6. The sum of contributions from each atom of the system in a zone is the total reaction work of the zone, which is shown as Wn (n = 1,2,3,4) in Fig. 4. Magnitudes of bond lengths and bond angles of atoms involved in bond breaking
210
and formation process of the TS1, TS2 and TS3 reaction pathways are shown in Tables S3, S4 and S5 respectively. TS1 pathway: Amplitude of reaction force curve in preparative stage (TS1R → α) is less deep and wider than that in relaxation stage (γ → TS1-I) and W1 < W4 , indicating that formation of diolic intermediate (TS1-I) from ammonia
215
and formic acid (TS1-R) is favorable. The preparative stage brings the reactants, ammonia and formic acid close to each other such that distance between ◦
C1 and N1 reduced by 0.37 A (Table S3). Also, the stretching of bonds, N1-H2 ◦
and C1=O1 by 0.05 and 0.09 A respectively, disturb the trigonal pyramidal structure of ammonia and sp2 hybridization of carbon atom. The work invested 220
for these changes is W1 : 21.9 kcal/mol (82.6% of the total electronic energy of activation ∆E ‡ : 26.6 kcal/mol), corresponds to potential energy required to reach the reaction force minimum from the reactant. The work W2 = 4.61 kcal/mol spent in the region ξ = α to β corresponds to potential energy difference between transition state and reaction force minimum. The energy is invested for
225
rearrangement of electron density due to stretching of the bonds N1-H2 and 11
Figure 3: Potential energy surfaces of TS1, TS2 and TS3 pathways as given by IRC calculations of amide bond formation between ammonia and formic acid.
12
Figure 4: Reaction force plots of TS1, TS2 and TS3 as given by IRC calculations of amide bond formation between ammonia and formic acid. Magnitudes of reaction works, W1 to W4 are in kcal/mol.
13
C1= O1. Beyond β, the reaction force increases and becomes maximum at ξ = γ, indicating completion of rearrangement of electron density, with potential energy difference between reaction force maximum and transition state, W3 = -8.0 kcal/mol. Finally, the system relaxes with structural changes (formation of ◦ 230
O1-H2 and C1-N1 bonds with 0.97 and 1.46 A respectively and increase of N1C1-O1 angle from 95.3◦ to 108.9◦ , confirms sp3 carbon) that involve the work, W4 = -24.6 kcal/mol, corresponding to potential energy difference between the TS1-I and geometry at γ. The reaction energy is the sum of all contributions, W1 to W4 , gives -6.06 kcal/mol, representing preferential formation of TS1-I
235
(diol intermediate) from ammonia and formic acid. This is in contrast to the result obtained from the free energy data. But, we seek agreement with inferences obtained from the reaction force profile of extended reaction path (ξ = -5.0 to 5.0 a0 amu1/2 , See Fig. S1). It shows that formation of TS1-I is not favorable as W1 (31.4 kcal/mol) > W4 (25.9 kcal/mol). Comparison of the reac-
240
tion works with that in reaction force profile of ξ = -3.0 to 3.0 a0 amu1/2 infers that while W1 is increased by 10 kcal/mol, W4 remains same. The extension to the reaction coordinate takes account of the additional work in the preparative region of the pathway and explored a comparatively stable reactant geometry. The study recognizes the importance of range considered for reaction coordinate
245
of the pathway. TS2 pathway: It describes the reaction that transforms diol intermediate (TS2-I) to formamide and water (TS2-P). It involves breaking of O2-H1 and C1-O1 bonds and formation of H1-O1 bond and simultaneous release of water as the reaction progresses. The reaction is favorable as amplitude of reaction
250
force curve in relaxation stage (γ → TS2-P) is larger than that in preparative stage (TS2-I → α). In the first stage, the TS2-I is activated by elongation of the bonds O2-H1 and C1-O1 that disturb sp3 hybridization around the carbon. It utilizes the work, W1 = 23.2 kcal/mol, that corresponds to potential energy difference between the reactive species (geometry at α) and reactant. The work
255
is 84.7% of total electronic energy of activation, 27.4 kcal/mol. Beyond, α, negative reaction force decreases to zero at ξ = β, that costs the work, W2 = 14
4.26 kcal/mol, invested for reordering of electron density due to stretching of the bonds. Further, reaction force increases to positive maximum at ξ = γ, where rearrangement of electron density due to breaking of bonds, O2-H1 and C1-O1 260
completes within the Born-Oppenheimer approximation. This involve the work W3 = -6.29 kcal/mol, which corresponds to potential energy difference between geometry at reaction force maximum and transition state. In the last stage, the structure at reaction force maximum, relaxes with formation of formamide and water, using the work, W4 = -26.75 kcal/mol. Summing up all the works W1
265
to W4 , yield the reaction energy of -5.59 kcal/mol. This indicates formation of formamide and water (TS2-P) from TS2-I is favorable reaction. Increase in range of reaction coordinate to ± 5.0 a0 amu1/2 enhances the magnitudes of W1 and W4 to 28.4 and 32.4 kcal/mol (See Fig. S1) and retains the trends discussed above.
270
TS3 pathways: The path delineates transformation of ammonia and formic acid (TS3-R) into formamide and water (TS3-P) in a single step. Comparison of reaction force amplitudes in preparative stage (TS3-R → α) and relaxation stage (γ → TS3-P) of the path infers that formation of TS3-P from TS3-R is energetically favorable reaction. Preparative stage involves elongation of bonds ◦
275
◦
N1-H2 (0.04 A), C1-O2 (0.29 A) and brings both the reactants close to each ◦
other so that distance between N1 and C1 reduces by 0.24 A. These changes requires the work W1 = 19.0 kcal/mol, corresponding to the potential energy difference between reactive species and reactants. The energy is 85.1% of total electronic energy of activation 22.31 kcal/mol. Between α and β, the negative 280
reaction force decreases to zero, indicating electronic reordering due to the structural changes, that cost the work, W2 = 3.33 kcal/mol. The rise of reaction force from β to γ includes the work W3 : -4.71 kcal/mol. This is equivalent energy involved in completion of rearrangement of electron density due to breaking of the bonds, N1-H2 and C1-O2. Beyond, ξ = γ, the structure relaxes involving
285
the work, W4 : -25.43 kcal/mol with formation of water and formamide. The reaction energy -7.83 kcal/mol which is the sum of all the works W1 to W4 substantiates the favorable formation of formamide. 15
Table 1: Magnitudes of atomic contributions to reaction energy, activation energy and reaction works of TS1 reaction pathway explored at B3LYP/6-31G(d,p) level of theory in gas phase. All the values of in kcal/mol.
Atom
∆E 0
∆E ‡
W1
W2
W3
W4
H1
0.10
0.15
0.15
0.00
-0.00
-0.04
H2
-12.00
8.72
5.18
3.53
-7.12
-13.56
H3
-0.02
0.59
0.57
0.02
-0.04
-0.57
H4
-0.78
0.74
0.70
0.04
-0.08
-1.44
H5
-0.20
0.06
0.04
0.02
-0.03
-0.24
O1
0.76
2.79
2.53
0.25
-0.18
-1.84
O2
-0.23
0.10
0.09
0.00
-0.00
-0.33
N1
5.94
7.61
7.47
0.14
-0.06
-1.61
C1 Patoms
0.33
5.84
5.24
0.61
-0.50
-5.01
-6.06
26.60
21.98
4.61
-8.02
-24.64
i
Favorable formation of TS3-P is also observed from reaction force profile of extended reaction coordinate (ξ = ± 5.0 a0 amu1/2 ) with reaction works W1 = 290
31.0 and W4 = 33.9 kcal/mol. Reaction force plots of the pathways reflected favorable formation of amide bond in the model reaction. Significant contribution to the activation energy of the pathways comes from structural changes in preparative stage. Magnitudes of W1 of TS1, TS2 and TS3 pathways calculated from reaction force profiles
295
obtained in the reaction coordinate range of ± 5.0 a0 amu1/2 are 31.4, 28.0 and 31.0 respectively, indicating that kinetic feasibility of both stepwise and concerted mechanisms is equal. Transition stage of the pathways α → β, is characterized for electronic activity. The evidence for electronic reordering in the region comes from Wiberg bond index profiles (See Fig. S2). Major changes
300
in the bond orders are observed in transition state region of all the pathways. The bond order profiles are further discussed in the following section.
16
Figure 5: Atomic contributions to the total potential energies for TS1, TS1 and TS3 pathways explored at B3LYP/6-31G(d,p) level of theory in gas phase.
17
Table 2: Magnitudes of atomic contributions to reaction energy, activation energy and reaction works of TS2 reaction pathway explored at B3LYP/6-31G(d,p) level of theory in gas phase. All the values of in kcal/mol.
Atom
∆E 0
∆E ‡
W1
W2
W3
W4
H1
-4.64
6.35
3.78
2.57
-5.17
-5.82
H2
0.03
0.57
0.50
0.07
-0.03
-0.51
H3
0.39
0.43
0.43
0.00
-0.00
-0.04
H4
0.25
0.37
0.35
0.02
-0.00
-0.11
H5
-0.03
0.16
0.14
0.01
-0.01
-0.17
O1
-2.80
7.32
7.01
0.31
-0.17
-9.95
O2
-0.88
1.53
1.39
0.15
-0.16
-2.26
N1
0.81
0.94
0.93
0.01
-0.01
-0.12
C1 Patoms
1.28
9.79
8.67
1.12
-0.74
-7.73
-5.59
27.44
23.19
4.26
-6.29
-26.75
i
3.3. Atomic contributions to energetics of reaction pathways The reaction energy, the electronic energy of activation and works invested in each stage of the pathways are further separated into atomic contributions. 305
Potential energies of TS1, TS2 and TS3 pathways as recovered from atomic contribution are shown in Fig. 5. Magnitudes of atomic contributions to reaction works, activation energies and total reaction energies of TS1, TS2 and TS3 pathways are shown in Tables 1, 2 and 3 respectively. The Wiberg bond index profiles of atoms, involved in bond forming and breaking processes of the
310
pathways shown in Fig. S2 are used to gain insights into change in electron population between atoms. Magnitudes of the bond indices and natural charges of a few atoms involved in bond breaking and formation processes of the reaction pathways are shown in Tables S6 and S7 respectively. Atomic contributions to reaction works of pathways explored in reaction coordinate range ± 5.0 a0
315
amu1/2 are shown in Tables S8 to S10. TS1 pathway: Largest preferential contribution to the reaction energy (∆E 0 = Σ4i=1 Wi ) comes from H2 (-12.0 kcal/mol). While N1 shares positive 18
reaction energy (5.94 kcal/mol) other atoms contribute reaction energies less than 1 kcal/mol. Also, atomic contribution to the the activation energy (∆E ‡ 320
= Σ2i=1 Wi ) is significant from H2 (8.72 kcal/mol), N1 (7.61 kcal/mol), C1 (5.84 kcal/mol) and O1 (2.79 kcal/mol). The dependence of the energy contributions on the regions defined by reaction force is as follows: In the first region, the atoms, H2, N1, C1 and O1 contribute to the potential energy with works W1 : 5.18, 7.47, 5.24 and 2.79 kcal/mol respectively. Larger contribution from H2,
325
N1 and C1 compared to O1 is reflected in mode of activation associated to the ◦
atoms. While decrease of distance between C1 and N1 by 0.37 A involves translation of both the reactants, activation of N1-H1 bond is by elongation of the ◦
bond (0.05 A) along with enhancement of
6
H3-N1-H2 by 8.1◦ (causes devia-
tion from trigonal pyramidal structure of ammonia), the atom O1 is activated 330
only by stretch of the bond C1-O1. The works of second and third regions are significantly from H2, by 3.53 and -7.12 kcal/mol respectively. The change in Wiberg bond indices of bonds N1-H2 and O1-H2 from ξ = α to γ (see Fig. S2) and decrease of distance between H2 and O1 primarily by translation of light atom H2, support the major contribution of H2 in both the regions. Finally,
335
in the fourth region, preferential contribution comes from H2 (-13.56 kcal/mol), C1 (-5.01 kcal/mol) as H2 is involved significantly in both the structural change ◦
(shrink of H2-O1 distance by 0.17 A) and electronic reordering (Wiberg bond index of bond H2-O1 increases from 0.43 to 0.72 a.u.); and atom C1 changes its hybridization from sp2 to sp3 . 340
Also, increase of positive charge of H2 (0.42 to 0.49 C) and negative charge on O1 (-0.70 to -0.78 C) from reactant to product state reflects significant localization of charge along the covalent bond between O1-H2, and reveals negative contribution of H2 to the reaction energy of proton transfer reaction pathway, TS1: TS1-R → TS1-I.
345
Magnitudes of atomic contributions to the potential energy curve of TS1TS pathway explored in the reaction coordinate range ± 5.0 a0 amu1/2 follow the trends discussed above. A significant increase of total activation energy from 27.6 kcal/mol (Table 1) to 36.1 kcal/mol (Table S8) is due to the rise 19
in energy share atoms N1 (12.4 kcal/mol) and C1 (7.4 kcal/mol). The data 350
summarizes that a major amount of energy in the pathway is invested to decrease the distance between N1 and C1. TS2 pathway: The atoms, H1 and O1 show significant favorable contribution to the total reaction energy -5.59 kcal/mol. A notable share of total activation energy (27.4 kcal/mol) comes from C1 (9.79 kcal/mol), H1 (6.35
355
kcal/mol) and O1 (7.32 kcal/mol). The region based division of these energies is as follows: In the preparative region, activation of the atoms C1, H1, O1, O2 and N1 by elongation of bonds, C1-O1, and O2-H1; shortening bond, C1-O2 and N1-C1, used the works 8.67, 3.78, 7.01, 1.39 and 0.93 kcal/mol respectively. Significant share of C1 and O1 is due to distortion in sp3 hybridization of carbon
360
caused by C1-O1 bond stretch and decreased electron population between the atoms, evidenced from reduced Wiberg bond index (See Fig. S2). Also, elongation of O2-H1 bond, particularly by translation of H1 reveals its contribution. A noteworthy work share in second and third regions is from H1 i.e, 2.57 and -5.17 kcal/mol respectively. The energies reflect the electronic activity in disso-
365
ciation of bond O2-H1 and formation of the bond O1-H1, supported by Wiberg bond index profiles. The energy of product region is based on work share of atoms, O1 (-9.95 kcal/mol), C1 (-7.73 kcal/mol), H1 (-5.82 kcal/mol) and O2 (-2.26 kcal/mol). While the contribution of O1 and H1 is due to their role in formation of water molecule, the energy contribution of C1 and O2 comes from
370
emergence of double bond between them (causes to sp2 hybridization state of C). The contribution of atoms H1 and O1 (atoms of water molecule) with reaction energies, -4.64 and -2.80 kcal/mol, drives the reaction towards favorable with total reaction energy -5.59 kcal/mol. The preferential contribution of the
375
atoms is supported by significant increase of negative charge on O1 by -0.15 C in the progress of reaction. It reveals localization of charge around O1 and strength of covalent bonds associated to it. The data unveils that preferential formation of water is prime cause for evolution of formamide in the reaction. The agreement between atomic resolution to energetic trends of pathway mod20
Table 3: Magnitudes of atomic contributions to reaction energy, activation energy and reaction works of TS3 reaction pathway explored at B3LYP/6-31G(d,p) level of theory. All the values of in kcal/mol.
Atom
∆E 0
∆E ‡
W1
W2
W3
W4
H1
0.16
0.41
0.33
0.08
-0.04
-0.22
H2
-4.20
4.49
2.87
1.62
-3.78
-4.19
H3
0.18
0.44
0.42
0.03
-0.03
-0.23
H4
-0.05
0.18
0.17
0.01
-0.03
-0.21
H5
-0.08
0.06
0.05
0.01
-0.02
-0.12
O1
0.65
0.74
0.74
0.00
-0.01
-0.09
O2
-4.01
5.13
4.76
0.37
-0.15
-9.00
N1
1.23
4.30
4.07
0.23
-0.07
-2.99
C1 Patoms
-1.72
6.54
5.58
0.97
-0.59
-7.67
-7.83
22.31
18.98
3.33
-4.71
-25.43
i
380
elled in the reaction coordinate range ± 5.0 a0 amu1/2 (see Table S9) and those discussed above, further confirms the appreciable role of water in the formation of formamide. TS3 pathway: The total reaction energy, ∆E 0 , (-7.83 kcal/mol) is shared significantly among H2 (-4.20 kcal/mol), O2 (-4.01 kcal/mol), C1 (-1.72 kcal/mol)
385
and N1 (1.23 kcal/mol). The total activation energy ∆E ‡ , 22.31 kcal/mol comes mainly from H2, O2, N1 and C1 with the energies, 4.49, 5.13, 4.30 and 6.54 kcal/mol respectively. The atomic level separation of these energies among the regions defined by reaction force revealed the following insights. The major activation energy share of the preparative region, i.e., 18.98 kcal/mol is contributed
390
by C1, O2, N1 and H2 with the works, 5.58, 4.76, 4.07 and 2.87 kcal/mol respectively. Work share of C1 and N1 is attributed to translation of both the reactants particularly by movement of atoms C1 and N1, which reduces the ◦
distance between them by 0.24 A. Apart from that, energy contribution of O2 and H2 is due to displacement of the atoms in stretching of the bonds C1-O2 ◦ 395
◦
(0.29 A) and N1-H2 (0.04 A) respectively. The stretching of bond N1-H2 also 21
deviates the trigonal pyramidal structure of ammonia. The work share of atoms in second and third regions (transition state region) is primarily by H2 with energies of 1.62 and -3.78 kcal/mol respectively. The support for involvement of atom in electronic reordering comes from Wiberg bond index profile (Fig. 400
S2). Finally, the total work of relaxation region -25.43 kcal/mol is shared significantly on O2 (-9.00 kcal/mol), C1 (-7.67 kcal/mol), N1 (-2.99 kcal/mol) and H2 (-4.19 kcal/mol). While the energy share of O2 and H2 is justified by their role in formation of water molecule, the energy contribution from C1 and N1 is involved in formation of partial double bond. The preferential energy share of O2 (-4.01 kcal/mol) and H2 (-4.01 kcal/mol)
405
to the total reaction energy (-7.83 kcal/mol), is justified by localization of charge around the atoms, which is evidenced from increase of negative charge on O2 (by 0.12 C) and positive charge on H2 (by 0.07 C). The data concludes that preferential amide bond formation between ammonia and formic acid is driven 410
by favorable formation of water molecule. Further verification to the results mentioned above comes from the atomic resolution to the energetic trends of the reaction pathway explored in reaction coordinate range ± 5.0 a0 amu1/2 .
4.
Conclusions We carried out B3LYP/6-31G(d,p) level of density functional theory calcu-
415
lations in gas phase to explore atomic contribution in amide bond formation between ammonia and formic acid using the concept of reaction force. Straight forward uncatalyzed stepwise and concerted reaction mechanisms are used to locate the transition states and intermediates on the reaction pathways. The data on relative free energy of optimized geometries and reaction energy cal-
420
culations on IRC pathways favor the formation of formamide and water. The reaction force profiles confirm that work invested in preparative region is less than that involved in relaxation region of the pathways and justifies the favorable formation of the product geometries. The profiles show that structural reorganization in preparative stage contributes significantly to activation energy
22
425
barrier of the pathways. The extension in range of reaction coordinate from ± 3.0 to ± 5.0 increased the reaction work in preparative region of TS3, close to that of TS1 and TS2 paths and supports equal competence between stepwise and concerted reaction mechanism of amide bond formation. The study reveals that structural changes that disturb the hybridization state of carbon, deviate
430
ammonia from its trigonal pyramidal structure are notable in determination of activation energy. Significant contribution from C1, N1, O1 or O2, H1 or H2 to activation energy is due to their involvement in changing the hybridization state of carbon and the pyramidal structure of ammonia. The Wiberg bond index profiles confirm the bond breaking and forming process along the pathways and
435
electronic activity in transition region (α to γ). Preferential contributions from hydrogen and oxygen atoms forming the water molecule are responsible for negative reaction energy of product geometries. Data on natural charges on atoms reveal that progress of reaction localizes more charge on hydrogen and oxygen atoms of water molecule and causes for favorable contribution from these atoms
440
to the total reaction energy. The atomic level inferences gained in the study help to characterize the pathways leading to amide bond formation between amino acids.
Acknowledgement We gratefully acknowledge Center for Computational Natural Science and 445
Bioinformatics (CCNSB), IIIT-Hyderabad for providing HPC resources. NVSK thanks Dr. U. Deva Priyakumar, Prof. Harjinder Singh and Dr. Punnagai Munusami of CCNSB, IIIT-Hyderabad for useful discussion in improving the work.
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HIGHLIGHTS OF THE ARTICLE Title: A reaction force perspective of a model amide bond formation reaction Ms. Ref. No.: COMPTC-D-18-00632R1 Authors: V Suresh Kumar Neelamraju , Tanashree Jaganade Affiliation: Center for Computational Natural Sciences and Bioinformatics (CCNSB), International Institute of Information Technology, Hyderabad - 500 032, India. Email: [email protected] 1. The reaction force profiles of amide bond formation between ammonia and formic acid show that structural reorganization in preparative stage contributes significantly to activation energy barrier of the pathways. 2. Significant contribution from carbon, nitrogen, oxygen and hydrogen to activation energy is due to their involvement in changing the hybridization state of carbon and the pyramidal structure of ammonia. 3. A comparison of reaction force profiles and reaction works in preparative region of TS1 and TS2 of stepwise path and TS3 of concerted path discloses that both the stepwise andconcerted mechanisms are equally competent in terms of kinetic feasibility. 4. Preferential contributions from hydrogen and oxygen atoms forming the water molecule are responsible for negative reaction energy of product geometries. 5. Data on natural charges on atoms reveal that progress of reaction localizes more charge on hydrogen and oxygen atoms of water molecule and causes for favorable contribution from these atoms to the total reaction energy.