The influence of a self consistent reaction field on the charge distribution of molecular systems is studied. Electrostatic isopotential maps are used to discuss the qualitative and quantitative aspects of such an influence

Eduardo A. Castro

Hugo O. Villar

English

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CROATICA CHEMICA ACTA CCACAA 58 (2) 153-160 (1985)CCA-1567YU ISSN 0011-1643UDC 541Original Scientific PaperA Self Consistent Reaction Field Study on ElectrostaticIsopotential MapsHugo O. ViIlar and Eduardo A. CastroINIFT A, Division Quimica Teorica, Sucursai 4, CasiHa de Correo 16, 1900 La Plata,ArgentinaReceived March 18, 1984The influence of a self consistent reaction field on the chargedistribution of molecular systems is studied. Electrostatic isopo-.tential maps are used to discuss the qualitative and quantitativeaspects of such an influence.INTRODUCTIONSeveral studies have been carried out in recent years using molecularelectrostatic isopotential maps (EPM)l. The EPM produced by electrons andnuclei in the surrounding space is an effective tool in predicting the reactivebehaviour towards electrophyles and protonation of simple systems. Further-more, there has recently been proposed a procedure for using the EPM topredict and interpret nucleophy1ic processes",It is well known that reaction field (RF) calculations are useful in pro-viding information relative to changes in molecular properties and most ofthe usual parameters in the absence of direct interactions (hydrogen bonding,for instance). Since a self consistent reaction field (SCRF) is expected tomodify the charge distribution of molecular systems, changes in the EPMshould be anticipated.The purpose of this paper is to study the qualitative aspects of this hypo-thesis. In order to develope this theme, we first study the inf1uence of a RF inthe EPM for a variety of molecules. We then examine some carbony1ic com-pounds, especially cyclopropylketones, which, under a certain viewpoint, maybe regarded as intermediate between aliphatic and arornatic". Finally, weanalyse the hydrogen bonding inf1uence on these carbony1ic compounds andthe SCRF technique.CALCULATION PROCEDUREThe EPM were determined using the charges provided by the SCRF-CNDO/2technique as described by Tapia and Constanciel-. In this approach, the SCF pro-cedure, including solvation effects, is based upon the following effective Fock ope-rator containing the solvent interaction:[h (r) - V (r) + ~ (2Jj - Kj)] e, (r) = Gi ([Ji (r) (1)jwhere h (r) + ~ (2Jj - Kj) denotes the usual Fock operator and V (r) the solvent fieldj .one-electron operator. Expression (1) gives a new set of SCF equations from which154 H. O. VILLAR AND E. A. CASTROthe molecular orbitals and energies may be obtained. Within the CNDO schemeused here, the only terms modified in the Fock matrix are the diagonal ones. Themodification is given by the following expression:- V" = f (D) ~ (ZB - po) rAHBwhere ZB and pu denote the nuclear and electronic charges respectively, rAB thetwo electron integrals and f (D) = - (1 - l/D) with D the square root of the dielec-tric constant. The EPM were generated by means of a Ouantum Chemistry Exchangeprogram". In all cases, the geometries were optimized at the vacuum level, employingthe previously reported geometries, except for small rings, where the MNDOtechnique" with the Davidon-Fletcher-Powell minimization procedure? was preferred.It is well known that these geometries are not properly described by the CNDO/2methodš, whereas the MNDO method predicts them accurately.RESULTS AND DISCUSSIONWe have studied several molecules, with different functional groups(alcoholic, halogen derivates, cyano groups, aldehydic, ketonic, ethers, hetero-aromatic compounds, etc.) There were no important changes observed in thequalitative aspects of the EPM, in most of the systems. Only significantchang es were noticed in the carbonylic compounds, where direct interactions--------O. ->________ o.~C~c~ HI(; 1Figure 1. EPM for p-fluorobenzonitrile. Left hand side: vacuum level, rtght handside: dielectric constant equal to 81. The positive part of the isoenergetic curves areindicated, and the energy values of the system on the curve are given in Kcal/mole.The fractions denote decimal fractions minimum energy for the zone s of chargeexcess. The asterisk shows the position Qf the minimum.SCRF STUDY ON EPM 15j(such as hydrogen bonding) also have a marked influence. Bifunctional systems,such as p-fluorobenzonitrile for instance, with two withdrawing groups, maybe strongly affected, as well as the localization of the minimum energyposition, which may be significatively changed. As it may be seen, a systemlike this may be protonated on either of the withdrawing groups, dependingon the dielectric constant of the medium (Figure 1).The EPM of a series of cyclopropyl ketones were obtained. The energydifference between the cis and the trans conformers is almost maintained, asthe dielectric constant is increased, the stabilization being slightly greaterfor the cis geometry. (the cis conformation is found experimentally to be themost stable"). Although the correlation amongst the EPM parameters {energyminimum, distance between the oxygen and the minimum energy position,etc.) between the members of the family remains unchanged, the value ofthe minimum is at least duplicated, and the distance between the O and theminimum is reduced by about 25%. The qualitative differences are evident,and they are shown in Figure 2. It may be seen that the EPM for a dielectricconstant 10 is closer to that of dielectric constant 81 than to that of dielectricconstant 1. This behaviour has been previously noted, and it can be attributedto the marked dependence of the Fock matrix elements on the dielectricconstant.It was formerly remarked other dependence between the dielectric con-stant and the Fock matrix elements may be useđ'", although its meaning isnot so clear as the one proposed by Constanciel and 'I'apia-.In the figures, we do not reproduce the values at the minimum since thesemiempirical techniques (such as CNDO) do not provide accurate quantita-tive values; they may simplly be considered as methods elaborated in orderto get proper qualitative correlations.1/5Figure 2a.156 H. O. VILLAR AND E. A. CASTROFigure 2b.D.Figure 2c. EPM for cyclopropane carbonyl a) vacuum level, b) dielectric constant 10,and c) dielectric constant 81.SCRF STUDY ON EPM 157\O.Figure 3a./o.25Figure 3b. EPM for isolated H2CO, a) vacuum level, b) dielectric constant 81.r158 H. O. VILLAR AND E. A. CASTROo.Figure 4a.25.Figure 4b. EPM for H2CO perturbed by a H20 molecule, a) vacuum level, b) di-electric constant 81.SCRF STUDY ON EPM 159DIRECT INTERACTIONS AND REACTION FIELD CALCULATIONS. RESULTS ANDDISSCUSSIONIn this section we shall deal strictly with the water formaldehide inter-action, and its relation with RF calculations and EPM of the latter. When awater molecule approaches formaidehyde, the CNDO/2 method reproducesa minimum, as expected experimentally because of the hydrogen bonding.This minimum is deeper the greater the dielectric constant, and it also dependson the hydrocarboned moiety, so that the stability of the hydrogen bond witha proton donor is a function of both of these properties. In Figure 3 weshow the isolated formaidehyde molecule and consider its interaction withareaction field generated by a medium with a dielectric constant 1 (part a)and 81 (part b).In Figure 4 a similar study is carried out, but for a water molecule withits mass center placed at 3.75 A from the mass center of formaidehyde, andin such away that both molecular planes are orthogonal. The strongest changesamongst the four pictures occur for those which consider areaction field andthose which do not. From the EPM the direct interactions seem to be of secondorder with respect to the RF studies. Obviously the consideration of asinglewater molecule will certainly not simulate the main contribution to the pola-rization of the system. The molecule which interacts directly, generating ahydrogen bond, will surely be the most important for a shell surroundingthe molecule under study, but only the consideration of at least a pair ofsolvation shells would provide an approximately accurate description of whatreally happens. On the other hand the consideration of this interacting mole-cule may affect the EPM as may be seen through the border lines betweenthe positive and negative zones of the molecules.Both the direct interactions and the RF should be considered in the studyof a system where direct interactions may exist.REFERENCES1. a) P. P o 1i t z e r and D. G. T r u h 1a r Ed., ChemicaL AppLications of Atomicand MoLecuLar ELectrostatic PotentiaLs. PLenum, New York, 1981.b) R. B o n a c cor s i, E. Ser oce o and J. Tom a s i, J. Chem. Phys. 52 (1970)5270.c) R. B onae cor s i, E. Ser oce o, C. Pet r o l o n g o, and J. Tom a s i,Theoret. Chim. Acta 20 (1971) 331.2. P. P o 1i t z e r, S. J. La u dr y and T. W ii r n h e 1m, J. Phys. Chem. 86(1982) 4767.3. F. H. All e n, Acta CrystaHogr. B37 (1981) 890.4. R. C o n s t ane i e 1 and O. Ta p i a, Theoret. Chim. Acta 48 (1978) 75.5. C. G e i s s ner - Pre t t e, QCPE Program 249 (1974).6. a) M. J. S. De war and W. T h i e 1, J. Am. Chem. Soc. 99 (1977) 4899.b) W. T h ie 1, QCPE Program 353 (1978).7. a) J. M. O r g t e g a and W. C. Rh e i n b old t, Iterative SoLution of NonLinearEquations with SeveraL VariabLes, Academic Press, New York - London 1975.b) R. F 1e t c h e r and M. J. D. P owell, Comp. J. 6 (1963) 163.c) W. C. D avi d o n, Comp. J. 10 (1968) 406.8. L. Car 1s e n, J. Comput. Chem. 3 (1982) 23.9. C. F o u r n i e r, B. Le mar i e, B. Bra i Ilon, D. P a q u e r, and M. V a-z a i x, BuH. Soc. Chim. France 9-10 (1980) 463.10. A. J. Du b e n and S. Mi e rtu s, Theoret. Chim. Acta 60 (1981) 327.160 H. O. VILLAR AND E. A. CASTROSAŽETAKStudij elektrostatičkih izopoiencijalnih mapa s pomoću samousklađenogareakcijskog poljaH. O. Vi!lar i E. A. CastroProučavan je utjecaj samousklađenog polja na raspodjelu naboja u molekul-skim sustavima. Upotrijebljene su elektrostatičke izopotencijalne mape za diskusijuo kvalitativnim i kvantitativnim aspektima tih utjecaja.

A Self Consistent Reaction Field Study on Electrostatic Isopotential Maps

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CROATICA CHEMICA ACTA CCACAA 58 (2) 153-160 (1985)CCA-1567YU ISSN 0011-1643UDC 541Original Scientific PaperA Self Consistent Reaction Field Study on ElectrostaticIsopotential MapsHugo O. ViIlar and Eduardo A. CastroINIFT A, Division Quimica Teorica, Sucursai 4, CasiHa de Correo 16, 1900 La Plata,ArgentinaReceived March 18, 1984The influence of a self consistent reaction field on the chargedistribution of molecular systems is studied. Electrostatic isopo-.tential maps are used to discuss the qualitative and quantitativeaspects of such an influence.INTRODUCTIONSeveral studies have been carried out in recent years using molecularelectrostatic isopotential maps (EPM)l. The EPM produced by electrons andnuclei in the surrounding space is an effective tool in predicting the reactivebehaviour towards electrophyles and protonation of simple systems. Further-more, there has recently been proposed a procedure for using the EPM topredict and interpret nucleophy1ic processes",It is well known that reaction field (RF) calculations are useful in pro-viding information relative to changes in molecular properties and most ofthe usual parameters in the absence of direct interactions (hydrogen bonding,for instance). Since a self consistent reaction field (SCRF) is expected tomodify the charge distribution of molecular systems, changes in the EPMshould be anticipated.The purpose of this paper is to study the qualitative aspects of this hypo-thesis. In order to develope this theme, we first study the inf1uence of a RF inthe EPM for a variety of molecules. We then examine some carbony1ic com-pounds, especially cyclopropylketones, which, under a certain viewpoint, maybe regarded as intermediate between aliphatic and arornatic". Finally, weanalyse the hydrogen bonding inf1uence on these carbony1ic compounds andthe SCRF technique.CALCULATION PROCEDUREThe EPM were determined using the charges provided by the SCRF-CNDO/2technique as described by Tapia and Constanciel-. In this approach, the SCF pro-cedure, including solvation effects, is based upon the following effective Fock ope-rator containing the solvent interaction:[h (r) - V (r) + ~ (2Jj - Kj)] e, (r) = Gi ([Ji (r) (1)jwhere h (r) + ~ (2Jj - Kj) denotes the usual Fock operator and V (r) the solvent fieldj .one-electron operator. Expression (1) gives a new set of SCF equations from which154 H. O. VILLAR AND E. A. CASTROthe molecular orbitals and energies may be obtained. Within the CNDO schemeused here, the only terms modified in the Fock matrix are the diagonal ones. Themodification is given by the following expression:- V" = f (D) ~ (ZB - po) rAHBwhere ZB and pu denote the nuclear and electronic charges respectively, rAB thetwo electron integrals and f (D) = - (1 - l/D) with D the square root of the dielec-tric constant. The EPM were generated by means of a Ouantum Chemistry Exchangeprogram". In all cases, the geometries were optimized at the vacuum level, employingthe previously reported geometries, except for small rings, where the MNDOtechnique" with the Davidon-Fletcher-Powell minimization procedure? was preferred.It is well known that these geometries are not properly described by the CNDO/2methodš, whereas the MNDO method predicts them accurately.RESULTS AND DISCUSSIONWe have studied several molecules, with different functional groups(alcoholic, halogen derivates, cyano groups, aldehydic, ketonic, ethers, hetero-aromatic compounds, etc.) There were no important changes observed in thequalitative aspects of the EPM, in most of the systems. Only significantchang es were noticed in the carbonylic compounds, where direct interactions--------O. ->________ o.~C~c~ HI(; 1Figure 1. EPM for p-fluorobenzonitrile. Left hand side: vacuum level, rtght handside: dielectric constant equal to 81. The positive part of the isoenergetic curves areindicated, and the energy values of the system on the curve are given in Kcal/mole.The fractions denote decimal fractions minimum energy for the zone s of chargeexcess. The asterisk shows the position Qf the minimum.SCRF STUDY ON EPM 15j(such as hydrogen bonding) also have a marked influence. Bifunctional systems,such as p-fluorobenzonitrile for instance, with two withdrawing groups, maybe strongly affected, as well as the localization of the minimum energyposition, which may be significatively changed. As it may be seen, a systemlike this may be protonated on either of the withdrawing groups, dependingon the dielectric constant of the medium (Figure 1).The EPM of a series of cyclopropyl ketones were obtained. The energydifference between the cis and the trans conformers is almost maintained, asthe dielectric constant is increased, the stabilization being slightly greaterfor the cis geometry. (the cis conformation is found experimentally to be themost stable"). Although the correlation amongst the EPM parameters {energyminimum, distance between the oxygen and the minimum energy position,etc.) between the members of the family remains unchanged, the value ofthe minimum is at least duplicated, and the distance between the O and theminimum is reduced by about 25%. The qualitative differences are evident,and they are shown in Figure 2. It may be seen that the EPM for a dielectricconstant 10 is closer to that of dielectric constant 81 than to that of dielectricconstant 1. This behaviour has been previously noted, and it can be attributedto the marked dependence of the Fock matrix elements on the dielectricconstant.It was formerly remarked other dependence between the dielectric con-stant and the Fock matrix elements may be useđ'", although its meaning isnot so clear as the one proposed by Constanciel and 'I'apia-.In the figures, we do not reproduce the values at the minimum since thesemiempirical techniques (such as CNDO) do not provide accurate quantita-tive values; they may simplly be considered as methods elaborated in orderto get proper qualitative correlations.1/5Figure 2a.156 H. O. VILLAR AND E. A. CASTROFigure 2b.D.Figure 2c. EPM for cyclopropane carbonyl a) vacuum level, b) dielectric constant 10,and c) dielectric constant 81.SCRF STUDY ON EPM 157\O.Figure 3a./o.25Figure 3b. EPM for isolated H2CO, a) vacuum level, b) dielectric constant 81.r158 H. O. VILLAR AND E. A. CASTROo.Figure 4a.25.Figure 4b. EPM for H2CO perturbed by a H20 molecule, a) vacuum level, b) di-electric constant 81.SCRF STUDY ON EPM 159DIRECT INTERACTIONS AND REACTION FIELD CALCULATIONS. RESULTS ANDDISSCUSSIONIn this section we shall deal strictly with the water formaldehide inter-action, and its relation with RF calculations and EPM of the latter. When awater molecule approaches formaidehyde, the CNDO/2 method reproducesa minimum, as expected experimentally because of the hydrogen bonding.This minimum is deeper the greater the dielectric constant, and it also dependson the hydrocarboned moiety, so that the stability of the hydrogen bond witha proton donor is a function of both of these properties. In Figure 3 weshow the isolated formaidehyde molecule and consider its interaction withareaction field generated by a medium with a dielectric constant 1 (part a)and 81 (part b).In Figure 4 a similar study is carried out, but for a water molecule withits mass center placed at 3.75 A from the mass center of formaidehyde, andin such away that both molecular planes are orthogonal. The strongest changesamongst the four pictures occur for those which consider areaction field andthose which do not. From the EPM the direct interactions seem to be of secondorder with respect to the RF studies. Obviously the consideration of asinglewater molecule will certainly not simulate the main contribution to the pola-rization of the system. The molecule which interacts directly, generating ahydrogen bond, will surely be the most important for a shell surroundingthe molecule under study, but only the consideration of at least a pair ofsolvation shells would provide an approximately accurate description of whatreally happens. On the other hand the consideration of this interacting mole-cule may affect the EPM as may be seen through the border lines betweenthe positive and negative zones of the molecules.Both the direct interactions and the RF should be considered in the studyof a system where direct interactions may exist.REFERENCES1. a) P. P o 1i t z e r and D. G. T r u h 1a r Ed., ChemicaL AppLications of Atomicand MoLecuLar ELectrostatic PotentiaLs. PLenum, New York, 1981.b) R. B o n a c cor s i, E. Ser oce o and J. Tom a s i, J. Chem. Phys. 52 (1970)5270.c) R. B onae cor s i, E. Ser oce o, C. Pet r o l o n g o, and J. Tom a s i,Theoret. Chim. Acta 20 (1971) 331.2. P. P o 1i t z e r, S. J. La u dr y and T. W ii r n h e 1m, J. Phys. Chem. 86(1982) 4767.3. F. H. All e n, Acta CrystaHogr. B37 (1981) 890.4. R. C o n s t ane i e 1 and O. Ta p i a, Theoret. Chim. Acta 48 (1978) 75.5. C. G e i s s ner - Pre t t e, QCPE Program 249 (1974).6. a) M. J. S. De war and W. T h i e 1, J. Am. Chem. Soc. 99 (1977) 4899.b) W. T h ie 1, QCPE Program 353 (1978).7. a) J. M. O r g t e g a and W. C. Rh e i n b old t, Iterative SoLution of NonLinearEquations with SeveraL VariabLes, Academic Press, New York - London 1975.b) R. F 1e t c h e r and M. J. D. P owell, Comp. J. 6 (1963) 163.c) W. C. D avi d o n, Comp. J. 10 (1968) 406.8. L. Car 1s e n, J. Comput. Chem. 3 (1982) 23.9. C. F o u r n i e r, B. Le mar i e, B. Bra i Ilon, D. P a q u e r, and M. V a-z a i x, BuH. Soc. Chim. France 9-10 (1980) 463.10. A. J. D u b e n and S. Mi e rtu s, Theoret. Chim. Acta 60 (1981) 327.160 H. O. VILLAR AND E. A. CASTROSAŽETAKStudij elektrostatičkih izopoiencijalnih mapa s pomoću samousklađenogareakcijskog poljaH. O. Vi!lar i E. A. CastroProučavan je utjecaj samousklađenog polja na raspodjelu naboja u molekul-skim sustavima. Upotrijebljene su elektrostatičke izopotencijalne mape za diskusijuo kvalitativnim i kvantitativnim aspektima tih utjecaja.

A Self Consistent Reaction Field Study on Electrostatic Isopotential Maps

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