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Benchmark binding energies of ammonium and alkyl-ammonium ions interacting with water. Are ammonium–water hydrogen bonds strong?
Chemical Physics Letters 618 (2015) 168–173
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Benchmark binding energies of ammonium and alkyl-ammonium ions interacting with water. Are ammonium–water hydrogen bonds strong? Valérie Vallet a,∗ , Michel Masella b a
Laboratoire PhLAM, UMR 8523, CNRS Université de Lille, F-59655 Villeneuve d’Ascq Cedex, France CEA Saclay, Laboratoire de Biologie Structurale et Radiobiologie, Service de Bioénergétique Biologie Structurale et Mécanismes, Institut de biologie et de technologies de Saclay, F-91191 Gif sur Yvette Cedex, France b
a r t i c l e
i n f o
Article history: Received 14 August 2014 In final form 3 November 2014 Available online 11 November 2014
a b s t r a c t Alkyl-ammonium ion/water interactions are investigated using high level quantum computations, yielding thermodynamics data in good agreement with gas-phase experiments. Alkylation and hydration lead to weaken the NH O hydrogen bonds. Upon complete hydration by four water molecules, their main features are close to those of the OH O bond in the isolated water dimer. Energy decomposition analyses indicate that hydration of alkyl-ammonium ions are mainly due to electrostatic/polarization effects, as for hard monoatomic cations, but with a larger effect of dispersion. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Protonated alkyl-ammonium ions and their interaction with water play a key role in chemistry and biology. These ions are common constituents of ionic liquids [1] and they play also a key role in protein structure and solubility, as well as in enzyme catalysis [2]. The interactions between an ammonium ion and a polar molecule are usually depicted at the microscopic level as a prototypical form of strong hydrogen bonds (HB) (see Refs. [3–5], for instance). As an HB corresponds mainly to a local interaction, this may explain why most of the theoretical quantum studies devoted so far to investigate the interaction properties of ammonium ions with water focused on hydrated NH+ systems [6–13], whereas 4 alkyl-ammonium ions have been much less investigated [14,15]. If the ammonium/water interaction is not expected to be strongly affected by alkylation, many discrepancies among ammonium and alkyl-ammonium ions have been reported experimentally. For instance, ion/water binding enthalpies decrease by about 1 kcal mol−1 in the series NH+ /CH3 NH+ /C2 H5 NH+ /n-C3 H7 NH+ 4 3 3 3 [16–18]. Moreover, recent experiments using infrared photodissociation spectroscopy and blackbody infrared radiative dissociation at 133 K, exhibited a different behavior for the NH+ and CH3 NH+ as 4 3 interacting with water clusters made of 19–21 molecules: NH+ is 4 preferentially located within the water clusters, whereas CH3 NH+ 3
∗ Corresponding author. E-mail address: [email protected] (V. Vallet). http://dx.doi.org/10.1016/j.cplett.2014.11.005 0009-2614/© 2014 Elsevier B.V. All rights reserved.
is located at their surface [19]. In the latter case, the hydrophomethyl group has to be at the origin of bic nature of the CH3 NH+ 3 these different behaviors. However, discrepancies at the level of the local interaction between the NH+ moiety and water molecules may also affect the behavior of these ions when interacting with large molecular systems. In the present Letter, we present an thorough theoretical analysis of the microscopic interactions between alkyl-ammonium ions and water molecules (from 1 to 4) using high level quantum methods. Our aim is to enlighten the similarities and discrepancies concerning the interactions between such ions and water. This provides helpful hints for building up accurate ‘ab initio’ forcefield approaches, i.e. molecular modeling (MM) approaches whose parameters are assigned by considering only theoretical quantum data, with no further refinement using experimental data. Such a development strategy for MM approaches should lead to wellsuited methods to investigate the behavior of the ions in different chemical environment and physical conditions, as solvated in water nano-droplets or in neat liquid water (see the recent study performed by one of us Ref. [20], for instance). Here, we investigated the interaction properties of ion/ , CH3 NH+ , C2 H5 NH+ , (water)nw systems where the ions are NH+ 4 3 3 + + n-C3 H7 NH+ , (CH ) NH and (CH ) NH . For each ion, we con3 2 3 3 3 2 sidered different hydrated systems containing water molecules up to saturating all the possible ion/water HBs. All systems were investigated at a high quantum level of theory, allowing one to extrapolate binding energies to the complete basis set limit. We investigated the nature of the microscopic forces affecting the local
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ion/water interactions using standard electronic population analysis and energy decomposition schemes, and we compare these properties to those of the most intensively studied system presenting a prototypical form of weak HB, i.e. the water dimer. Lastly, as the hydration properties of the ions K+ and NH+ are close, we will 4 also discuss some hydrated K+ cluster properties for comparison purposes. 2. Theoretical methods All quantum calculations have been performed with the gaussian09 [21], the molpro [22], the turbomole [23], and the gamess [24,25] packages of programs. All computations were performed using the frozen core (FC) approximation. To compute accurate interaction energies of the various ion/water clusters, we first optimized the complex geometries at the MP2 level with augmented correlation consistent triple- basis sets (aug-cc-pVTZ). We computed then the cluster total energies by performing single point energy calculations at the MP2/aug-cc-pVXZ//MP2/aug-cc-pVTZ level, with X = T, Q and 5. The corresponding Hartree–Fock EHF and correlation Ecorr energy components were used to extrapolate the complex total energies to their complete basis set (CBS) limit using a three-point exponential formula for EHF [26,27] and a two-point extrapolation for Ecorr [28]. The thermodynamic quantities (enthalpy and entropy) were computed at 298.15 K from the system vibrational frequencies estimated at the MP2/aug-cc-pVTZ level of theory, using harmonic oscillator partition functions and by applying the standard 0.953 scaling factor to the frequencies [29]. The electronic population analyses were performed using the Natural Population Analysis (NPA) method [30], as implemented in the nbo program v 3.1 [31]. Lastly, insights into the intermolecular interactions were provided by energy decomposition analysis (EDA) making use of the reduced variational space (RVS) [32] method at the HF/aug-cc-pVTZ level and of the localized molecular orbital EDA (LMO-EDA) [33] scheme at the MP2/aug-cc-pVTZ level. All EDAs were performed by considering structures optimized at the MP2/aug-cc-pVTZ level. We will compare our computed EDA data to those estimated from other quantitative decompositions, like the symmetry-adapted perturbation theory (SAPT) method [34,35] at the MP2 level, or with the absolutely localized molecular orbitals (ALMO) [36] at the DFT/BP86 level. EDA methods decompose the interaction energy into three common components, namely the electrostatic Eelec , the exchangerepulsion Eexc−rep and the polarization Epol component (the latter one is denoted induction Eind in the SAPT approach). However, an additional component is also computed, namely a charge-transfer Ect term (RVS and ALMO approaches) or a dispersion Edisp one (SAPT and LMO-EDA schemes). Thus EDA outputs have to be compared with caution, keeping in mind that (1) polarization interaction of LMO-EDA schemes includes both the polarization and chargetransfer contributions of RVS and ALMO schemes and (2) that unlike RVS, ALMO strictly produces a self-consistent polarization energy, and separates more adequately polarization from charge-transfer contributions than RVS does (see the recent review of Gordon and coworkers [37] where available EDA schemes are compared). 3. Results and discussion 3.1. Hydrogen bond geometries and stretching NH/CN vibrational spectra Geometrical and vibrational data regarding intermolecular NH O HBs and ion intramolecular NH and CN bonds are summarized in Table 1. The stretching harmonic vibrational frequencies
Figure 1. Schematic representation of (CH3 )2 NH+ (H2 O)2 . 2
NH reported in that table have been tentatively assigned to NH bonds interacting with a water molecule based on the atomic weights in the normal coordinates. All the frequency shifts induced by ion/water interactions discussed below are computed by comparing the hydrated ion cluster stretching frequency NH (or CN ) to the average of the corresponding frequencies in the isolated gas-phase cation. In all hydrated ion clusters, the improper HOH–HN dihedral angle values are included within 163◦ and 180◦ . As illustrated by the schematic representation (Figure 1) of methyl ammonium solvated by two water molecules, the molecules interact thus with the ammonium hydrogens HN in quasi planar structures, regardless of the ion. The shortest ion carbon/water oxygen distance is about 3.52± 0.02 A˚ in all hydrated ion clusters, which exactly equals the equilibrium carbon/oxygen distance in the isolated methane/water dimer [38]. hydration leads to the increase of the NH O Successive NH+ 4 hydrogen bond length, Rhb , from 1.64 (nw = 1) up to 1.83 A˚ (nw = 4), and to the decrease of the NH bond length, from 1.054 down to ˚ However, compared to isolated gas-phase geometries, the 1.030 A. with water yields a small lengthening of the NH interaction of NH+ 4 ˚ regardless of nw . Note that the presence bonds, from 0.01 to 0.03 A, of water molecules has no effect on the length of the NH bonds not involved in ion/water HBs. All the latter NH O HB features are observed in all alkylated ion hydrated clusters. Alkylation of NH+ yields also the increase of Rhb in ion/water 4 dimers, from 0.05 (CH3 NH+ ) up to 0.10 A˚ ((CH3 )3 NH+ ). The nature 3 of the alkyl group in mono-alkylated ammonium ions has a weak impact on the latter distance, which slightly increases at the rate of 0.01 A˚ with respect to the alkyl chain length, regardless of nw . We note also that hydration yields a slight shortening of the CN bonds, which decrease by 0.01 A˚ per water molecule added. Compared to the NH vibrational spectra of the isolated ions, the interaction of a NH bond with a water molecule leads to a strong red shift NH in the frequency of the corresponding NH bond stretching vibrational mode. The red shift varies from 582 cm−1 in the NH+ /H2 O dimer down to 243 cm−1 in the (CH3 )3 NH+ /H2 O 4 dimer. For a given ion, the red shift NH decreases as the number of interacting water molecules nw increases, at a rate of about 100–150 cm−1 per water molecule added, regardless of the ion. For a given number of interacting water molecules, successive methleads also to a decrease of NH , at a rate of about ylation of NH+ 4 80–90 cm−1 per methyl group added. The CN vibrational spectra is much less affected by ion/water interactions.
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Table 1 Structural, vibrational and natural population analysis (NPA) data of isolated ions and of hydrated ion clusters. nw : cluster number of water molecules. q(N): NPA nitrogen charge. q(HN): mean NPA charge of NH moiety hydrogens with their standard deviation in parenthesis. NH and CN : harmonic frequencies corresponding to stretching NH and CN vibrational modes, in cm−1 . CN frequencies are reported in brackets and, in italic, frequencies corresponding to NH groups interacting with water in hydrated clusters. qc : total charge transferred from the water lone pairs towards the NH anti-bonding orbitals. All charges in e. Ion
nw
r(N-X)
r(NH O)
q(N)
q(HN)
NH /CN
qc
NH+ 4
0 1 2 3 4
1.022 1.054 (1.019) 1.042 (1.017) 1.035 (1.016) 1.300
1.643 1.714 1.772 1.828
−0.82 −0.85 −0.87 −0.89 −0.90
0.46 (0.00) 0.45 (0.01) 0.44 (0.02) 0.44 (0.02) 0.45 (0.00)
3394-3527-3527-3527 2912-3456-3561-3561 3095-3109-3515-3582 3193-3240-3241-3567 3252-3326-3329-3331
na 0.036 0.051 0.058 0.062
0 1 2 3
1.022 (1.504) 1.045 (1.019) (1.496) 1.037 (1.018) (1.491) 1.032 (1.487)
1.698 1.754 1.803
−0.65 −0.67 −0.70 −0.72
0.44 (0.00) 0.44 (0.02) 0.44 (0.02) 0.44 (0.00)
3423-3519-3519 [968] 3060-3479-3543 [995] 3181-3207-3531 [1016] 3249-3301-3301[1034]
na 0.028 0.043 0.052
0 1 2 3
1.022 (1.514) 1.044 (1.020) (1.504) 1.036 (1.019) (1.500) 1.031 (1.494)
1.711 1.779 1.812
−0.65 −0.67 −0.70 −0.72
0.44 (0.00) 0.44 (0.02) 0.44 (0.02) 0.44 (0.00)
3413-3514-3519 [860] 3085-3468-3534 [880] 3192-3230-3523 [888] 3251-3310-3313 [900]
na 0.026 0.039 0.049
0 1 2 3
1.022 (1.514) 1.043 (1.020)(1.505) 1.036 (1.019) (1.499) 1.031 (1.494)
1.723 1.775 1.820
−0.65 −0.67 −0.69 −0.72
0.44 (0.00) 0.44 (0.02) 0.44 (0.03) 0.44 (0.00)
3413-3516-3520 [966] 3098-3470-3537 [987] 3195-3231-3520 [1009] 3253-3312-3316 [1021]
na 0.026 0.039 0.048
0 1 2
1.022 (1.497) 1.040 (1.020) (1.490) 1.034 (1.485)
1.730 1.777
−0.49 −0.52 −0.55
0.43 (0.00) 0.46 (0.03) 0.45 (0.00)
3444-3505 [886-1029] 3147-3495 [903-1111] 3233-3261 [915-1123]
na 0.025 0.038
0 1
1.022 (1.493) 1.037 (1.487)
1.749
−0.37 −0.41
0.42 (na) 0.46 (na)
3458 [821-1004-1004] 3215 [835-1018-1018]
na 0.021
CH3 NH+ 3
C2 H5 NH+ 3
C3 H7 NH+ 3
(CH3 )2 NH+ 2
(CH3 )3 NH+
Compared to isolated ion data, the CN frequencies are blue shifted in hydrated clusters, from about 20 cm−1 in dimers up to 100 cm−1 in tetramers. Comparable blue shifts were reported for the CO stretching frequency of a methanol molecule when acting as HB proton acceptor in water or methanol clusters [39,40]. For common red shifting HBs XH-Y, like those occurring in pure water clusters, the length of the intramolecular XH bond increases up to 0.03 A˚ and the corresponding stretching frequency is red shifted by hundreds of cm−1 compared to single molecule data [41]. This feature is also observed here for NH bonds. However, contrary to pure water clusters, for which both the length of the XH bond and the red shift in the corresponding stretching frequency XH increase as the cluster size grows, for NH bonds, both the latter quantities decrease with respect to the hydrated ammonium cluster size. As the strength of common red shifting HBs is usually reported to be proportional to the magnitude of both the XH bond lengthening and the corresponding XH red shift [42], our present results suggest that the ‘strong’ NH O HBs become weaker and weaker as the hydrated ion cluster size increases, so that most of their geometrical and vibrational features in the NH+ /water tetramer are close to 4 those of the weak HB occurring in the water dimer. For instance, the HB length is 1.83 A˚ in NH+ /(H2 O)4 and 1.90 A˚ in the water dimer 4 [43], and the water dimer OH red shift is about 170 cm−1 as reported both experimentally and theoretically, a value very close to our computed average NH red shift in NH+ /(H2 O)4 , about 185 cm−1 4 (for the water dimer, see Ref. [44] and the references mentioned therein). Moreover, ion alkylation also leads to the weakening of NH O HBs, whereas it was shown to reinforce OH O HBs in alcohol and ether-oxide/water dimers, as compared to the water dimer [45]. The NH O HB destabilization induced by hydration has to result from the overall strong water oxygen–oxygen electrostatic repulsive effects occurring in cation first hydration shells, as discussed in Ref. [46], for instance. As the negative electrostatic charge of the carbons bonded to the ion nitrogen is overall strong (see below), we may argue that strong enough carbon/water oxygen electrostatic repulsive effects are also responsible for NH O HB destabilization in alkylated ion hydrated systems.
3.2. Binding energies at the CBS limit and thermodynamical data The total ion hydration energies by nH2 O E tot (nw ) and the corresponding stepwise hydration energies Enw −1,nw have been calculated on the basis of the gas-phase reactions nw H2 O + Ion → Ion/(H2 O)nw
(1)
Ion/(H2 O)nw −1 + H2 O → Ion(H2 O)nw
(2)
The hydration energies at the CBS limit and the computed thermodynamic data given in Table 2 cover the additions from one up to four water molecules. Concerning the hydration energies, it is noteworthy that the CBS limit is reached within 0.2–0.4 kcal mol−1 with basis set of quadruple zeta quality (see Supporting Information). As expected from the above discussions concerning the hydrated ion cluster geometry and vibrational properties, the ion hydration energies decrease (1) as nw increases and (2) as the number of HN hydrogens substituted by a methyl group increases. For instance, the first stepwise hydration energy E0,1 gradually increases from −20.5 up to −16.2 kcal mol−1 in the series NH+ /CH3 NH+ /(CH3 )2 NH+ /(CH3 )3 NH+ . That energy also 4 3 2 decreases when increasing the alkyl chain length, however, it seems to converge as soon as the propyl-ammonium ion. All the stepwise hydration enthalpies Hnw −1,nw computed from MP2 data at the CBS limit and by considering the harmonic approximation (with scaled frequencies) to compute the thermodynamic corrections are in a particularly good agreement with available experimental data, within less than 0.6 kcal mol−1 on average. We note also the same very good agreement between theory and experiment for the stepwise hydration entropies Snw −1,nw . The agreement is achieved here within less than 2 cal mol−1 K−1 on average. Interestingly, the Snw −1,nw are fairly constant, about 24 ± 2 cal mol−1 K−1 , regardless of the ion and nw . This is to be expected as the entropy change for water addition is dominated by the loss of three translational degrees of freedom upon the formation of an additional internal hydrogen bond between the cation and the added water molecule.
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Table 2 Gas-phase binding energies and thermodynamical data concerning the ion hydration stepwise reactions. PA: difference in proton affinity between the unprotonated ion form and water. Etot : cluster total binding energy from quantum MP2 computations at the CBS limit. Enw −1,nw : quantum stepwise gas-phase hydration energy. Hnw −1,nw and Snw −1,nw : stepwise hydration enthalpy and entropy estimates computed from the CBS binding energies and from cluster harmonic vibrational frequencies. In bracket, enthalpies correspond to averaged data from the NIST WEBBOOK data base [18], for the other ions and for the stepwise entropies, they are taken the experimental data (NH+ 4 from [49]). All energy values in kcal mol−1 and all entropy data in cal mol−1 K−1 . Ion
Quantity
NH+ 4
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
39.9
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
51.1
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
50.5
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
55.4
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
58.2
CH3 NH+ 3
CH3 (CH2 )NH+ 3
CH3 (CH2 )2 NH+ 3
(CH3 )2 NH+ 2
(CH3 )3 NH+
−Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
PA 16.2
nw = 1
2
3
4
20.5 20.5 20.0 [19.2] 24.0 [23.9]
37.6 17.2 15.1 [15.3] 24.0 [22]
52.1 14.5 13.6 [13.1] 21.5 [23.7]
64.7 12.6 11.1 [11.5] 21.8 [25.2]
18.5 18.5 17.2 [17.8] 22.8 [21.8]
34.2 15.7 14.3 [14.6] 26.7 [24.2]
47.8 13.6 13.1 [12.4] 18.7 [24.1]
17.6 17.6 16.4 [17.5] 22.1 [–]
32.7 14.9 13.6 [14.7] 25.5 [–]
45.9 13.2 11.7 [–] 25.7 [–]
17.3 17.3 16.0 [15.0] 24.6 [22.9]
32.2 14.9 13.4 [11.6] 25.4 [24.7]
45.2 13.0 11.6 [10.3] 22.9 [24.4]
17.1 17.1 15.8 [15.0] 22.0 [22.9]
31.9 14.8 13.4 [13.5] 29.5 [24.7]
62.4 16.2 15.5 [14.5] 24.6 [24.1]
We computed also the proton affinities (PA) of the unprotonated ion forms and of water, according to the same protocol as for the cluster binding energies. The differences PAs in the computed PA values between the unprotonated ion forms and water are reported in Table 2. They are 6.5± 0.5 % higher than the experimental ones [16]. Such discrepancies has to result from non canceling errors due to the harmonic approximation we used to compute the thermodynamical corrections to the PA values. However, we observe a linear inverse relation between our PAs and our computed hydration enthalpies H0,1 , as experimentally reported [17,47] (here, the coefficient of regression is 0.997). For the series CH3 NH+ /(CH3 )2 NH+ /(CH3 )3 NH+ , we note that both their 3 2 corresponding PA and H0,1 values correlate linearly with their number of methyl groups (the coefficient of regression is 0.99, regardless of the quantity considered). This suggests that the apparent correlation between PA and H0,1 values originates from two different phenomena. The proton H+ moiety of a methylated ion strongly polarizes its CH bonds, which leads to strengthen the proton affinity, whereas the ion methyl groups destabilize the ion/water HBs (see also our discussions below). However, as the linear inverse relation between PA and H0,1 values is reported for a large set of B/BH+ chemical entities, the latter hypothesis concerning the origin of such a relation needs to be further investigated and discussed.
3.3. Electronic population analysis The NPA charges for the nitrogen (N) and its hydrogens (HN) are summarized in Table 1. For nitrogen bonded carbons and for
carbon hydrogens, these charges are constant, regardless of the ion and the cluster size: −0.29 and +0.21 ± 0.01 e, respectively. The hydrogen charges q(HN) are constant, about +0.45 ± 0.01 e, regardless of the ion and the cluster size. They are slightly affected by the presence of water molecules. They decrease by an amount of 0.03 e per water molecule added. This amount is close to the magnitude of the charge transferred qc from a water molecule towards the NH+ n core (see below). The nitrogen charge q(N) increases by about +0.15 e in the series NH+ /CH3 NH+ /(CH3 )2 NH+ /(CH3 )3 NH+ , whereas it is constant in 4 3 2 + /C H NH /n-C3 H7 NH+ , regardless of the water the series CH3 NH+ 5 2 3 3 3 cluster size. Alkylation yields thus the dilution of the negative charge of the ammonium nitrogen atom. According to standard orbital interpretation of hydrogen bonding (cf. Ref. [48]), NH O HBs may be interpreted as resulting from the interaction between water lone pairs (lp) and NH anti-bonding ∗ . The strength of such an interaction can be quantiorbitals NH fied using NBO data by considering the amount of electronic charge ∗ according to transferred qc from the water lps towards a given NH qc ≈ 2
ld |F| ∗ 2 NH
lone-pairs
∗ − l
,
(3)
here, F is the Fock operator, * and l are the energies (in terms of ∗ and of an lp, respectively. diagonal Fock matrix elements) of NH The computed charges qc are summarized in Table 1. Their magnitude, when rescaled by the number of cluster NH O HBs, ranges from 0.01 to 0.04 e, regardless of the ion. The strongest value is observed for NH+ , while qc is almost constant for alkylated ions. 4
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Table 3 Energy decompositions for ion/water dimers. All data in kcal mol−1 . All results from our own computations, at the exception of the SAPT data taken from Ref. [35], the ALMO data taken from Ref. [36] and the LMO-EDA CCSD(T) data taken from Ref. [33]. Ion/water dimer
Method
Etot
Eelec
Eexch-rep
K+ /H2 O
LMO-EDA (MP2) SAPT (MP2) RVS(HF) ALMO (BP86)
−17.6 −17.6 −16.9 −14.5
−19.6 −18.8 −19.6
7.0 7.1 6.9 −10.9
−4.4 −4.3 −3.6 −3.1
– – −0.7 −0.4
−0.6 −1.7 – –
/H2 O NH+ 4
LMO-EDA (MP2) LMO-EDA (CCSD(T)) SAPT (MP2) RVS(HF)
−20.7 −20.8 −21.0 −18.4
−25.4 −25.4 −24.2 −25.3
18.3 18.2 15.3 18.2
−11.9 −11.8 −8.2 −7.5
– – – −3.8
−1.8 −1.9 −4.0 –
/H2 O CH3 NH+ 3
LMO-EDA (MP2) RVS(HF)
−18.5 −15.9
−22.8 −22.7
15.9 15.8
−9.6 −6.0
– −3.0
−2.1 –
C2 H5 NH+ /H2 O 3
LMO-EDA (MP2) RVS (HF)
−17.7 −21.8
−21.9 14.0
15.3 −5.7
−9.0 −2.8
– –
−2.1 −15.7
/H2 O nC3 H7 NH+ 3
LMO-EDA (MP2) RVS (HF) LMO-EDA (MP2) RVS (HF)
−17.3 −21.4 −17.1 −19.9
−21.5 15.0 −21.1 −21.0
15.2 −5.5 14.7 14.6
−8.7 −3.4 −8.3 −5.3
– – – −8.2
−2.3 −15.1 −2.3 –
LMO-EDA (MP2) RVS (HF)
−16.1 −13.0
−20.0 −19.8
14.1 13.9
−7.7 −4.8
– −2.3
−2.5 –
/H2 O (CH3 )2 NH+ 2 (CH3 )3 NH+ /H2 O
These values agree with those reported for typical red-shifting HBs, like those occurring in water or alcohol clusters [45] and in monoatomic anion/water dimers [48]. The total amount of charge transferred qtot c from all the water molecules towards the NH+ n core increases as nw increases, accord1/2
ing to the power law function nw , regardless of the ion. The non-linear behavior of qtot with respect to nw can result from c charge-transfer saturation effects. However, as already mentioned for the geometry and vibrational properties, we may here also argue that the qtot c non-linear behavior results mainly from the water/ water strong electrostatic repulsive effects occurring in ion first hydration shells. As they lead to the lengthening of NH O HBs, they ∗ interactions. lead also to the weakening of water lp/NH 3.4. Interaction energy analysis Table 3 summarizes the interaction energy decompositions performed either at the MP2 level with the LMO-EDA scheme or at the /H2 O Hartree–Fock level with the RVS scheme. For the dimers NH+ 4 and K+ /H2 O, the earlier data of Lee and coworkers [35] (from the SAPT/MP2 scheme) and of Khaliullin and coworkers [36] (from the ALMO/BP86 approach) are also reported in that table, together /H2 O data of Su and coworkers [33] (from the LMOwith the NH+ 4 EDA/CCSD(T) scheme). From both our RVS/HF and LMO-EDA/MP2 results for the K+ and NH+ /water dimers, it clearly appears that the magnitudes of all 4 the energy components are significantly stronger in the NH+ dimer 4 than in the K+ one, whereas both their total binding energies differ only by 15% (i.e. 3 kcal mol−1 ). For instance, the magnitudes of the NH+ /H2 O exchange-repulsion, polarization and dispersion energy 4 components are at least twice as large than for K+ . The SAPT/MP2 scheme led to similar results. This may be interpreted as resulting from the shortest ion/water distance occurring in the NH+ dimer 4 than in the K+ one (1.64 and 2.61 A˚ at the MP2/aug-cc-pVTZ level, respectively). The LMO-EDA/MP2 data for alkyl-ammonium/water dimers are close to the NH+ ones. Nevertheless, the magnitude of the 4 dispersion component for alkylated ions is slightly larger than for NH+ , and it increases with respect to the number of the 4 carbon atoms. This agrees with the standard picture of the water/methane interaction, dominated by dispersion at medium range.
Epol/ind
Ect
Edisp
Contrary to Edisp , the magnitudes of the components Eexch-rep , . For the Eelec and Epol are smaller for alkylated ions than for NH+ 4 electrostatic and polarization components, this may be considered as surprising when considering the NPA charges because (1) the nitrogen charge in smaller in alkylated ions than in NH+ and (2) the 4 HN hydrogen charges are remarkably constant in all ions. However, we have to keep in mind that (1) an atomic charge is not a quantum observable and (2) ion/water electrostatic effects are strongly affected by the charges located on all the ion atoms and not only on those interacting with water at short range. Concerning the latter point 2, we may note that computing the Eelec component from a static point charge model (the charge sets being the NPA ones), yields a difference of +5 kcal mol−1 in that component between the dimers (CH3 )3 NH+ /H2 O and NH+ /H2 O, in agreement with the data 4 of Table 3. As expected from the brief presentation of the various EDA schemes (see Section 2), it is interesting to note for the dimer NH+ /H2 O that the sum of the polarization/induction and charge4 transfer components estimated from the RVS/HF and ALMO/BP86 schemes almost exactly equals our LMO-EDA/MP2 Epol estimate, as well as the SAPT/MP2 Eind one. Moreover, the LMO-EDA/MP2 and SAPT/MP2 estimates of Edisp is as small as the SAPT/MP2 and RVS/HF estimates of Ect . All the energy decomposition schemes suggest thus a comparable weight for both dispersion and charge-transfer effects in the NH+ /H2 O dimer, each effect rep4 resenting from 10% to 15% of its interaction energy. Hence, the ammonium/water interaction is not governed by only exchangerepulsion/electrostatic/polarization effects as in the case of the hard cation K+ (see Table 3), but it is also influenced by overall weak, but strong enough when considered together, dispersion and chargetransfer effects. 4. Conclusions We have performed a comprehensive theoretical analysis of the alkylation influence on the ion/water interaction in small hydrated ammonium and alkyl-ammonium clusters. Our results show that a specific NH O HB is weakened by alkylation and by the interactions of water molecules with the other hydrogens of the cationic NH+ n core. In clusters where the ammonium first hydration shell is complete, the NH O HB weakening is so strong that the geometrical and vibrational properties of these HBs are close to those of the weak HB occurring in the gas-phase water dimer.
V. Vallet, M. Masella / Chemical Physics Letters 618 (2015) 168–173
Alkylation yields the decrease in magnitude of the ammonium nitrogen negative charge, while it has no effect on the ion HN hydrogen ones. However, the charge distribution within alkylammonium ions doesn’t strengthen the alkyl-ammonium/water interaction, as one might expect by considering only the latter charges, but to weaken it. This shows that alkyl-ammonium/water interactions are not driven only by local NH O HBs. They are also noticeably influenced by electrostatic non-local interactions involving the ion alkyl groups. Lastly, the overall weak contribution of charge-transfer effects to the ammonium/water interaction and the weakening of local NH O HBs as the size of the hydrated ion cluster grows explain why simple molecular modeling approaches, where ammonium/water interactions are described as sums of repulsive, electrostatic, polarization and dispersion energy terms usually provide accurate results concerning the solvation of ammonium ions in neat water, as shown by one of us recently [20]. Supplementary material Archive file with all Gaussian and Turbomole frequencies output files. Acknowledgments This work was granted access to the HPC resources of [CCRT/CINES/IDRIS] under the allocation 2014-[6100] by GENCI (Grand Equipement National de Calcul Intensif). We acknowledge an access to the supercomputing systems ‘Fusion’ and ‘Blue’ operated by the Laboratory Computing Resource Center at Argonne National Laboratory. We have also used the PhLAM computing facility financed by the French National Research Agency under contract ANR-11-LABX-0005 Chemical and Physical Properties of the Atmosphere (CaPPA). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.cplett.2014.11.005. References [1] N.V. Plechkova, K.R. Seddon, Chem. Soc. Rev. 37 (2008) 123, http://dx.doi.org/ 10.1039/B006677J. [2] A. Leninger, Biochemistry, Worth Publishers, 1970. [3] A.J. Illies, T.H. Morton, Int. J. Mass. Spectr. 167–168 (1997) 431, http://dx.doi.org/10.1016/S0168-1176(97)00067-0 (in Honour of Chava Lifshitz). [4] T. Steiner, Angew. Chem. Int. Ed. 41 (2002) 48, http://dx.doi.org/10.1002/ 1521-3773(20020104)41:1<48::AID-ANIE48>3.0.CO;2-U. [5] Y. Yang, O. Kühn, G. Santambrogio, D.J. Goebbert, K.R. Asmis, J. Chem. Phys. 129 (2008) 224302, http://dx.doi.org/10.1063/1.3028211. [6] A. Pullman, A.M. Armbruster, Int. J. Quantum Chem. 8 (1974) 169, http://dx.doi.org/10.1002/qua.560080820. [7] A. Pullman, A.M. Armbruster, Chem. Phys. Lett. 36 (5) (1975) 558, http://dx.doi.org/10.1016/0009-2614(75)85337-1. [8] J.C. Jiang, H.-C. Chang, Y.T. Lee, S.H. Lin, J. Phys. Chem. A 103 (1999) 3123, http://dx.doi.org/10.1021/jp9838543. [9] F. Brugé, M. Bernasconi, M. Parrinello, J. Am. Chem. Soc. 121 (1999) 10883, http://dx.doi.org/10.1021/ja990520y. [10] E.G. Diken, N.I. Hammer, M.A. Johnson, R.A. Christie, K.D. Jordan, J. Chem. Phys. 123 (2005) 164309, http://dx.doi.org/10.1063/1.2074487. [11] J. Douady, F. Calvo, F. Spiegelman, J. Chem. Phys. 129 (2008) 154305, http://dx.doi.org/10.1063/1.2987304.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Benchmark binding energies of ammonium and alkyl-ammonium ions interacting with water. Are ammonium–water hydrogen bonds strong? Valérie Vallet a,∗ , Michel Masella b a
Laboratoire PhLAM, UMR 8523, CNRS Université de Lille, F-59655 Villeneuve d’Ascq Cedex, France CEA Saclay, Laboratoire de Biologie Structurale et Radiobiologie, Service de Bioénergétique Biologie Structurale et Mécanismes, Institut de biologie et de technologies de Saclay, F-91191 Gif sur Yvette Cedex, France b
a r t i c l e
i n f o
Article history: Received 14 August 2014 In final form 3 November 2014 Available online 11 November 2014
a b s t r a c t Alkyl-ammonium ion/water interactions are investigated using high level quantum computations, yielding thermodynamics data in good agreement with gas-phase experiments. Alkylation and hydration lead to weaken the NH O hydrogen bonds. Upon complete hydration by four water molecules, their main features are close to those of the OH O bond in the isolated water dimer. Energy decomposition analyses indicate that hydration of alkyl-ammonium ions are mainly due to electrostatic/polarization effects, as for hard monoatomic cations, but with a larger effect of dispersion. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Protonated alkyl-ammonium ions and their interaction with water play a key role in chemistry and biology. These ions are common constituents of ionic liquids [1] and they play also a key role in protein structure and solubility, as well as in enzyme catalysis [2]. The interactions between an ammonium ion and a polar molecule are usually depicted at the microscopic level as a prototypical form of strong hydrogen bonds (HB) (see Refs. [3–5], for instance). As an HB corresponds mainly to a local interaction, this may explain why most of the theoretical quantum studies devoted so far to investigate the interaction properties of ammonium ions with water focused on hydrated NH+ systems [6–13], whereas 4 alkyl-ammonium ions have been much less investigated [14,15]. If the ammonium/water interaction is not expected to be strongly affected by alkylation, many discrepancies among ammonium and alkyl-ammonium ions have been reported experimentally. For instance, ion/water binding enthalpies decrease by about 1 kcal mol−1 in the series NH+ /CH3 NH+ /C2 H5 NH+ /n-C3 H7 NH+ 4 3 3 3 [16–18]. Moreover, recent experiments using infrared photodissociation spectroscopy and blackbody infrared radiative dissociation at 133 K, exhibited a different behavior for the NH+ and CH3 NH+ as 4 3 interacting with water clusters made of 19–21 molecules: NH+ is 4 preferentially located within the water clusters, whereas CH3 NH+ 3
∗ Corresponding author. E-mail address: [email protected] (V. Vallet). http://dx.doi.org/10.1016/j.cplett.2014.11.005 0009-2614/© 2014 Elsevier B.V. All rights reserved.
is located at their surface [19]. In the latter case, the hydrophomethyl group has to be at the origin of bic nature of the CH3 NH+ 3 these different behaviors. However, discrepancies at the level of the local interaction between the NH+ moiety and water molecules may also affect the behavior of these ions when interacting with large molecular systems. In the present Letter, we present an thorough theoretical analysis of the microscopic interactions between alkyl-ammonium ions and water molecules (from 1 to 4) using high level quantum methods. Our aim is to enlighten the similarities and discrepancies concerning the interactions between such ions and water. This provides helpful hints for building up accurate ‘ab initio’ forcefield approaches, i.e. molecular modeling (MM) approaches whose parameters are assigned by considering only theoretical quantum data, with no further refinement using experimental data. Such a development strategy for MM approaches should lead to wellsuited methods to investigate the behavior of the ions in different chemical environment and physical conditions, as solvated in water nano-droplets or in neat liquid water (see the recent study performed by one of us Ref. [20], for instance). Here, we investigated the interaction properties of ion/ , CH3 NH+ , C2 H5 NH+ , (water)nw systems where the ions are NH+ 4 3 3 + + n-C3 H7 NH+ , (CH ) NH and (CH ) NH . For each ion, we con3 2 3 3 3 2 sidered different hydrated systems containing water molecules up to saturating all the possible ion/water HBs. All systems were investigated at a high quantum level of theory, allowing one to extrapolate binding energies to the complete basis set limit. We investigated the nature of the microscopic forces affecting the local
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ion/water interactions using standard electronic population analysis and energy decomposition schemes, and we compare these properties to those of the most intensively studied system presenting a prototypical form of weak HB, i.e. the water dimer. Lastly, as the hydration properties of the ions K+ and NH+ are close, we will 4 also discuss some hydrated K+ cluster properties for comparison purposes. 2. Theoretical methods All quantum calculations have been performed with the gaussian09 [21], the molpro [22], the turbomole [23], and the gamess [24,25] packages of programs. All computations were performed using the frozen core (FC) approximation. To compute accurate interaction energies of the various ion/water clusters, we first optimized the complex geometries at the MP2 level with augmented correlation consistent triple- basis sets (aug-cc-pVTZ). We computed then the cluster total energies by performing single point energy calculations at the MP2/aug-cc-pVXZ//MP2/aug-cc-pVTZ level, with X = T, Q and 5. The corresponding Hartree–Fock EHF and correlation Ecorr energy components were used to extrapolate the complex total energies to their complete basis set (CBS) limit using a three-point exponential formula for EHF [26,27] and a two-point extrapolation for Ecorr [28]. The thermodynamic quantities (enthalpy and entropy) were computed at 298.15 K from the system vibrational frequencies estimated at the MP2/aug-cc-pVTZ level of theory, using harmonic oscillator partition functions and by applying the standard 0.953 scaling factor to the frequencies [29]. The electronic population analyses were performed using the Natural Population Analysis (NPA) method [30], as implemented in the nbo program v 3.1 [31]. Lastly, insights into the intermolecular interactions were provided by energy decomposition analysis (EDA) making use of the reduced variational space (RVS) [32] method at the HF/aug-cc-pVTZ level and of the localized molecular orbital EDA (LMO-EDA) [33] scheme at the MP2/aug-cc-pVTZ level. All EDAs were performed by considering structures optimized at the MP2/aug-cc-pVTZ level. We will compare our computed EDA data to those estimated from other quantitative decompositions, like the symmetry-adapted perturbation theory (SAPT) method [34,35] at the MP2 level, or with the absolutely localized molecular orbitals (ALMO) [36] at the DFT/BP86 level. EDA methods decompose the interaction energy into three common components, namely the electrostatic Eelec , the exchangerepulsion Eexc−rep and the polarization Epol component (the latter one is denoted induction Eind in the SAPT approach). However, an additional component is also computed, namely a charge-transfer Ect term (RVS and ALMO approaches) or a dispersion Edisp one (SAPT and LMO-EDA schemes). Thus EDA outputs have to be compared with caution, keeping in mind that (1) polarization interaction of LMO-EDA schemes includes both the polarization and chargetransfer contributions of RVS and ALMO schemes and (2) that unlike RVS, ALMO strictly produces a self-consistent polarization energy, and separates more adequately polarization from charge-transfer contributions than RVS does (see the recent review of Gordon and coworkers [37] where available EDA schemes are compared). 3. Results and discussion 3.1. Hydrogen bond geometries and stretching NH/CN vibrational spectra Geometrical and vibrational data regarding intermolecular NH O HBs and ion intramolecular NH and CN bonds are summarized in Table 1. The stretching harmonic vibrational frequencies
Figure 1. Schematic representation of (CH3 )2 NH+ (H2 O)2 . 2
NH reported in that table have been tentatively assigned to NH bonds interacting with a water molecule based on the atomic weights in the normal coordinates. All the frequency shifts induced by ion/water interactions discussed below are computed by comparing the hydrated ion cluster stretching frequency NH (or CN ) to the average of the corresponding frequencies in the isolated gas-phase cation. In all hydrated ion clusters, the improper HOH–HN dihedral angle values are included within 163◦ and 180◦ . As illustrated by the schematic representation (Figure 1) of methyl ammonium solvated by two water molecules, the molecules interact thus with the ammonium hydrogens HN in quasi planar structures, regardless of the ion. The shortest ion carbon/water oxygen distance is about 3.52± 0.02 A˚ in all hydrated ion clusters, which exactly equals the equilibrium carbon/oxygen distance in the isolated methane/water dimer [38]. hydration leads to the increase of the NH O Successive NH+ 4 hydrogen bond length, Rhb , from 1.64 (nw = 1) up to 1.83 A˚ (nw = 4), and to the decrease of the NH bond length, from 1.054 down to ˚ However, compared to isolated gas-phase geometries, the 1.030 A. with water yields a small lengthening of the NH interaction of NH+ 4 ˚ regardless of nw . Note that the presence bonds, from 0.01 to 0.03 A, of water molecules has no effect on the length of the NH bonds not involved in ion/water HBs. All the latter NH O HB features are observed in all alkylated ion hydrated clusters. Alkylation of NH+ yields also the increase of Rhb in ion/water 4 dimers, from 0.05 (CH3 NH+ ) up to 0.10 A˚ ((CH3 )3 NH+ ). The nature 3 of the alkyl group in mono-alkylated ammonium ions has a weak impact on the latter distance, which slightly increases at the rate of 0.01 A˚ with respect to the alkyl chain length, regardless of nw . We note also that hydration yields a slight shortening of the CN bonds, which decrease by 0.01 A˚ per water molecule added. Compared to the NH vibrational spectra of the isolated ions, the interaction of a NH bond with a water molecule leads to a strong red shift NH in the frequency of the corresponding NH bond stretching vibrational mode. The red shift varies from 582 cm−1 in the NH+ /H2 O dimer down to 243 cm−1 in the (CH3 )3 NH+ /H2 O 4 dimer. For a given ion, the red shift NH decreases as the number of interacting water molecules nw increases, at a rate of about 100–150 cm−1 per water molecule added, regardless of the ion. For a given number of interacting water molecules, successive methleads also to a decrease of NH , at a rate of about ylation of NH+ 4 80–90 cm−1 per methyl group added. The CN vibrational spectra is much less affected by ion/water interactions.
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Table 1 Structural, vibrational and natural population analysis (NPA) data of isolated ions and of hydrated ion clusters. nw : cluster number of water molecules. q(N): NPA nitrogen charge. q(HN): mean NPA charge of NH moiety hydrogens with their standard deviation in parenthesis. NH and CN : harmonic frequencies corresponding to stretching NH and CN vibrational modes, in cm−1 . CN frequencies are reported in brackets and, in italic, frequencies corresponding to NH groups interacting with water in hydrated clusters. qc : total charge transferred from the water lone pairs towards the NH anti-bonding orbitals. All charges in e. Ion
nw
r(N-X)
r(NH O)
q(N)
q(HN)
NH /CN
qc
NH+ 4
0 1 2 3 4
1.022 1.054 (1.019) 1.042 (1.017) 1.035 (1.016) 1.300
1.643 1.714 1.772 1.828
−0.82 −0.85 −0.87 −0.89 −0.90
0.46 (0.00) 0.45 (0.01) 0.44 (0.02) 0.44 (0.02) 0.45 (0.00)
3394-3527-3527-3527 2912-3456-3561-3561 3095-3109-3515-3582 3193-3240-3241-3567 3252-3326-3329-3331
na 0.036 0.051 0.058 0.062
0 1 2 3
1.022 (1.504) 1.045 (1.019) (1.496) 1.037 (1.018) (1.491) 1.032 (1.487)
1.698 1.754 1.803
−0.65 −0.67 −0.70 −0.72
0.44 (0.00) 0.44 (0.02) 0.44 (0.02) 0.44 (0.00)
3423-3519-3519 [968] 3060-3479-3543 [995] 3181-3207-3531 [1016] 3249-3301-3301[1034]
na 0.028 0.043 0.052
0 1 2 3
1.022 (1.514) 1.044 (1.020) (1.504) 1.036 (1.019) (1.500) 1.031 (1.494)
1.711 1.779 1.812
−0.65 −0.67 −0.70 −0.72
0.44 (0.00) 0.44 (0.02) 0.44 (0.02) 0.44 (0.00)
3413-3514-3519 [860] 3085-3468-3534 [880] 3192-3230-3523 [888] 3251-3310-3313 [900]
na 0.026 0.039 0.049
0 1 2 3
1.022 (1.514) 1.043 (1.020)(1.505) 1.036 (1.019) (1.499) 1.031 (1.494)
1.723 1.775 1.820
−0.65 −0.67 −0.69 −0.72
0.44 (0.00) 0.44 (0.02) 0.44 (0.03) 0.44 (0.00)
3413-3516-3520 [966] 3098-3470-3537 [987] 3195-3231-3520 [1009] 3253-3312-3316 [1021]
na 0.026 0.039 0.048
0 1 2
1.022 (1.497) 1.040 (1.020) (1.490) 1.034 (1.485)
1.730 1.777
−0.49 −0.52 −0.55
0.43 (0.00) 0.46 (0.03) 0.45 (0.00)
3444-3505 [886-1029] 3147-3495 [903-1111] 3233-3261 [915-1123]
na 0.025 0.038
0 1
1.022 (1.493) 1.037 (1.487)
1.749
−0.37 −0.41
0.42 (na) 0.46 (na)
3458 [821-1004-1004] 3215 [835-1018-1018]
na 0.021
CH3 NH+ 3
C2 H5 NH+ 3
C3 H7 NH+ 3
(CH3 )2 NH+ 2
(CH3 )3 NH+
Compared to isolated ion data, the CN frequencies are blue shifted in hydrated clusters, from about 20 cm−1 in dimers up to 100 cm−1 in tetramers. Comparable blue shifts were reported for the CO stretching frequency of a methanol molecule when acting as HB proton acceptor in water or methanol clusters [39,40]. For common red shifting HBs XH-Y, like those occurring in pure water clusters, the length of the intramolecular XH bond increases up to 0.03 A˚ and the corresponding stretching frequency is red shifted by hundreds of cm−1 compared to single molecule data [41]. This feature is also observed here for NH bonds. However, contrary to pure water clusters, for which both the length of the XH bond and the red shift in the corresponding stretching frequency XH increase as the cluster size grows, for NH bonds, both the latter quantities decrease with respect to the hydrated ammonium cluster size. As the strength of common red shifting HBs is usually reported to be proportional to the magnitude of both the XH bond lengthening and the corresponding XH red shift [42], our present results suggest that the ‘strong’ NH O HBs become weaker and weaker as the hydrated ion cluster size increases, so that most of their geometrical and vibrational features in the NH+ /water tetramer are close to 4 those of the weak HB occurring in the water dimer. For instance, the HB length is 1.83 A˚ in NH+ /(H2 O)4 and 1.90 A˚ in the water dimer 4 [43], and the water dimer OH red shift is about 170 cm−1 as reported both experimentally and theoretically, a value very close to our computed average NH red shift in NH+ /(H2 O)4 , about 185 cm−1 4 (for the water dimer, see Ref. [44] and the references mentioned therein). Moreover, ion alkylation also leads to the weakening of NH O HBs, whereas it was shown to reinforce OH O HBs in alcohol and ether-oxide/water dimers, as compared to the water dimer [45]. The NH O HB destabilization induced by hydration has to result from the overall strong water oxygen–oxygen electrostatic repulsive effects occurring in cation first hydration shells, as discussed in Ref. [46], for instance. As the negative electrostatic charge of the carbons bonded to the ion nitrogen is overall strong (see below), we may argue that strong enough carbon/water oxygen electrostatic repulsive effects are also responsible for NH O HB destabilization in alkylated ion hydrated systems.
3.2. Binding energies at the CBS limit and thermodynamical data The total ion hydration energies by nH2 O E tot (nw ) and the corresponding stepwise hydration energies Enw −1,nw have been calculated on the basis of the gas-phase reactions nw H2 O + Ion → Ion/(H2 O)nw
(1)
Ion/(H2 O)nw −1 + H2 O → Ion(H2 O)nw
(2)
The hydration energies at the CBS limit and the computed thermodynamic data given in Table 2 cover the additions from one up to four water molecules. Concerning the hydration energies, it is noteworthy that the CBS limit is reached within 0.2–0.4 kcal mol−1 with basis set of quadruple zeta quality (see Supporting Information). As expected from the above discussions concerning the hydrated ion cluster geometry and vibrational properties, the ion hydration energies decrease (1) as nw increases and (2) as the number of HN hydrogens substituted by a methyl group increases. For instance, the first stepwise hydration energy E0,1 gradually increases from −20.5 up to −16.2 kcal mol−1 in the series NH+ /CH3 NH+ /(CH3 )2 NH+ /(CH3 )3 NH+ . That energy also 4 3 2 decreases when increasing the alkyl chain length, however, it seems to converge as soon as the propyl-ammonium ion. All the stepwise hydration enthalpies Hnw −1,nw computed from MP2 data at the CBS limit and by considering the harmonic approximation (with scaled frequencies) to compute the thermodynamic corrections are in a particularly good agreement with available experimental data, within less than 0.6 kcal mol−1 on average. We note also the same very good agreement between theory and experiment for the stepwise hydration entropies Snw −1,nw . The agreement is achieved here within less than 2 cal mol−1 K−1 on average. Interestingly, the Snw −1,nw are fairly constant, about 24 ± 2 cal mol−1 K−1 , regardless of the ion and nw . This is to be expected as the entropy change for water addition is dominated by the loss of three translational degrees of freedom upon the formation of an additional internal hydrogen bond between the cation and the added water molecule.
V. Vallet, M. Masella / Chemical Physics Letters 618 (2015) 168–173
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Table 2 Gas-phase binding energies and thermodynamical data concerning the ion hydration stepwise reactions. PA: difference in proton affinity between the unprotonated ion form and water. Etot : cluster total binding energy from quantum MP2 computations at the CBS limit. Enw −1,nw : quantum stepwise gas-phase hydration energy. Hnw −1,nw and Snw −1,nw : stepwise hydration enthalpy and entropy estimates computed from the CBS binding energies and from cluster harmonic vibrational frequencies. In bracket, enthalpies correspond to averaged data from the NIST WEBBOOK data base [18], for the other ions and for the stepwise entropies, they are taken the experimental data (NH+ 4 from [49]). All energy values in kcal mol−1 and all entropy data in cal mol−1 K−1 . Ion
Quantity
NH+ 4
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
39.9
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
51.1
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
50.5
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
55.4
PA −Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
58.2
CH3 NH+ 3
CH3 (CH2 )NH+ 3
CH3 (CH2 )2 NH+ 3
(CH3 )2 NH+ 2
(CH3 )3 NH+
−Etot −Enw −1,nw −Hnw −1,nw −Snw −1,nw
PA 16.2
nw = 1
2
3
4
20.5 20.5 20.0 [19.2] 24.0 [23.9]
37.6 17.2 15.1 [15.3] 24.0 [22]
52.1 14.5 13.6 [13.1] 21.5 [23.7]
64.7 12.6 11.1 [11.5] 21.8 [25.2]
18.5 18.5 17.2 [17.8] 22.8 [21.8]
34.2 15.7 14.3 [14.6] 26.7 [24.2]
47.8 13.6 13.1 [12.4] 18.7 [24.1]
17.6 17.6 16.4 [17.5] 22.1 [–]
32.7 14.9 13.6 [14.7] 25.5 [–]
45.9 13.2 11.7 [–] 25.7 [–]
17.3 17.3 16.0 [15.0] 24.6 [22.9]
32.2 14.9 13.4 [11.6] 25.4 [24.7]
45.2 13.0 11.6 [10.3] 22.9 [24.4]
17.1 17.1 15.8 [15.0] 22.0 [22.9]
31.9 14.8 13.4 [13.5] 29.5 [24.7]
62.4 16.2 15.5 [14.5] 24.6 [24.1]
We computed also the proton affinities (PA) of the unprotonated ion forms and of water, according to the same protocol as for the cluster binding energies. The differences PAs in the computed PA values between the unprotonated ion forms and water are reported in Table 2. They are 6.5± 0.5 % higher than the experimental ones [16]. Such discrepancies has to result from non canceling errors due to the harmonic approximation we used to compute the thermodynamical corrections to the PA values. However, we observe a linear inverse relation between our PAs and our computed hydration enthalpies H0,1 , as experimentally reported [17,47] (here, the coefficient of regression is 0.997). For the series CH3 NH+ /(CH3 )2 NH+ /(CH3 )3 NH+ , we note that both their 3 2 corresponding PA and H0,1 values correlate linearly with their number of methyl groups (the coefficient of regression is 0.99, regardless of the quantity considered). This suggests that the apparent correlation between PA and H0,1 values originates from two different phenomena. The proton H+ moiety of a methylated ion strongly polarizes its CH bonds, which leads to strengthen the proton affinity, whereas the ion methyl groups destabilize the ion/water HBs (see also our discussions below). However, as the linear inverse relation between PA and H0,1 values is reported for a large set of B/BH+ chemical entities, the latter hypothesis concerning the origin of such a relation needs to be further investigated and discussed.
3.3. Electronic population analysis The NPA charges for the nitrogen (N) and its hydrogens (HN) are summarized in Table 1. For nitrogen bonded carbons and for
carbon hydrogens, these charges are constant, regardless of the ion and the cluster size: −0.29 and +0.21 ± 0.01 e, respectively. The hydrogen charges q(HN) are constant, about +0.45 ± 0.01 e, regardless of the ion and the cluster size. They are slightly affected by the presence of water molecules. They decrease by an amount of 0.03 e per water molecule added. This amount is close to the magnitude of the charge transferred qc from a water molecule towards the NH+ n core (see below). The nitrogen charge q(N) increases by about +0.15 e in the series NH+ /CH3 NH+ /(CH3 )2 NH+ /(CH3 )3 NH+ , whereas it is constant in 4 3 2 + /C H NH /n-C3 H7 NH+ , regardless of the water the series CH3 NH+ 5 2 3 3 3 cluster size. Alkylation yields thus the dilution of the negative charge of the ammonium nitrogen atom. According to standard orbital interpretation of hydrogen bonding (cf. Ref. [48]), NH O HBs may be interpreted as resulting from the interaction between water lone pairs (lp) and NH anti-bonding ∗ . The strength of such an interaction can be quantiorbitals NH fied using NBO data by considering the amount of electronic charge ∗ according to transferred qc from the water lps towards a given NH qc ≈ 2
ld |F| ∗ 2 NH
lone-pairs
∗ − l
,
(3)
here, F is the Fock operator, * and l are the energies (in terms of ∗ and of an lp, respectively. diagonal Fock matrix elements) of NH The computed charges qc are summarized in Table 1. Their magnitude, when rescaled by the number of cluster NH O HBs, ranges from 0.01 to 0.04 e, regardless of the ion. The strongest value is observed for NH+ , while qc is almost constant for alkylated ions. 4
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Table 3 Energy decompositions for ion/water dimers. All data in kcal mol−1 . All results from our own computations, at the exception of the SAPT data taken from Ref. [35], the ALMO data taken from Ref. [36] and the LMO-EDA CCSD(T) data taken from Ref. [33]. Ion/water dimer
Method
Etot
Eelec
Eexch-rep
K+ /H2 O
LMO-EDA (MP2) SAPT (MP2) RVS(HF) ALMO (BP86)
−17.6 −17.6 −16.9 −14.5
−19.6 −18.8 −19.6
7.0 7.1 6.9 −10.9
−4.4 −4.3 −3.6 −3.1
– – −0.7 −0.4
−0.6 −1.7 – –
/H2 O NH+ 4
LMO-EDA (MP2) LMO-EDA (CCSD(T)) SAPT (MP2) RVS(HF)
−20.7 −20.8 −21.0 −18.4
−25.4 −25.4 −24.2 −25.3
18.3 18.2 15.3 18.2
−11.9 −11.8 −8.2 −7.5
– – – −3.8
−1.8 −1.9 −4.0 –
/H2 O CH3 NH+ 3
LMO-EDA (MP2) RVS(HF)
−18.5 −15.9
−22.8 −22.7
15.9 15.8
−9.6 −6.0
– −3.0
−2.1 –
C2 H5 NH+ /H2 O 3
LMO-EDA (MP2) RVS (HF)
−17.7 −21.8
−21.9 14.0
15.3 −5.7
−9.0 −2.8
– –
−2.1 −15.7
/H2 O nC3 H7 NH+ 3
LMO-EDA (MP2) RVS (HF) LMO-EDA (MP2) RVS (HF)
−17.3 −21.4 −17.1 −19.9
−21.5 15.0 −21.1 −21.0
15.2 −5.5 14.7 14.6
−8.7 −3.4 −8.3 −5.3
– – – −8.2
−2.3 −15.1 −2.3 –
LMO-EDA (MP2) RVS (HF)
−16.1 −13.0
−20.0 −19.8
14.1 13.9
−7.7 −4.8
– −2.3
−2.5 –
/H2 O (CH3 )2 NH+ 2 (CH3 )3 NH+ /H2 O
These values agree with those reported for typical red-shifting HBs, like those occurring in water or alcohol clusters [45] and in monoatomic anion/water dimers [48]. The total amount of charge transferred qtot c from all the water molecules towards the NH+ n core increases as nw increases, accord1/2
ing to the power law function nw , regardless of the ion. The non-linear behavior of qtot with respect to nw can result from c charge-transfer saturation effects. However, as already mentioned for the geometry and vibrational properties, we may here also argue that the qtot c non-linear behavior results mainly from the water/ water strong electrostatic repulsive effects occurring in ion first hydration shells. As they lead to the lengthening of NH O HBs, they ∗ interactions. lead also to the weakening of water lp/NH 3.4. Interaction energy analysis Table 3 summarizes the interaction energy decompositions performed either at the MP2 level with the LMO-EDA scheme or at the /H2 O Hartree–Fock level with the RVS scheme. For the dimers NH+ 4 and K+ /H2 O, the earlier data of Lee and coworkers [35] (from the SAPT/MP2 scheme) and of Khaliullin and coworkers [36] (from the ALMO/BP86 approach) are also reported in that table, together /H2 O data of Su and coworkers [33] (from the LMOwith the NH+ 4 EDA/CCSD(T) scheme). From both our RVS/HF and LMO-EDA/MP2 results for the K+ and NH+ /water dimers, it clearly appears that the magnitudes of all 4 the energy components are significantly stronger in the NH+ dimer 4 than in the K+ one, whereas both their total binding energies differ only by 15% (i.e. 3 kcal mol−1 ). For instance, the magnitudes of the NH+ /H2 O exchange-repulsion, polarization and dispersion energy 4 components are at least twice as large than for K+ . The SAPT/MP2 scheme led to similar results. This may be interpreted as resulting from the shortest ion/water distance occurring in the NH+ dimer 4 than in the K+ one (1.64 and 2.61 A˚ at the MP2/aug-cc-pVTZ level, respectively). The LMO-EDA/MP2 data for alkyl-ammonium/water dimers are close to the NH+ ones. Nevertheless, the magnitude of the 4 dispersion component for alkylated ions is slightly larger than for NH+ , and it increases with respect to the number of the 4 carbon atoms. This agrees with the standard picture of the water/methane interaction, dominated by dispersion at medium range.
Epol/ind
Ect
Edisp
Contrary to Edisp , the magnitudes of the components Eexch-rep , . For the Eelec and Epol are smaller for alkylated ions than for NH+ 4 electrostatic and polarization components, this may be considered as surprising when considering the NPA charges because (1) the nitrogen charge in smaller in alkylated ions than in NH+ and (2) the 4 HN hydrogen charges are remarkably constant in all ions. However, we have to keep in mind that (1) an atomic charge is not a quantum observable and (2) ion/water electrostatic effects are strongly affected by the charges located on all the ion atoms and not only on those interacting with water at short range. Concerning the latter point 2, we may note that computing the Eelec component from a static point charge model (the charge sets being the NPA ones), yields a difference of +5 kcal mol−1 in that component between the dimers (CH3 )3 NH+ /H2 O and NH+ /H2 O, in agreement with the data 4 of Table 3. As expected from the brief presentation of the various EDA schemes (see Section 2), it is interesting to note for the dimer NH+ /H2 O that the sum of the polarization/induction and charge4 transfer components estimated from the RVS/HF and ALMO/BP86 schemes almost exactly equals our LMO-EDA/MP2 Epol estimate, as well as the SAPT/MP2 Eind one. Moreover, the LMO-EDA/MP2 and SAPT/MP2 estimates of Edisp is as small as the SAPT/MP2 and RVS/HF estimates of Ect . All the energy decomposition schemes suggest thus a comparable weight for both dispersion and charge-transfer effects in the NH+ /H2 O dimer, each effect rep4 resenting from 10% to 15% of its interaction energy. Hence, the ammonium/water interaction is not governed by only exchangerepulsion/electrostatic/polarization effects as in the case of the hard cation K+ (see Table 3), but it is also influenced by overall weak, but strong enough when considered together, dispersion and chargetransfer effects. 4. Conclusions We have performed a comprehensive theoretical analysis of the alkylation influence on the ion/water interaction in small hydrated ammonium and alkyl-ammonium clusters. Our results show that a specific NH O HB is weakened by alkylation and by the interactions of water molecules with the other hydrogens of the cationic NH+ n core. In clusters where the ammonium first hydration shell is complete, the NH O HB weakening is so strong that the geometrical and vibrational properties of these HBs are close to those of the weak HB occurring in the gas-phase water dimer.
V. Vallet, M. Masella / Chemical Physics Letters 618 (2015) 168–173
Alkylation yields the decrease in magnitude of the ammonium nitrogen negative charge, while it has no effect on the ion HN hydrogen ones. However, the charge distribution within alkylammonium ions doesn’t strengthen the alkyl-ammonium/water interaction, as one might expect by considering only the latter charges, but to weaken it. This shows that alkyl-ammonium/water interactions are not driven only by local NH O HBs. They are also noticeably influenced by electrostatic non-local interactions involving the ion alkyl groups. Lastly, the overall weak contribution of charge-transfer effects to the ammonium/water interaction and the weakening of local NH O HBs as the size of the hydrated ion cluster grows explain why simple molecular modeling approaches, where ammonium/water interactions are described as sums of repulsive, electrostatic, polarization and dispersion energy terms usually provide accurate results concerning the solvation of ammonium ions in neat water, as shown by one of us recently [20]. Supplementary material Archive file with all Gaussian and Turbomole frequencies output files. Acknowledgments This work was granted access to the HPC resources of [CCRT/CINES/IDRIS] under the allocation 2014-[6100] by GENCI (Grand Equipement National de Calcul Intensif). We acknowledge an access to the supercomputing systems ‘Fusion’ and ‘Blue’ operated by the Laboratory Computing Resource Center at Argonne National Laboratory. We have also used the PhLAM computing facility financed by the French National Research Agency under contract ANR-11-LABX-0005 Chemical and Physical Properties of the Atmosphere (CaPPA). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.cplett.2014.11.005. References [1] N.V. Plechkova, K.R. Seddon, Chem. Soc. Rev. 37 (2008) 123, http://dx.doi.org/ 10.1039/B006677J. [2] A. Leninger, Biochemistry, Worth Publishers, 1970. [3] A.J. Illies, T.H. Morton, Int. J. Mass. Spectr. 167–168 (1997) 431, http://dx.doi.org/10.1016/S0168-1176(97)00067-0 (in Honour of Chava Lifshitz). [4] T. Steiner, Angew. Chem. Int. Ed. 41 (2002) 48, http://dx.doi.org/10.1002/ 1521-3773(20020104)41:1<48::AID-ANIE48>3.0.CO;2-U. [5] Y. Yang, O. Kühn, G. Santambrogio, D.J. Goebbert, K.R. Asmis, J. Chem. Phys. 129 (2008) 224302, http://dx.doi.org/10.1063/1.3028211. [6] A. Pullman, A.M. Armbruster, Int. J. Quantum Chem. 8 (1974) 169, http://dx.doi.org/10.1002/qua.560080820. [7] A. Pullman, A.M. Armbruster, Chem. Phys. Lett. 36 (5) (1975) 558, http://dx.doi.org/10.1016/0009-2614(75)85337-1. [8] J.C. Jiang, H.-C. Chang, Y.T. Lee, S.H. Lin, J. Phys. Chem. A 103 (1999) 3123, http://dx.doi.org/10.1021/jp9838543. [9] F. Brugé, M. Bernasconi, M. Parrinello, J. Am. Chem. Soc. 121 (1999) 10883, http://dx.doi.org/10.1021/ja990520y. [10] E.G. Diken, N.I. Hammer, M.A. Johnson, R.A. Christie, K.D. Jordan, J. Chem. Phys. 123 (2005) 164309, http://dx.doi.org/10.1063/1.2074487. [11] J. Douady, F. Calvo, F. Spiegelman, J. Chem. Phys. 129 (2008) 154305, http://dx.doi.org/10.1063/1.2987304.
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