- Email: [email protected]
Monte Carlo and molecular orbital study of carbon-centered radicals in water
Journal of Molecular Structure (Theochem) , 306 (1994) 41-48 0166-1280/94/%07.00 0 1994 - Elsevier Science B.V. All rights reserved
41
Monte Carlo and molecular orbital study of carboncentered radicals in water. Solvent effects on the conformation and stability of CH(OH)CN, CH(OH):! and CH(CN)2 Hideto Takase, Osamu Kikuchi* Department
(Received
of Chemistry, 25 October
University of Tsukuba,
1993; accepted
Tsukuba 305, Japan
2 November
1993)
Abstract Monte Carlo simulations and MO calculations were carried out for three carbon-centered radicals, CH(OH)CN, CH(OH)2 and CH(CN)*, in H20, and the relative stability of these radicals was examined in connection with the substitution pattern. The solvation free energy changes along the OH rotation were calculated for CH(OH)CN and CH(OH)2 by statistical perturbation theory, and the energy minimum conformations of these radicals were determined. The solvation free energy differences among the three radicals were calculated by the mutation technique, and merostabilization energy of CH(OH)CN in water was calculated to be -1752kcalmol-’ , which is much larger than that in the gas phase. The electronic structures of these radicals in the HZ0 solution were calculated by ab initio ROHF MIDI-4* MO method including the solvent Hz0 molecules represented by point charge approximation. The calculated charge and spin populations indicated that the large stabilization energy of CH(OH)CN in HZ0 was caused by a strong interaction between the OH group of CH(OH)CN and H20, and this effect was found only in CH(OH)CN which is substituted asymmetrically by electron-donor and electron-acceptor groups.
Introduction
assisted by experimental effects have been discussed
It has been predicted theoretically that the carboncentered radical which is substituted asymmetrically by electron-donor and electron-acceptor substituents is more stabilized than the radical which is substituted symmetrically by the same substituents. Baldock and co-workers [1,2] and Katritzky and Soti [3] proposed the “merostabilization” concept on the basis of the theoretical study on the stabilization of radicals reported by Dewar [4] and synthesized new merostabilized radicals. Viehe and co-workers also suggested the similar concept which was denoted “capto-dative” radical stabilization and
substitution
* Corresponding author. SSDZ0166-1280(93)03596-Y
works [5,6]. Similar in terms of asymmetric
effects [7-91.
However, there have been few quantum mechanical calculations which give clear evidences for such stabilization. Crans et al. calculated the captodative stabilization energy for CH(NH2)BH2 and CH(NH2)CN using ab initio UHF MO method with the 4-31G basis set [IO]. The capto-dative stabilization energy is different from the merostabilization energy, and does not necessarily reflect the stabilization energy of the asymmetrical substitution of radicals. Leroy and co-workers reported the stabilization energy of various substituted carbon-centered radicals, although no evident stabilization energy was found [ 1 l- 131.
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem)
42
The radical stabilization has been calculated including the solvent effect. Katritzky et al. introduced the self-consistent reaction field (SCRF) into UHF-INDO MO method and calculated the merostabilization energy of asymmetrically substituted carbon-centered radicals in solution [14]. The calculated results strongly suggested the evident stabilization in the high dielectric constant medium, Karelson et al. applied SCRF UHF-MNDO and SCRF UHF-AM1 MO methods to the CH(OH)CN and CH(NH2)CN radicals [15]. Since SCRF is based on the continuum model, microscopic effects of the solvent effect can hardly be analyzed by these methods. In this paper, the hybrid method of Monte Carlo (MC) simulation and MO calculation has been applied to CH(OH)CN, CH(OH)z and CH(CN)z in HzO, and revealed the relative stability of these radicals. Free energy changes along the rotation of the OH bond were calculated and the conformational stability of the radicals in H20 was examined. Merostabilization energy was estimated by calculating the free energy differences among the three radicals. Solvent effects on the electronic structures of radicals were examined by ab initio ROHF MIDI-4* MO calculations including the solvent molecules represented by simple point charge
o/c\ CS
.N
Ii
H
H
MO calculation in the gas phase
All MO calculations were performed by ab initio ROHF MO method with the MIDI-4* basis set using our ABINIT program. Geometry optimization calculations were carried out for seven conformations shown in Fig. 1. The potential energy variations along the rotation of the OH bond were calculated for CH(OH)CN and CH(OH)*. In the case of CH(OH)z, simultaneous rotation of two OH bonds was not carried out, and the potential energy curves from EZ to ZZ and that from EZ to EE were calculated. Merostabilization energy, AE,, of CH(OH)CN in the gas phase was calculated by the following equation. AEM
= &H(OH)CN
- (ECHO
o/c\0 b
H
In the MC simulation, the intermolecular potential functions between solvent-solvent and solute-solvent molecules must be determined.
o0cAo A
I! (II EE)
Fig. 1. Seven conformations
-k
Intermolecular potential functions
I
I
(II C,)
Calculation
'N
(I 2)
I!
approximation, in which the configuration of solvent molecules was generated by MC simulation.
H.O/C\ C*
(1 W
306 (1994) 41-48
of CH(OH)CN,
(II EZ)
(II ZZ)
CH(OH)* and CH(CN)2.
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem)
Table 1 Determined Molecule
potential function parameters Site
306 (1994) 41-48
for H20, CH(OH)CN,
CH(OH)CN
CH(OH),
CH(CN)z
0 H C H 0 H(DH) C(CN) N C H 0 HPH) C H CKN) N
CH(OH)2 and CH(CN)?
A
((kcal~12mol-‘)1/2) H20a
43
850 _ 1700 _ 564 _ 1700 800 1700 564 _ 1700 _ 1700 800
4 W
ikcal A6 mol-‘)‘/2) 38.7 _ 30.8 _ 31.6 _ 33.6 31.3 30.8 _ 31.6 _ 30.8 _ 33.6 31.3
-0.702 0.351 0.155 0.253 -0.824 0.689 0.109 -0.382 0.053 0.174 -0.527 0.4135 0.356 0.104 0.086 -0.316
“Ref. 16.
For H20-HzO, the potential function which was determined in our previous paper [ 161 was used. This potential function was determined to reproduce well the interaction energy of the Hz0 dimers calculated by ab initio MIDI-4* calculations. The same procedure was used to determine the potential functions for the solute-H20 systems which reproduce well the ROHF MIDI-4* energies. In this procedure, the structure of each solute molecule was fixed at its energy minimum conformation except CH(OH)2. For CH(OH)2, the EZ conformer, which is the most stable among the planar conformers was used. The Hz0 molecule was located randomly around the solute molecule. The number of calculated dimer configurations were 142, 148 and 142 for the CH(OH)CN-H20, CH(OH)2-H20 and CH(CN)2-H20 dimers, respectively. The calculated interaction energies for the dimers were used to determine the soluteHz0 intermolecular potential functions which are constructed by Lennard-Jones (LJ) (12-6) terms and coulomb terms;
The A and C are LJ parameters and q is atomic charge. In the fitting of the parameters, LJ parameters were restricted to having similar values for the same group in the three radicals. For example, the same LJ parameters were used for the N atoms in CH(OH)CN and CH(CN);?. Atomic charges for two OH groups in CH(OH)2 were restricted to have same values to keep the symmetry of electronic structure in the ZZ and EE conformations. Determined parameters are listed in Table 1. MC simulation MC simulation was carried out according to the standard Metropolis method [17] with NVT ensemble. Each system consists of one solute molecule and 213 Hz0 molecules in a cubic cell. The volume of the cell was determined from the density of pure Hz0 (1.0gcmP3) and the temperature of the system was set at 298 K. Spherical cutoff at a half distance of the cell length was used for intermolecular interaction. Owicki-Scheraga preference sampling method [18] was employed. In this method, the probability of moving the solvent is proportional to 1/(r2 + c), where r is the distance
44
H. Takase and 0. KikuchiJJ. Mol. Struct. (Theochem)
Table 2 Calculated ROHF MIDI-4* energies of CH(OH)CN,
CH(OH)s
and CH(CN)t
in vacua
Molecule
Conformation
Total energy (au.)
AE (kcalmol-‘)a
CH(OH)CN
E Z
-205.890388 -205.887673 -189.051263 - 189.048078 -189.044136 -189.040975 -222.719118
0.0 1.70 0.0 2.00 4.47 4.46 0.0
CH(OH)z
c2
.EZ zz EE CHtCN)z aEnergy relative to the mi~mum
energy of each molecule.
between centers of solute and solvent molecules and the constant c was set at 150 A2 in the present study. The amounts of transformation and rotation of solvent molecules were adjusted to yield the acceptance ratio of 3040% for the sampled configuration. Full simulation was carried out through 5000K steps. Equilibrium of the system was established in the preceding 2000K steps and the averaging was carried out in the following 3000 K steps for each system. Free energy change along the rotation of the OH bond was calculated by the statistical perturbation theory (SPT) [19] with the double wide sampling technique; the rotation step was set at 15”. The total free energy change, AFy was obtained by adding the solvation free energy change, AFsoiV, which was calculated by the MC simulation, to the energy change of the solute in the gas phase, AE’, calculated by the MO method. Free energy differences between two radicals were calculated by the mutation method. This can be performed by Table 3 Averaged total (Et&, (kcalmol-‘)
306 (1994) 41-48
solvent-solvent
(ES,) and solute-solvent
adjusting the coupling parameter X from 0 to I in the following equation [20]: C(X) = 50 + X(6 - 50)
(3)
where COand
A point charge approximation was employed to introduce the solvent effect into the MO calculation. On every 30 K step in the latter 3000K steps of the MC simulation, the Hz0 molecules located inside the cutoff length from the solute molecule were replaced by point charges which were set on each atom. The amounts of point (ES,) interaction
energies obtained
System
E tot
&
ES,
Hz0
-10.69
-
-
CH(OH)CN (E) in Hz0 CH(OH)CN (Z) in Hz0 CH(OH)I (C,) in Hz0 CH(OH)s (EZ) in Hz0 CH(OHf2 (ZZ) in Hz0 CH(OH)2 (EE) in Hz0 CH(CN)2 in H20
-10.80 -10.84 -10.72 -10.75 -10.82 - 10.77 -10.75
-10.61 -10.57 -10.58 -10.61 - 10.62 - 10.63 -10.66
-52.01 -68.30 -38.96 -41.68 -53.62 -41.13 -29.15
by MC simulation
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem) 306 (1994) 41-48
45
-
E
in vacua
2
Rotation angle (degree)
Fig. 2. Calculated free energy change along the OH rotation from CH(OH)CN (E) to CH(OH)CN (Z) in vacua and in H20.
charges are the same as the atomic charges determined for the potential function parameters. MO calculations of the solute molecule which feels the electrostatic field generated by the point charges were performed, and the charge density and spin population of the solute molecule were obtained by averaging the results of 100 calculations. Results and discussion The energies of the three radicals in the gas phase are listed in Table 2. The planar E conformation is the energy minimum conformation for CH(OH)CN, while the nonplanar C, conformation is the most stable for CH(OH)z. The calculated merostabilization energy is -3.26 kcalmol-’ in the gas phase, and stabilization energy was small. This agrees with the results previously reported [lo-l 31. 8
Fig. 4. Calculated free energy change along the OH rotation from CH(OH)z (EZ) to CH(OH)2 (ZZ) and that from CH(OH)z (EZ) to CH(OH)z (EE) in vacua and in H20.
Averaged interation energies of each system calculated by MC simulation are listed in Table 3. The solute-solvent interaction energy (ES,) of the Z conformer of CH(OH)CN is more stable than ES, of the E conformer. The ZZ conformer of CH(OH)* has a larger E,, value than other conformers. Figure 2 shows AF for CH(OH)CN caused by the OH rotation. Although the E conformer has minimum energy in the gas phase, the Z conformer is -5.20 kcal mol-’ more stable than the E conformer in HzO. Figure 3 shows the variations of -AFso’” and dipole moment of CH(OH)CN along the OH rotation; dipole moment was calculated for the model molecule which has charges of potential function parameters. A strong correlation was found between -AFso’” and the dipole moment, and the large stabilization of the Z conformer
7 6
67
5 4i
$j 6 E
I0 5 a, SL 4 3 ‘E 2
3 g 2P z 1 C
0 E
30
60
90
120
Rotation angle (degree)
150
05 -1 180 Z
Fig. 3. Variations of dipole moment and solvation free energy along the OH rotation from CH(OH)CN (E) to CH(OH)CN (Z).
760
.
zz
Q (iigree)
160’ E”Z
6 (degree)
EE
Fig. 5. Variations of dipole moment and solvation free energy along the OH rotation from CH(OH)* (EZ) to CH(OH)2 (ZZ) and that from CH(OH)I (EZ) to CH(OH)2 (EE).
H. Takase and 0. KfkuchijJ. Mol. Struct. (Theochem)
46
306 (1994) 41-48
3-
z
-
CH(OH)CN
-i5 -io 0 Pair InteractionEnergy (kcal/mol)
-20
Fig. 6. The energy pair distributions radicals.
-
CHIN
4
6
I
04 /, 2
3
7
8
between Hz0 and the
Fig, 8. The radiai distribution functions between the N atom of the radicals and the 0 atom of H20.
induced by the solvent is attributed to a large dipole moment of the Z conformer. Figure 4 shows the free energy change AF from EZ to ZZ conformers and that from EZ to EE conformers of CH(OH)*. The most stable planar conformer is the ZZ conformer in H20. It can be seen from Fig. 4 that the ZZ conformer has the largest stabilization energy by solvent _ AFSo’v;this is due to a large dipole moment of the ZZ conformer (Fig. 5). The ZZ conformer is less stable than the energy minimum C2 conformation in the gas phase by 4.47 kcal mol-' , which can be compensated by a large solvent effect for the ZZ conformation(-6.09 kcal mol-‘). Therefore, we speculated that the ZZ conformer is the energy minimum conformer in HzO, and focused on the energy differences among CH(OH)CN (Z), CH(OH)2 (ZZ) and CH (CN)2 radicals. Figure 6 shows the energy pair distribution between the solute molecule and H20. Clear
differences are observed among the three radicals. In the CH(OH)CN solution, very stable pairs are observed between the solute molecule and H20. The examination of the solution structure revealed that, in these pairs, the strong interaction was caused mainly by the interaction between the OH group of CH(OH)CN and HzO. This is reflected by large atomic charges on 0 and H of the OH group in CH(OH)CN (Table l), and this OH bond polarization can be attributed to two substituents having opposite electron properties, the el~tron-donor and electron-acceptor groups. This trend can not be found in CH(OH):! and CH(CN)z which are substituted symmetrically. The radial distribution functions (RDF) between the 0 atom of the solute molecule and the 0 atom of H20 are shown in Fig. 7. The first peak appears at a shorter O-O distance for CH(OH)CN than CH(OH)2. The RDF between the N atom of the solute molecule and the 0 30
__ -------
25
CH(OH)CN
z 3 g s
CH(OH)*
-
CH(OH)CN
tf
CH
20 15
it$ 10 15 +’
. 3
5 0
4
6
7
Fig. 7. The radial distribution functions between the 0 atom of the radicals and the 0 atom of H20.
0
0.2
0.4
0.6
0.8
1
7,
Fig. 9. Calculated solvation free energy change for the mutation from CH(OH)CN to CH(OH)2 and that from CH(OH)CN to CH(CN)2.
47
H. Takase and 0. Kikuchi/.l. Mol. Struct. (Theochem,I 306 (1994) 41-48 Table 4 Atomic charge (q) and spin (p) populations
of CH(OH)CN,
CH(OH)r
and CH(CN)2 in Hz0
Molecule
Atom
q(vacu0)
q(HzO)
aq
p(vacu0)
P(HzO)
AP
CH(OH)CN
C H 0 HWH) C(CN) N C H 0 H(OH) C
0.312 0.117 -0.242 0.171 0.208 -0.566 0.183 0.089 -0.294 0.158 0.300 0.140 0.294 -0.514
0.344 0.176 -0.332 0.257 0.207 -0.652 0.186 0.124 -0.376 0.221 0.337 0.167 0.325 -0.577
0.032 0.059 -0.090 0.086 -0.001 -0.086 0.003 0.035 -0.082 0.063 0.037 0.027 0.031 -0.063
0.768 0.008 0.101 0.002 0.023 0.098 0.853 0.013 0.066 0.001 0.803 0.005 0.006 0.090
0.743 0.007 0.103 0.002 0.041 0.104 0.860 0.012 0.063 0.001 0.803 0.005 0.009 0.087
-0.025 -0.001 0.002 0.000 0.018 0.006 0.007 -0.001 -0.003 0.000 0.000 0.~ 0.003 -0.003
CH(OH)z
CH(CN)z
&N) N
atom of Hz0 are shown in Fig. 8. The first peak for CH(OH)CN is higher than CH( CN)z . These trends observed in RDF reflect the stronger interaction between CH(OH)CN and H20. Figure 9 shows the solvation free energy curve of mutation between CH~OH)CN (Z) and CH(OH)2 (ZZ) and that between CH(OH)CN (2;) and CH(CN),; X = 0 corresponds to CH(OH)CN. Two directions of mutation by the double wide sampling were averaged to obtain the curves. As is shown in Fig. 9, the solvation free energy of CH(OH)CN (Z) is largest among the three radicals. The solvation free energies of CH(OH)2 (ZZ) and CH(CN)2 were 7.78 and 19.68 kcal mol-’ relative to CH(OH)CN, respectively. These free energy differences were added to the solute energies of CH(OH)2 (ZZ) and CH(CN), in the gas phase and the merostabili~tion energy of CH(OH)CN in the Hz0 solution was calculate to be -17.52kcalmol-‘. This stabilization energy is much larger than the gas phase value and comparable to the values reported by Karelson et al. [15]
which were calculated by UHF SCRF MNDO and AM1 methods with the macroscopic dielectric constant factor g = -0.00785. The charge density and spin population of CH(OH)CN, CH(OH)2 and CH(CN)z which were calculated in the Hz0 point charge solution are listed in Table 4. It must be pointed out that the atomic point charges in the potential functions of Eq. (2) were determined to reproduce well the solute-Hz0 interaction energies, and do not necessarily agree with the atomic charges in Table 4 which were evaluated from Mulliken population of the isolated radical molecule. Two interesting features are found in the charge distribution of the ~H(OH)CN radical. The polar~tion of the O-H bond induced by the solvent is larger than that of CH(OH);!. The development of the negative charge on the N atom in the solution is larger than that of CH(CN)2. These solvent effects indicate that the resonance forms II and III of CH(OH)CN (Fig. 10) become important in the Hz0 solution, and the large merostabilization energy of the
Fig. 10. The resonance structures of CH(OH)CN.
48
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem)
CH(OH)CN radical is expected especially in the H20 solution. The importance of charge separated structures II and III in the H20 solution is also reflected by the spin population on the C(CN) atom in CH(OH)CN (Table 4).
Conclusion MC simulations and MO calculations for the CH(OH)CN, CH(OH)2 and CH(CN)z radicals have shown that merostabilization is expected in the CH(OH)CN radical, and the stabilization energy is much larger in the HZ0 solution. In the CH(OH)CN radical, the polarization of the OH group is promoted by the electron-acceptor CN group, and a large stabilization energy is obtained in the Hz0 solution by the interaction between the polarized OH group and the solvent. This effect is not expected for the symmetrically substituted radicals.
References 1 R.W. Baldock, P. Hudson, A.R. Katritzky and F. Soti, Heterocycles, 1 (1973) 67.
306 (1994) 41-48
2 R.W. Baldock, P. Hudson, A.R. Katritzky and F. Soti, J. Chem. Sot., Perkin Trans. 1, (1974) 1422. 3 A.R. Katritzky and F. Soti, J. Chem. Sot., Perkin Trans. 1, (1974) 1427. 4 M.J.S. Dewar, J. Am. Chem. Sot., 74 (1952) 3353. 5 H.G. Viehe, R. Merenyi, L. Stella and Z. Janousek, Angew. Chem., Int. Ed. Engl., 18 (1979) 917. 6 H.G. Viehe, Z. Janousek, R. Merenyi and L. Stella, Act. Chem. Res., 18 (1985) 148. 7 D.R. Arnold and R.W.R. Humphreys, J. Chem. Sot., Chem. Commun., (1978) 181. 8 R.W.R. Humphreys and D.R. Arnold, Can. J. Chem., 57 (1979) 2652. 9 W.J. Leigh and D.R. Arnold, J. Chem. Sot., Chem. Commun., (1978) 406. 10 D. Crans, T. Clark and P.v.R. Schleyer, Tetrahedron Lett., 21 (1980) 3681. 11 G. Leroy and D. Peeters, J. Mol. Struct., 85 (1981) 133. 12 G. Leroy, D. Peeters and C. Vilante, J. Mol. Struct., 88 (1982) 217. 13 G. Leroy, Int. J. Quantum Chem., 23 (1983) 271. 14 A.R. Katritzky, MC. Zerner and M.M. Karelson, J. Am. Chem. Sot., 108 (1986) 7213. 15 M. Karelson, T. Tamm, A.R. Katritzky, M. Szafran and M.C. Zerner, Int. J. Quantum Chem., 37 (1990) 1. 16 H. Takase and 0. Kikuchi, Chem. Phys., in press. 17 N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, J. Chem. Phys., 21(1953) 1087. 18 J.C. Owicki and H.A. Scheraga, Chem. Phys. Lett., 47 (1977) 600. 19 R.W. Zwanzig, J. Chem. Phys., 22 (1954) 1420. 20 W.L. Jorgensen and C. Ravimohan, J. Chem. Phys., 83 (1985) 3050.
41
Monte Carlo and molecular orbital study of carboncentered radicals in water. Solvent effects on the conformation and stability of CH(OH)CN, CH(OH):! and CH(CN)2 Hideto Takase, Osamu Kikuchi* Department
(Received
of Chemistry, 25 October
University of Tsukuba,
1993; accepted
Tsukuba 305, Japan
2 November
1993)
Abstract Monte Carlo simulations and MO calculations were carried out for three carbon-centered radicals, CH(OH)CN, CH(OH)2 and CH(CN)*, in H20, and the relative stability of these radicals was examined in connection with the substitution pattern. The solvation free energy changes along the OH rotation were calculated for CH(OH)CN and CH(OH)2 by statistical perturbation theory, and the energy minimum conformations of these radicals were determined. The solvation free energy differences among the three radicals were calculated by the mutation technique, and merostabilization energy of CH(OH)CN in water was calculated to be -1752kcalmol-’ , which is much larger than that in the gas phase. The electronic structures of these radicals in the HZ0 solution were calculated by ab initio ROHF MIDI-4* MO method including the solvent Hz0 molecules represented by point charge approximation. The calculated charge and spin populations indicated that the large stabilization energy of CH(OH)CN in HZ0 was caused by a strong interaction between the OH group of CH(OH)CN and H20, and this effect was found only in CH(OH)CN which is substituted asymmetrically by electron-donor and electron-acceptor groups.
Introduction
assisted by experimental effects have been discussed
It has been predicted theoretically that the carboncentered radical which is substituted asymmetrically by electron-donor and electron-acceptor substituents is more stabilized than the radical which is substituted symmetrically by the same substituents. Baldock and co-workers [1,2] and Katritzky and Soti [3] proposed the “merostabilization” concept on the basis of the theoretical study on the stabilization of radicals reported by Dewar [4] and synthesized new merostabilized radicals. Viehe and co-workers also suggested the similar concept which was denoted “capto-dative” radical stabilization and
substitution
* Corresponding author. SSDZ0166-1280(93)03596-Y
works [5,6]. Similar in terms of asymmetric
effects [7-91.
However, there have been few quantum mechanical calculations which give clear evidences for such stabilization. Crans et al. calculated the captodative stabilization energy for CH(NH2)BH2 and CH(NH2)CN using ab initio UHF MO method with the 4-31G basis set [IO]. The capto-dative stabilization energy is different from the merostabilization energy, and does not necessarily reflect the stabilization energy of the asymmetrical substitution of radicals. Leroy and co-workers reported the stabilization energy of various substituted carbon-centered radicals, although no evident stabilization energy was found [ 1 l- 131.
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem)
42
The radical stabilization has been calculated including the solvent effect. Katritzky et al. introduced the self-consistent reaction field (SCRF) into UHF-INDO MO method and calculated the merostabilization energy of asymmetrically substituted carbon-centered radicals in solution [14]. The calculated results strongly suggested the evident stabilization in the high dielectric constant medium, Karelson et al. applied SCRF UHF-MNDO and SCRF UHF-AM1 MO methods to the CH(OH)CN and CH(NH2)CN radicals [15]. Since SCRF is based on the continuum model, microscopic effects of the solvent effect can hardly be analyzed by these methods. In this paper, the hybrid method of Monte Carlo (MC) simulation and MO calculation has been applied to CH(OH)CN, CH(OH)z and CH(CN)z in HzO, and revealed the relative stability of these radicals. Free energy changes along the rotation of the OH bond were calculated and the conformational stability of the radicals in H20 was examined. Merostabilization energy was estimated by calculating the free energy differences among the three radicals. Solvent effects on the electronic structures of radicals were examined by ab initio ROHF MIDI-4* MO calculations including the solvent molecules represented by simple point charge
o/c\ CS
.N
Ii
H
H
MO calculation in the gas phase
All MO calculations were performed by ab initio ROHF MO method with the MIDI-4* basis set using our ABINIT program. Geometry optimization calculations were carried out for seven conformations shown in Fig. 1. The potential energy variations along the rotation of the OH bond were calculated for CH(OH)CN and CH(OH)*. In the case of CH(OH)z, simultaneous rotation of two OH bonds was not carried out, and the potential energy curves from EZ to ZZ and that from EZ to EE were calculated. Merostabilization energy, AE,, of CH(OH)CN in the gas phase was calculated by the following equation. AEM
= &H(OH)CN
- (ECHO
o/c\0 b
H
In the MC simulation, the intermolecular potential functions between solvent-solvent and solute-solvent molecules must be determined.
o0cAo A
I! (II EE)
Fig. 1. Seven conformations
-k
Intermolecular potential functions
I
I
(II C,)
Calculation
'N
(I 2)
I!
approximation, in which the configuration of solvent molecules was generated by MC simulation.
H.O/C\ C*
(1 W
306 (1994) 41-48
of CH(OH)CN,
(II EZ)
(II ZZ)
CH(OH)* and CH(CN)2.
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem)
Table 1 Determined Molecule
potential function parameters Site
306 (1994) 41-48
for H20, CH(OH)CN,
CH(OH)CN
CH(OH),
CH(CN)z
0 H C H 0 H(DH) C(CN) N C H 0 HPH) C H CKN) N
CH(OH)2 and CH(CN)?
A
((kcal~12mol-‘)1/2) H20a
43
850 _ 1700 _ 564 _ 1700 800 1700 564 _ 1700 _ 1700 800
4 W
ikcal A6 mol-‘)‘/2) 38.7 _ 30.8 _ 31.6 _ 33.6 31.3 30.8 _ 31.6 _ 30.8 _ 33.6 31.3
-0.702 0.351 0.155 0.253 -0.824 0.689 0.109 -0.382 0.053 0.174 -0.527 0.4135 0.356 0.104 0.086 -0.316
“Ref. 16.
For H20-HzO, the potential function which was determined in our previous paper [ 161 was used. This potential function was determined to reproduce well the interaction energy of the Hz0 dimers calculated by ab initio MIDI-4* calculations. The same procedure was used to determine the potential functions for the solute-H20 systems which reproduce well the ROHF MIDI-4* energies. In this procedure, the structure of each solute molecule was fixed at its energy minimum conformation except CH(OH)2. For CH(OH)2, the EZ conformer, which is the most stable among the planar conformers was used. The Hz0 molecule was located randomly around the solute molecule. The number of calculated dimer configurations were 142, 148 and 142 for the CH(OH)CN-H20, CH(OH)2-H20 and CH(CN)2-H20 dimers, respectively. The calculated interaction energies for the dimers were used to determine the soluteHz0 intermolecular potential functions which are constructed by Lennard-Jones (LJ) (12-6) terms and coulomb terms;
The A and C are LJ parameters and q is atomic charge. In the fitting of the parameters, LJ parameters were restricted to having similar values for the same group in the three radicals. For example, the same LJ parameters were used for the N atoms in CH(OH)CN and CH(CN);?. Atomic charges for two OH groups in CH(OH)2 were restricted to have same values to keep the symmetry of electronic structure in the ZZ and EE conformations. Determined parameters are listed in Table 1. MC simulation MC simulation was carried out according to the standard Metropolis method [17] with NVT ensemble. Each system consists of one solute molecule and 213 Hz0 molecules in a cubic cell. The volume of the cell was determined from the density of pure Hz0 (1.0gcmP3) and the temperature of the system was set at 298 K. Spherical cutoff at a half distance of the cell length was used for intermolecular interaction. Owicki-Scheraga preference sampling method [18] was employed. In this method, the probability of moving the solvent is proportional to 1/(r2 + c), where r is the distance
44
H. Takase and 0. KikuchiJJ. Mol. Struct. (Theochem)
Table 2 Calculated ROHF MIDI-4* energies of CH(OH)CN,
CH(OH)s
and CH(CN)t
in vacua
Molecule
Conformation
Total energy (au.)
AE (kcalmol-‘)a
CH(OH)CN
E Z
-205.890388 -205.887673 -189.051263 - 189.048078 -189.044136 -189.040975 -222.719118
0.0 1.70 0.0 2.00 4.47 4.46 0.0
CH(OH)z
c2
.EZ zz EE CHtCN)z aEnergy relative to the mi~mum
energy of each molecule.
between centers of solute and solvent molecules and the constant c was set at 150 A2 in the present study. The amounts of transformation and rotation of solvent molecules were adjusted to yield the acceptance ratio of 3040% for the sampled configuration. Full simulation was carried out through 5000K steps. Equilibrium of the system was established in the preceding 2000K steps and the averaging was carried out in the following 3000 K steps for each system. Free energy change along the rotation of the OH bond was calculated by the statistical perturbation theory (SPT) [19] with the double wide sampling technique; the rotation step was set at 15”. The total free energy change, AFy was obtained by adding the solvation free energy change, AFsoiV, which was calculated by the MC simulation, to the energy change of the solute in the gas phase, AE’, calculated by the MO method. Free energy differences between two radicals were calculated by the mutation method. This can be performed by Table 3 Averaged total (Et&, (kcalmol-‘)
306 (1994) 41-48
solvent-solvent
(ES,) and solute-solvent
adjusting the coupling parameter X from 0 to I in the following equation [20]: C(X) = 50 + X(6 - 50)
(3)
where COand
A point charge approximation was employed to introduce the solvent effect into the MO calculation. On every 30 K step in the latter 3000K steps of the MC simulation, the Hz0 molecules located inside the cutoff length from the solute molecule were replaced by point charges which were set on each atom. The amounts of point (ES,) interaction
energies obtained
System
E tot
&
ES,
Hz0
-10.69
-
-
CH(OH)CN (E) in Hz0 CH(OH)CN (Z) in Hz0 CH(OH)I (C,) in Hz0 CH(OH)s (EZ) in Hz0 CH(OHf2 (ZZ) in Hz0 CH(OH)2 (EE) in Hz0 CH(CN)2 in H20
-10.80 -10.84 -10.72 -10.75 -10.82 - 10.77 -10.75
-10.61 -10.57 -10.58 -10.61 - 10.62 - 10.63 -10.66
-52.01 -68.30 -38.96 -41.68 -53.62 -41.13 -29.15
by MC simulation
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem) 306 (1994) 41-48
45
-
E
in vacua
2
Rotation angle (degree)
Fig. 2. Calculated free energy change along the OH rotation from CH(OH)CN (E) to CH(OH)CN (Z) in vacua and in H20.
charges are the same as the atomic charges determined for the potential function parameters. MO calculations of the solute molecule which feels the electrostatic field generated by the point charges were performed, and the charge density and spin population of the solute molecule were obtained by averaging the results of 100 calculations. Results and discussion The energies of the three radicals in the gas phase are listed in Table 2. The planar E conformation is the energy minimum conformation for CH(OH)CN, while the nonplanar C, conformation is the most stable for CH(OH)z. The calculated merostabilization energy is -3.26 kcalmol-’ in the gas phase, and stabilization energy was small. This agrees with the results previously reported [lo-l 31. 8
Fig. 4. Calculated free energy change along the OH rotation from CH(OH)z (EZ) to CH(OH)2 (ZZ) and that from CH(OH)z (EZ) to CH(OH)z (EE) in vacua and in H20.
Averaged interation energies of each system calculated by MC simulation are listed in Table 3. The solute-solvent interaction energy (ES,) of the Z conformer of CH(OH)CN is more stable than ES, of the E conformer. The ZZ conformer of CH(OH)* has a larger E,, value than other conformers. Figure 2 shows AF for CH(OH)CN caused by the OH rotation. Although the E conformer has minimum energy in the gas phase, the Z conformer is -5.20 kcal mol-’ more stable than the E conformer in HzO. Figure 3 shows the variations of -AFso’” and dipole moment of CH(OH)CN along the OH rotation; dipole moment was calculated for the model molecule which has charges of potential function parameters. A strong correlation was found between -AFso’” and the dipole moment, and the large stabilization of the Z conformer
7 6
67
5 4i
$j 6 E
I0 5 a, SL 4 3 ‘E 2
3 g 2P z 1 C
0 E
30
60
90
120
Rotation angle (degree)
150
05 -1 180 Z
Fig. 3. Variations of dipole moment and solvation free energy along the OH rotation from CH(OH)CN (E) to CH(OH)CN (Z).
760
.
zz
Q (iigree)
160’ E”Z
6 (degree)
EE
Fig. 5. Variations of dipole moment and solvation free energy along the OH rotation from CH(OH)* (EZ) to CH(OH)2 (ZZ) and that from CH(OH)I (EZ) to CH(OH)2 (EE).
H. Takase and 0. KfkuchijJ. Mol. Struct. (Theochem)
46
306 (1994) 41-48
3-
z
-
CH(OH)CN
-i5 -io 0 Pair InteractionEnergy (kcal/mol)
-20
Fig. 6. The energy pair distributions radicals.
-
CHIN
4
6
I
04 /, 2
3
7
8
between Hz0 and the
Fig, 8. The radiai distribution functions between the N atom of the radicals and the 0 atom of H20.
induced by the solvent is attributed to a large dipole moment of the Z conformer. Figure 4 shows the free energy change AF from EZ to ZZ conformers and that from EZ to EE conformers of CH(OH)*. The most stable planar conformer is the ZZ conformer in H20. It can be seen from Fig. 4 that the ZZ conformer has the largest stabilization energy by solvent _ AFSo’v;this is due to a large dipole moment of the ZZ conformer (Fig. 5). The ZZ conformer is less stable than the energy minimum C2 conformation in the gas phase by 4.47 kcal mol-' , which can be compensated by a large solvent effect for the ZZ conformation(-6.09 kcal mol-‘). Therefore, we speculated that the ZZ conformer is the energy minimum conformer in HzO, and focused on the energy differences among CH(OH)CN (Z), CH(OH)2 (ZZ) and CH (CN)2 radicals. Figure 6 shows the energy pair distribution between the solute molecule and H20. Clear
differences are observed among the three radicals. In the CH(OH)CN solution, very stable pairs are observed between the solute molecule and H20. The examination of the solution structure revealed that, in these pairs, the strong interaction was caused mainly by the interaction between the OH group of CH(OH)CN and HzO. This is reflected by large atomic charges on 0 and H of the OH group in CH(OH)CN (Table l), and this OH bond polarization can be attributed to two substituents having opposite electron properties, the el~tron-donor and electron-acceptor groups. This trend can not be found in CH(OH):! and CH(CN)z which are substituted symmetrically. The radial distribution functions (RDF) between the 0 atom of the solute molecule and the 0 atom of H20 are shown in Fig. 7. The first peak appears at a shorter O-O distance for CH(OH)CN than CH(OH)2. The RDF between the N atom of the solute molecule and the 0 30
__ -------
25
CH(OH)CN
z 3 g s
CH(OH)*
-
CH(OH)CN
tf
CH
20 15
it$ 10 15 +’
. 3
5 0
4
6
7
Fig. 7. The radial distribution functions between the 0 atom of the radicals and the 0 atom of H20.
0
0.2
0.4
0.6
0.8
1
7,
Fig. 9. Calculated solvation free energy change for the mutation from CH(OH)CN to CH(OH)2 and that from CH(OH)CN to CH(CN)2.
47
H. Takase and 0. Kikuchi/.l. Mol. Struct. (Theochem,I 306 (1994) 41-48 Table 4 Atomic charge (q) and spin (p) populations
of CH(OH)CN,
CH(OH)r
and CH(CN)2 in Hz0
Molecule
Atom
q(vacu0)
q(HzO)
aq
p(vacu0)
P(HzO)
AP
CH(OH)CN
C H 0 HWH) C(CN) N C H 0 H(OH) C
0.312 0.117 -0.242 0.171 0.208 -0.566 0.183 0.089 -0.294 0.158 0.300 0.140 0.294 -0.514
0.344 0.176 -0.332 0.257 0.207 -0.652 0.186 0.124 -0.376 0.221 0.337 0.167 0.325 -0.577
0.032 0.059 -0.090 0.086 -0.001 -0.086 0.003 0.035 -0.082 0.063 0.037 0.027 0.031 -0.063
0.768 0.008 0.101 0.002 0.023 0.098 0.853 0.013 0.066 0.001 0.803 0.005 0.006 0.090
0.743 0.007 0.103 0.002 0.041 0.104 0.860 0.012 0.063 0.001 0.803 0.005 0.009 0.087
-0.025 -0.001 0.002 0.000 0.018 0.006 0.007 -0.001 -0.003 0.000 0.000 0.~ 0.003 -0.003
CH(OH)z
CH(CN)z
&N) N
atom of Hz0 are shown in Fig. 8. The first peak for CH(OH)CN is higher than CH( CN)z . These trends observed in RDF reflect the stronger interaction between CH(OH)CN and H20. Figure 9 shows the solvation free energy curve of mutation between CH~OH)CN (Z) and CH(OH)2 (ZZ) and that between CH(OH)CN (2;) and CH(CN),; X = 0 corresponds to CH(OH)CN. Two directions of mutation by the double wide sampling were averaged to obtain the curves. As is shown in Fig. 9, the solvation free energy of CH(OH)CN (Z) is largest among the three radicals. The solvation free energies of CH(OH)2 (ZZ) and CH(CN)2 were 7.78 and 19.68 kcal mol-’ relative to CH(OH)CN, respectively. These free energy differences were added to the solute energies of CH(OH)2 (ZZ) and CH(CN), in the gas phase and the merostabili~tion energy of CH(OH)CN in the Hz0 solution was calculate to be -17.52kcalmol-‘. This stabilization energy is much larger than the gas phase value and comparable to the values reported by Karelson et al. [15]
which were calculated by UHF SCRF MNDO and AM1 methods with the macroscopic dielectric constant factor g = -0.00785. The charge density and spin population of CH(OH)CN, CH(OH)2 and CH(CN)z which were calculated in the Hz0 point charge solution are listed in Table 4. It must be pointed out that the atomic point charges in the potential functions of Eq. (2) were determined to reproduce well the solute-Hz0 interaction energies, and do not necessarily agree with the atomic charges in Table 4 which were evaluated from Mulliken population of the isolated radical molecule. Two interesting features are found in the charge distribution of the ~H(OH)CN radical. The polar~tion of the O-H bond induced by the solvent is larger than that of CH(OH);!. The development of the negative charge on the N atom in the solution is larger than that of CH(CN)2. These solvent effects indicate that the resonance forms II and III of CH(OH)CN (Fig. 10) become important in the Hz0 solution, and the large merostabilization energy of the
Fig. 10. The resonance structures of CH(OH)CN.
48
H. Takase and 0. Kikuchi/J. Mol. Struct. (Theochem)
CH(OH)CN radical is expected especially in the H20 solution. The importance of charge separated structures II and III in the H20 solution is also reflected by the spin population on the C(CN) atom in CH(OH)CN (Table 4).
Conclusion MC simulations and MO calculations for the CH(OH)CN, CH(OH)2 and CH(CN)z radicals have shown that merostabilization is expected in the CH(OH)CN radical, and the stabilization energy is much larger in the HZ0 solution. In the CH(OH)CN radical, the polarization of the OH group is promoted by the electron-acceptor CN group, and a large stabilization energy is obtained in the Hz0 solution by the interaction between the polarized OH group and the solvent. This effect is not expected for the symmetrically substituted radicals.
References 1 R.W. Baldock, P. Hudson, A.R. Katritzky and F. Soti, Heterocycles, 1 (1973) 67.
306 (1994) 41-48
2 R.W. Baldock, P. Hudson, A.R. Katritzky and F. Soti, J. Chem. Sot., Perkin Trans. 1, (1974) 1422. 3 A.R. Katritzky and F. Soti, J. Chem. Sot., Perkin Trans. 1, (1974) 1427. 4 M.J.S. Dewar, J. Am. Chem. Sot., 74 (1952) 3353. 5 H.G. Viehe, R. Merenyi, L. Stella and Z. Janousek, Angew. Chem., Int. Ed. Engl., 18 (1979) 917. 6 H.G. Viehe, Z. Janousek, R. Merenyi and L. Stella, Act. Chem. Res., 18 (1985) 148. 7 D.R. Arnold and R.W.R. Humphreys, J. Chem. Sot., Chem. Commun., (1978) 181. 8 R.W.R. Humphreys and D.R. Arnold, Can. J. Chem., 57 (1979) 2652. 9 W.J. Leigh and D.R. Arnold, J. Chem. Sot., Chem. Commun., (1978) 406. 10 D. Crans, T. Clark and P.v.R. Schleyer, Tetrahedron Lett., 21 (1980) 3681. 11 G. Leroy and D. Peeters, J. Mol. Struct., 85 (1981) 133. 12 G. Leroy, D. Peeters and C. Vilante, J. Mol. Struct., 88 (1982) 217. 13 G. Leroy, Int. J. Quantum Chem., 23 (1983) 271. 14 A.R. Katritzky, MC. Zerner and M.M. Karelson, J. Am. Chem. Sot., 108 (1986) 7213. 15 M. Karelson, T. Tamm, A.R. Katritzky, M. Szafran and M.C. Zerner, Int. J. Quantum Chem., 37 (1990) 1. 16 H. Takase and 0. Kikuchi, Chem. Phys., in press. 17 N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, J. Chem. Phys., 21(1953) 1087. 18 J.C. Owicki and H.A. Scheraga, Chem. Phys. Lett., 47 (1977) 600. 19 R.W. Zwanzig, J. Chem. Phys., 22 (1954) 1420. 20 W.L. Jorgensen and C. Ravimohan, J. Chem. Phys., 83 (1985) 3050.