41 G. Klopman and P.Andreozzi dilute aqueous solutions.2 Although the relationship between the model system [formamide+(H20)5molecules (1) representing an aqueous formamide solution and (formamide)5 molecules (2) representing pure liquid formamide J and the liquid I I II '733 state was crude some valuable structural information was obtained. A comparison of the interaction energies of the linear formamide tetramer with that of the mixed linear-cyclic tetramers indicated that linear chains are more stable than mixed linear-cyclic systems for the pure liquid. Calculations also showed that the inter- action energy of H20(5)with the CH proton is very small so that a totally hydrated formamide molecule might be sufficiently accurately represented by considering only four HzO molecules in the first hydration shell.In some cases attempts are being made to include many molecules of solvent in the calculation of solute-solvent supersystems. For this purpose Monte Carlo techniques have proven to be particularly useful. As they are usually applied to calculations on liquids Monte Carlo methods are used to generate a series of configurations and orientations of the solute-solvent aggregate which are then weighted appropriately to calculate average thermodynamic properties of the J. F. Hinton and R.D. Harpool J. Amer. Chem. Soc. 1977.99 349. Theoreticai Chemistry system. As Clementi3 points out these statistical properties are important factors to be considered for a realistic description of an ensemble of interacting molecules.. In one Monte Carlo study Owicki and Scheraga investigated the structure and properties of liquid water4 and dilute aqueous methane’ in the isothermal-isobaric ensemble at 298 K and atmospheric pressure. The method provided reasonable estimates of the internal energy heat capacity and mean molar volume for each system. Energy probability distribution functions were used to help describe the hydrogen-bonding interactions in the liquids. It was found that the hydrogen- bonding environment in water is better described as a continuum of bent or stretched bonds rather than relatively discrete sets of bonded and non-bonded interactions. Interactions between water molecules in the solvation shell of methane are more stable and more sharply distributed than those in the bulk liquid.The size of this effect diminishes with increasing distance from methane supporting the view that non-polar solutes increase the degree of hydrogen-bond-ing or ‘structure’ in their hydration shell. Clementi6 also used a Monte Carlo technique to study the structure of a number of alkali-metal halides surrounded by a cluster of 200 water molecules. Co-ordination numbers and hydration-shell radii for the cations and anions were computed and information about the cluster size and shape was also determined. Another quantum mechanical model which has been used quite extensively to study solute-solvent interactions is based on the development of pair or higher- order potentials. The basic idea is to perform thorough ab irzitio calculations for small systems in which only one or two solvent molecules are explicitly included.An analytical many-body potential is then fitted to the data. Assuming that the pair potentials are transferable one can then include many solvent molecules interac- ting with the solute. This procedure is much easier to use than straightforward quantum mechanical calculations of a supermolecule with hundreds of solvent molecules. One excellent example of this approach to the treatment of solvation effects was a series of papers by Clementi and co-workers. In an introductory paper Clementi3 outlines a theoretical and computational model used to describe complex chemical systems of interacting species. His methodology operationally links both quantum chemistry and statistical thermodynamics and is subsequently tested by considering the interaction of water with various biomolecules.In the first two papers of the series SCF-LCAO-MO computations were presented for 21amino-acids’ and the four bases of DNA’ interacting with one molecule of water at a large number of positions and orientations around each biomolecule. The 1690 computed total energies for the HzO-amino complexes and the 368 computed total energies for the H20-base complexes were then fitted with an analytical potential of the form E =1 1 (-Aib/r +B;b/ry + C;b/rii)+E(biomolecule)+E(water) i j#i where i and j designate two atoms one in the biomolecule and the second in the E. Clementi Bull. SOC.chim. belges 1976,85,969.‘J. C. Owicki and H. A. Scheraga J Amer. Chem. SOC., 1977,99,7403. J. C. Owicki and H. A. Scheraga J. Amer. Chem. SOC., 1977.99 7413. E. Clementi R. Barsotti J. Fromm and R. 0.Watts Theor. Chim. Acta 1976 43 101. ’E. Clementi F. Cavallone and R. Scordamaglia J. Amer. Chem. SOC.,1977 99 5531. R. Scordamaglia F. Cavallone and E. Clementi J. Amer. Chem. SOC., 1977 99 5545. G. Klopman and P.Andreozzi water molecule a is an index that distinguishes the electronic environment of an atom in the biomolecules b is an index that distinguishes between either a hydro- gen or the oxygen atom in the HzOmolecule A B and C are fitting constants and E(biomolecu1e) and E(water) are the total energies of the biomolecule and of the water molecule respectively at infinite separation from the other.Contour energy maps can then be used to illustrate the structural organization of water around the various biomolecules. Some of these are shown in Figure 1. In 15 12 9 6 3 0 leu ala 0 i-. 0 3 .9 12 15 0 3 6 9. 12 15 0 3 6 9. I2 I5 0 3 6 .9 12 15 adenine guanine cytosine thymine Figure 1 Structural organization of water around various biomolecules (Reproduced by permission from Bull. SOC. chim. belges 1976,85 969) the concluding paper of the series Bolis and Clementig investigate the reliability and transferability of their library of pair potentials using phenylalanine as a test case. They computed the interaction with a molecule of water at 75 different positions relative to phenylalanine in the SCF-LCAO-MO approximation.The interaction energies for the complex using the fitted pair potentials displayed a reasonable agreement with those computed in the ab initio framework with an error of about 1kcal mol-'. Attempts have also been made to simulate the solvent molecules of solute- solvent clusters by point charges or point dipoles. One successful attempt in this area was the fractional-charge model developed by Noell and Morokuma. lo This model consists of placing fractional point charges at the location of solvent atomic centres. Neither electrons nor atomic basic functions are explicitly associated with such centres. If desired however a specified number of solvent molecules may be G. Bolis and E.Clementi J. Amer. Chern.Soc. 1977,99,5550. J. 0.Noell and K. Morokuma J. Phys. Chern. 1976,80,2675. Theoretical Chemistry included explicitly in the usual ab initio framework. One may consider this as a solute core to which additional solvent molecules may be added as fractionally charged centres. The fractional charges chosen are those which reproduce the calculated or experimental dipole moment of the solvent molecule. Extensive testing of the model for the hydration of Li' and F-was performed to assess the applicability of the method. As expected it was found that the inter- action energies between the ions and their solvent hosts were nearly independent of whether the first-shell water molecules are explicitly included. The fractional- charge model was also applied to the electronic structure of H3N-BH3 in the crystal state.In this case H3N-BH3 in the centre of a unit cell acted as a solute and ten nearest neighbours as the solvent systems. Finally the method was used to study changes in the nature of the complex H3N-HF associated with hydration. Here it was found that addition of the first hydration shell has a significant effect on the general characteristic of the potential energy surface for the complex. The mini- mum on the potential energy surface has shifted to a longer H-F distance and shorter N-H distance. In addition one has a levelling of the potential energy surface and a conformation representative of a proton-transferred-type structure (NH,'-.-F-) now has an energy ca. 5 kcal mol-' above the minimum (compared with 27 kcal mol-') in the gas phase.Despite the reported success of the above method it must be noted that the model lacks the proper short-range repulsive behaviour owing to the fact that orbitals are not explicitly associated with fractionally charged solvent molecules. The method does not include short-range exchange repulsion which prevents the meaningful optimization of solvent conformations. Furthermore although the method accurately depicts the electrostatic interaction between solute and solvent and the polarization of solute by soIvent it is not capable of representing charge- transfer or exchange interactions nor of assessing the polarization of solvent by solute. A related method which has been used to study interactions in solution considers the solvent molecules as point dipoles.Ab initio calculations are then performed on the solute in the presence of dipolar fields. Simons," for example reported on some initial attempts af developing such a model for anion-solvent interactions and the hydration energy of solvated electrons. The dipole representation of water molecules was a rather poor approximation for the study of anion-solvent interactions. Simons's fixed finite dipole model also was not capable of providing an accurate description for the properties of the hydrated electron. A somewhat different approach for studying solute-solvent interactions is based on modifying the hamiltonian of the system to include the solvent field effect. One recent example involved the use of CND0/2 with a modified shell repulsion potential for calculation of the properties of alkali halide salts in water.I2 The shell interaction potential was approximated by a simple function containing several empirically chosen parameters characteristic of each atom.These parameters were selected to obtain the correct dependence of the total energy on the interatomic distance for certain simple systems. The formation energies of the hydrates of alkali-metal ions and halide ions calculated in this manner agreed with experimen- " J. Simons Internat. J. Quantum Chem. 1977 11,971. l2 A. V. Bandura N. P. Novoselov and R. A. Evaresto Theor. and Exp. Chem. 1977,12,463. G. Klopman and P. Andreozti tal values within limits of 1-3 kcalmol-' whereas with the normal CND0/2 procedure they were 1.5-3 times larger than the experimental ones.Electrostatic molecular potential^'^ have often been used to represent the potential around molecules. The resulting diagrams allow one to visualize the potential wells where solvent molecules are likely to be found. It has now been shown that to generate such potential maps it is not necessary to determine accurate molecular wave function^.'^ Indeed a model where the molecule is composed of completely localized electron pairs is often sufficient to generate very accurate potential maps. This model was recently extended by Bonaccorsi Scrocco and Tomasi15 to include the polarization of the solute by the solvent. These authors derived an analytical expression of the polarization term in the interaction energy between a molecule and a point-like charge.The molecule is partitioned into a number of groups defined with respect to each bond and each lone pair and suitable group polarizabilities are associated with the groups. The polarization energy is cal- culated with similar procedures on the same basis set as the electrostatic term permitting one to compare numerical values of similar accuracy. The method was used to study the approach of a point charge along two opposite directions of the molecular axis of HCN and along the nitrogen lone-pair axis for several amines. Some attempts have also been made to develop quantum mechanical models for dipole-dipole and van der Waals interactions in molecular systems. Gavezzotti and Simonetta16 developed a model to account for intermolecular co-operation and dipole-dipole interactions during molecular rearrangements in organic crystals.They found that the simplest way to study the energetic changes accompanying the reorientational motion of crystals was to consider a molecular cluster made up of a finite number of molecules and to calculate the pairwise interactions of each molecule with all others in the cluster. A given rearrangement was visualized as the displacement of one or more internal co-ordinates of one fundamental molecule. Then one or more other molecules in the cluster were allowed appropriate motions with respect to which the cluster energy was minimized. The model was success- fully applied to the study of the role of intermolecular co-operation in lowering rotational barriers of some naphthalene and benzene derivatives.For van der Waals systems a valence-bond-type method has been used to calculate the long-range interaction potentials between molecule^.^^ Calculations showed that the anisotropic electrostatic interactions even for compounds with no net dipole were of the same order of magnitude as the dispersion terms. The anisotropic forces are believed to have important effects on some crystal properties. Solvation of Monoatomic Ions.-A great number of quantum mechanical studies have been made to investigate the solvation of various cations and anions in water and other solvents. One extensive Monte Carlo study by Clement? dealt with the hydration of alkali-metal ions in clusters of up to 200 water molecules.The study produced valuable information on the cluster size and shape around the ions and l3 R. Bonaccorsi E. Scrocco and J. Tomasi J. Chem. Phys. 1970,52 5270. l4 R. Bonaccorsi E. Scrocco and J. Tomasi J. Amer. Chem. SOC.,1977,99,4546. R. Bonaccorsi E. Scrocco and J. Tomasi Theor. Chim. Acta 1977,43,63. l6 A. Gaveuotti and M. Simonetta Actu Cryst. 1976 A32 997. P. E. S. Wormer F. Mulder and A. Van Der Avoird Internat. J. Quantum Chem. 1977 11,959. Theoretical Chemistry 47 gave reasonable estimates of the co-ordination numbers and hydration-shell radii of alkali-metal cations. Using the supermolecule technique Pullman'' also studied the solvation and fixation of the metal cations of Groups I and 11.She found that the bond energies for the cations interacting with H20 increased in the following order Be2+> Mg2' >Ca2' >Li' >Na' >IS'. This order was rationalized on the basis of two observations first the electrostatic attraction for dications should be larger than for monocations and secondly within each group of metals the exchange repulsion term favours the ion of smaller ionic radius. The same order of bond energies was determined in another non-empirical investigation of these cations interacting with HF and NH3 as ~olvents.'~ On going from HF to H20 to NH3 the bond energy of the ion-solvent complex increased. These results were also explained in terms of the electronegativity and effective size of the F 0 and N atoms involved in the donor-acceptor interactions.Ab initio calculations2' for the solvation of A13+ and Cu2' failed to reproduce the experimental hydration numbers and hydration enthalpies when solvation shells beyond the first were neglected. However a model of A13+ with six water mole- cules in the first hydration shell and twelve in the second shell yielded a computed hydration energy of 1041 kcal mol-' in reasonable agreement with the experimen- tal enthalpy of 1116 kcal mol-'. This model also accounts for the SN1mechanism proposed for the exchange of water molecules between the hydration sphere of A13' and the bulk solvent. Provided that the exchange is considered to take place between the first and second hydration shells the activation energy for the S,l process (1)is 21 kcal mol-' compared with 38 kcal mol-' for the SN2process (2).SN' [A1(H20)6]3' [A1(H20)5(H202S)]3+ SN2 [A1(H20) (H2O2')I3' __* [A1(H2O)7I3' (2) In general quantum mechanical studies on the solvation of anions are inherently more difficult than those for cations owing to the size and polarizability of the anions. We previously mentioned some difficulties encountered in the calculations of anion-solvent systems using point dipoles to represent the ~olvent.~ One suc- cessful anion-solvent study was a recent CND0/2 investigation of the optimal co-ordination number (n)of the aquo-complexes of Br- and I-. It was found that the optimal co-ordination occurs when these ions are surrounded by six water molecules.21 Solvation of Organic Cations.-A number of attempts have been made to investi- gate the influence of a solvent on the relative stability of organic cations.For example McManus and Worley2* studied halonium ion-carbocation equilibria (3) using MIND0/3 to evaluate the importance of carbocation solvation. All of the cyclic chloronium ions which they studied were 10-30 kcal mol-' more stable than A. Pullman Bull. SOC.chim. belges. 1976 85 963. '' V. M. Pinchuk Y. A. Kruglyak and M. D. Dolgushin Theor. and Exp. Chem. 1977,12 116. 2o H. Veillard J. Amer. Chem. SOC.,1977,99 7194. 2' V. B. Volkov and D. A. Zhogolev Chem. Phys. Letters 1977 49 591. 22 S. P. McManus and S. D. Worley Tetrahedron Letters 1977 555. G.Klopman and P.Andreozti a their open chloroalkyl carbocation isomers suggesting that chlorine is quite effective in internally solvating the carbocations in the absence of solvent.MIND0/3 predicted that a tertiary carbocation is more than 10 kcal mol-’ less stable than its isomeric chloronium ion. Since the experimental value is known to be between 0 and 2kcal mol-’ in solution in S02ClF they concluded that the solvent must supply a substantial amount of stabilization to the open carbocation. J~rgensen~~ reported MIND0/3 and perturbation theory calculations for complexes of carbocations with an HCI molecule to provide insight into the relative extent of specific solvation at carbocation centers. He found that specific solvation at positively charged carbons becomes less favourable with increasing charge delocalization.For example the relatively localized homocubyl cation (3) was better stabilized24 by the solvated leaving group than the more delocalized pyra- midal ion (4) and the bishomoaromatic ion (5),having the relative energies 0.0,3.2 and 6.6 kcal mol-’ respectively. Interestingly enough the gas-phase energies are in a distinctly different order (4)< (5)< (3). Thus it is concluded that the relative energies of isomeric carbonium ions may vary appreciably from solution to the gas phase and caution must be exercised in using relative energies of carbonium ions in the gas phase as a gauge for the relative energies of intermediates in solution. (4) Since Jorgensen’s model considered explicitly only interactions with one solvent molecule it was believed that introducing additional solvent molecules could eliminate the discrepancy between the solvation energy of the delocalized and localized isomers.To probe this issue more thoroughly Jorgensen and Munr~e~~ studied the influence of increasing solvation on the relative energies of bisected and bridged ethyl cations. Their MIND0/3 results revealed that the solvation energy difference for these cations showed no sign of being reduced even after addition of up to five solvent molecules supporting their view that additional solvation will not return the energetic order to that for the isolated ions in the gas phase. Another study of interactions between solvent and organic ions involved an investigation of the nature of solvation and hydrogen-bonding of pyridinium ions in H20 at the STO-3G Relative solvation enthalpies for the transfer of a series of pyridinium ions from the gas phase to water were calculated by combining 23 W.L. Jorgensen J. Amer. Chem. SOC.,1977,99 280. 24 W. L. Jorgensen J. Amer. Chem. Soc. 1977,99,4272. 25 W. L. Jorgensen and J. E. Munroe Tetrahedron Letters 1977 581. 26 E. M. Arnett B. Chawla L. Bell M. Taagepera W. J. Hehre and R. W. Taft J. Amer. Chem. SOC. 1977,99,5729. Theoretical Chemistry relative heats of ionization in the gas phase and in water with relative heats of solvation of the corresponding neutral pyridines. Both the hydrogen bonds from water to the pyridines (6) and from the pyridinium ions to water (7) were investigated.As expected the hydrogen bond between the pyridinium ions and water was very strong and accounted for most of the difference between the gas-phase basicities and those in water. Theoretical calculations have also been used to study the influence of solvent on the isomer distribution of electrophilic reactions. For example Rayez and Dannenberg” carried out INDO calculations for orrho- meta- and para-pro- tonated toluene in the gas phase and in the presence of one or two trifluoroacetic acid solvent molecules. The calculated percentage of ortho meta- and para-products was found to be in agreement with experiment. The paralortho ratio significantly decreased upon solvation whereas the para/meta ratio remained large supporting the idea that relative cationic solvation might be quite important in consideration of normal organic reactivities.Association of Monoatomic ions with Organic Molecules.-The stability of various conformers of a molecule can be affected by co-ordination with cations. For example CND0/2 calculations have shown that the non-planar conformers of but-l-ene,*’ which are less stable in the free state than the planar cis form have larger stabilization energies when co-ordinated with Na+ ions. These changes are believed to be particularly important in biochemical molecules where the presence of a cation may favour a structure susceptible to producing specific enzymatic action. It is thus not surprising to find that a number of such studies have found their way into a theoretical investigation.Pullman and co-workers have written an interesting series of papers on the binding of cations to biomolecules. Ab inirio computations were performed on the binding of the Na’ ion to the purine and pyrimidine bases of the nucleic acids.2g The bases uracil (8) cytosine (9),guanine (lo) and adenine (11)are shown along -32.9 0 ~.:10“ 0 @’ -28.7 H (8) (9) 27 J. C. Rayez and J. J. Dannenberg Tetrahedron Letters 1977 671. 28 V. W.Meiler D. Deininger and D. Michel 2.phys. Chem. (Leipzig) 1977 258 139 29 D. Perahia A. Pullman and B. Pullman Theor.Chim. Acta 1977 43 207. G. Klopman and P. Andreozzi -48.2 0 0 -14.6 -24.0 with the favoured binding site of the cation. The calculated binding energies in kcalmol-' were -32.9 -51.73 -53.89 and -26.35 for (8) (9) (lo) and (11) respectively.These computations indicate two principal differences between these interactions. First for bases containing both oxygen and nitrogen cation binding at an individual oxygen binding site is favoured over binding at the nitrogen atom. This inversion in the intrinsic binding ability of Na' compared with H' is due to the exchange repulsive component of the binding energy which for the same distance is larger for nitrogen than for oxygen. Secondly we note the appearance in cytosine and guanine of bridged positions between a nitrogen and a carbonyl oxygen as the preferred binding sites. In the electrostatic potential energy maps for free cytosine and guanine the nitrogen and oxygen atoms were associated with separate minima and the bridge position was less favourable.However the equilibrium distance for a proton is smaller than for Na+ so that the proton can move into the potential minima close to the heteroatoms. In a second paper of the series Pullman et ~1.~'reported ab initio computations on the binding of alkali-metal and alkaline-earth cations to the phosphate group to determine the effects of binding on the conformational properties of the phos- phodiester Iinkage and the polar head of phospholipids. Using an extended STO- 3G basis set they studied the interactions of Na+ Mg" K" and Ca2' with the dimethyl phosphate anion [(12) as the mode1 for the phosphodiester linkage] at a bridged (B) and an external (E) site with three fundamental conformations.In all cases strongest binding corresponded to the B-site the two bivalent cations bind- ing more strongly than the univalent ones. Fixation of the cations at the B-site did not influence the order of conformational preference with respect to the torsion about the P-Oe,,, bonds existing in the free molecule. However binding of cations to the external E-site was able to produce substantial modification in the order of conformational stabilities. Thus depending on the site of binding cations may or may not perturb the intrinsic conformational preference of the phos- phodiester linkage. The authors also studied the interaction of Na' at the B- and E-sites of ethanolamine phosphate (EP) (13) in an attempt to investigate the effects of cation binding on the conformational properties of phospholipids.The intrinsically pre- ferred conformation for the free EP was a highly folded structure associated with (a4, as)= (270°,30"). The most stable form of the Na',EP adduct was substantially 30 B. Pullman N. Gresh H. Berthod and A. Pullman Theor. Chim. Actu 1977 44 151. TheoreticaI Chemistry H different however with (a4, as)= (-30° 1SOO). Thus fixation of the cation at B had the effect of extending the structure of the polar head with respect to a,. On the other hand considering Na’ binding with the E-site the most stable conformation is very nearly the same as that for free EP. Again it was found that the site of binding may have a profound influence on the conformation of a ligand.3 Theoretical Aspects of Hydrogen Bonding Studies on its Origin and Nature.-Among the various factors involved in molecu- lar association hydrogen-bonding is probably the most important. It is thus not surprising to find that the study of its origin and nature continues to generate considerable theoretical interest. Various energy-decomposition schemes have been used in the past to describe the factors responsible for its occurrence. Most of them attempt to separate the total interaction energy into electrostatic exchange and polarization energies. Morokuma et al.31now propose a new energy-decom- position scheme where the influence of charge transfer is evaluated as well. The procedure involves the manipulation of a matrix generated by the Hartree-Fock molecular orbitals of the isolated molecules.In their article the authors describe the specific steps for modifying the Gaussian 70 package for the calculation of these new energy components. This energy-decomposition analysis was applied to the study of (H20)2 (HFL H3N...HF and other complexes in which the proton donor is HF H20 NH3 or CH and the proton acceptor is HF H20 or NH3.32 The essential energy components in hydrogen-bonding include electrostatic polarization exchange repulsion charge transfer and their coupling. For ‘normal’ hydrogen bonds in which the proton acceptor is F 0,or N and the proton donor is a polar bond F-H 0-H or N-H the hydrogen bond is strongly electrostatic in nature with a small but significant contribution from charge transfer.Although charge transfer plays only a minor role in strong more electrostatic hydrogen bonds such as H3N- .HF it is essential for the stabilization of weaker bonds such as H3N-..HCH3 and H20.* .HCH3. During hydrogen-bond formation the electron density on the hydrogen-bonding proton decreases owing to exchange repulsion and polarization while its concentration on the acceptor atom is principally due to charge transfer and polarization. Charge-redistribution effects in the non-interacting parts of the donor and acceptor are controlled by the polarization term and generally follow an alternating charge pattern. The energy components of some lithium complexes K. Kitaura and K. Morokuma Infernat.J. Quantum Chem. 1977,10 325. 32 H. Urneyama and K.Morokuma J. Amer. Chem. SOC.,1977.99 1316. G. Klopman and P. Andreozzi (LiFX and (LiH)* were compared with the hydrogen-bonded (HF)2 complex. Based on these comparative findings it appears that hydrogen-bonding is a unique type of association which always involves a short polar and strong H-X bond as the proton donor. Since the polarity is moderate the electrostatic energy is not too great and exchange repulsion prevents the hydrogen from approaching too closely to the proton acceptor. Because of all these effects hydrogen bonds are always intermediate to weak interactions. .~~ A similar conclusion was reached by Dolgushin et ~ 1 These authors investi- gated the nature of the hydrogen bond by a comparative analysis of the interactions of Li+ F- OH- and H20 with H20.In agreement with Morokuma’s results they found the exchange terms to be repulsive but largely offset by the larger elec- trostatic attraction. In addition they found that the total charge of the proton- donor or proton-acceptor system is the critical point for hydrogen-bond formation. If the donor system is negatively charged or if the acceptor system is positively charged no hydrogen bond results. If on the other hand the acceptor system is negatively charged a strong hydrogen bond can exist. .~~ Clark et ~ 1 investigated the electronic reorganizations accompanying core and valence-shell ionization in some simple hydrogen-bonded systems including H,N-.H20 and (H20)3, (H20)*,HF-.H20 using a 4-3 1G and double-zeta basis set.The relaxation energies for a given core hole were found to increase on going from monomer to dimer irrespective of whether the binding energy for the core level increased or decreased. Core holes in the dimers caused substantial changes in the hydrogen-bond energies compared with the neutral systems. Structural Studies.-A number of studies were aimed at investigating the role of intramolecular and intermolecular hydrogen-bonding in determining the stereo- .~~ chemistry of molecular systems. For example Newton et ~ 1 attempted to determine the role of intramolecular factors in the planarity of the carbon-oxygen framework in the a-hydroxycarbonyl moiety of many a-hydroxy-acids and carboxylates. STO 4-31G calculations on three a-hydroxycarbonyl systems glyco- lic acid (14) the glycolate anion (15) and glycoaldehyde (16) gave equilibrium (14) (15) (16) conformations corresponding to internally hydrogen-bonded structures.Rotations of the a-hydroxy-group were calculated to cost much less energy than distortions which destroyed the planarity of the carbon-oxygen framework. These results were consistent with the crystal-state structures of the molecules where inter- molecular hydrogen-bonding takes precedence over internal hydrogen-bonding. Although the relative stabilities of these structures may be partly explained in 33 M. D. Dolgushin and V. M. Pinchuk Theor. Chim. Acta 1977 45 157. 34 D. T. Clark and B. J. Crornarty Theor. Chim. Ada 1977 44,181. 35 M. D. Newton and G. A. Jeffrey J. Amer. Chem.Soc. 1977,99,2413. TheoreticaI Chemistry terms of intramolecular hydrogen bonds analysis of the charge distribution indicated that the short-range 0-He. -0effects are smaller than those generally found in intermolecular hydrogen-bonding. Furthermore no weakening of the 0-H bond of the a-hydroxy-group was found when the acid and the aldehyde were compared with non-hydrogen-bonded conformations. In a related study Vishveshwara and Pople36 investigated the stereochemistry of the a-amino counterparts of glycolic acid (14) and glycoaldehyde (16). Using a 4-31G basis set they calculated the equilibrium geometry of glycine (17) and a-aminoacetaldehyde (18)as well as the effect of rotation of the a-amino-group on the relative stabilities of these compounds.The most stable conformations cor- responded to structures in which the amine group forms two bifurcated hydrogen bonds with the carbonyl oxygen. The rotational potential energy surfaces of the acid and the aldehyde also showed two other stable conformations. For glycine this corresponded to a structure with a hydrogen bond between the hydroxyl proton and nitrogen (19) lying only 2.2 kcal mol-' above (17). For a-aminoacetaldehyde the second local minimum lay only 1.4kcal mol-' above (18) and was stabilized by a strong interaction between the aldehyde proton and the nitrogen lone-pair electrons (20). (17) (18) (19) (20) Quantum mechanical methods were also used to study the effects of hydrogen-bonding on peptide bonds. In one such st~dy,~' the peptide unit was modelled by truns-N-methylacetamide (NMA) (2l) which was allowed to interact with various hydrogen-bonding species such as water formamide imidazole CH3NH3' and HCOO-.PRDDO calculations indicated that all of the species made non-planar deformations of the peptide unit more difficult. The effects of these species on the flexibility and electronic charge distribution of NMA can be understood by recog- nizing that hydrogen bonds to either the carbonyl or the amine group of the peptide linkage will stabilize (22) more than (21). Partial and full hydration of the peptide H H f .H H-C p H-\ +/ C=N (21) (22) unit were also studied. It was found that many of the effects of a full hydration shell could be simulated by the interaction of only two water molecules.36 S. Vishveshwara and J. Pople J. Amer. Chem. Soc. 1977,98 2422. 37 S. Scheiner and C. W. Kern J. Amer. Chem. SOC.,1977,99,7042. G. Klopman and P.Andreozzi In a somewhat related work molecular orbital calculations were used to study the hydrolysis of formamide as a model for the hydrolysis of peptides by carboxy- peptidase A.38A proton donor H30+was positioned near the nitrogen atom of the model substrate. Nucleophilic attack by a water dimer a model for the basic form of Glu-270 led to hydrolysis of the peptide (23). A Li cation positioned proximate to the carbonyl oxygen was seen to facilitate hydrolysis. The electrophile first polarizes the carbonyl bond of the substrate reducing the negative charge on the oxygen and making the carbon more susceptible to nucleophilic attack.Li' and [Be(OH)(NH3)2]+,believed to be good models for Zn2' and its Iigands were found to be more effective at catalysing the hydrolysis than were various hydrogen- bonding species like NH4+. Theoretical Aspects of Proton Transfer.-A number of theoretical studies have been related to the question of proton transfer in hydrogen-bonded systems. Iwata and M~rokuma~~ examined the ground and various excited states of the formic acid monomer'and dimer (24) with an STO-3G basis set. The two-configuration elec- 01...H 4 -04 / \ Hl--Cl C2-H3 \ / 02-HZ...O3 (24) tron hole potential method was used for the calculation of the excited state of the dimers. The potential energy curves for the symmetrical simultaneous movement of two bridging protons for all of the states were studied and it was found that proton transfer in the ground state was the one with the lowest barrier.The authors did not find an excited state with a low barrier for the hydrogen exchange. However they note that since the transitions being considered ti-r* and T-T* are not' directly involved in weakening the 0-2-H-2 bond or strengthening the H-2-a.0-3 bond the barrier should not change drastically upon excitation. As a result states which should have low barriers for proton exchange are those involv- ing an excitation from the 0-2-H-2 u-orbital or to the 0-2-H-2 u*-orbital. The potential energy surface for the proton transfer in the H2S dimer4' was also calculated.Despite the limited basis set used the calculated energy of 38 S. Scheiner and W. N. Lipscomb J. Amer. Chem. SOC.,1977,99 3466. 39 S. Iwata and K. Morokuma Theor. Chim. Acta 1977,44323. 40 K. Pecul Theor. Chim. Acta 1977.44 77. Theoretical Chemistry 55 207 kcal mol-' was in fairly good agreement with the experimental value of 151-199kcal mol-' for the energy of proton transfer. On the basis of their results the authors suggest that the H2S dimer can be stable at any orientation of the monomers. The behaviour of the hydrogen-bonded proton in malonaldehyde [skeleton as in (25)] continues to stir the interest of theoreticians and its dynamics have been dH0 I I AH I H (25) studied by determining the reaction co-ordinates from the gradients of potential obtained with a CNDO/2 The motion along the reaction co-ordinate was calculated considering all vibrational motions perpendicular to the reaction co-ordinate.It was found that a rapid transformation occurs between the two asymmetric conformers through a low potential barrier. One of the interesting features of this work was the finding that the distribution of the hydrogen-bonded proton on the reaction co-ordinate varied with the increase of temperature. The mean position of the proton was symmetric in the low-temperature range and became asymmetrically oriented only at high temperature. The existence of an out-of-plane vibrational motion with a negative force constant led the investigators to suggest that the motion of the proton proceeds along an ellipse-like orbit.The possibility of tunnelling in the proton-exchange reactions between methyl- oxonium ion and methyl alcohol methyl alcohol and methoxide ion hydronium ion and water and water and hydroxide ion was investigated by STO 4-31Gcal-culations on the proton transfer in the above The calculated tunnelling frequencies were about two orders of magnitude larger than the experimental values for the four systems considered. Small perturbations such as the rotation of methyl groups were found to destroy the symmetry of the profiles and were believed to be responsible for the discrepancies between calculated and experi- mental results. In a recent paper attempts were made to study proton-transfer mechanisms in the water dimer and trimer coupled to an envir~nment.~~ The environment was simulated by reaction fields together with uniform external electric fields.The reaction fields were varied with respect to the direction of the dipo!e moment of the supermolecule and g the solute-surrounding coupling tensor was used to gauge the reaction field strength. For negative g values the proton potential curve dimer has only one minimum. For positive g values however a second minimum is apparent in the region corresponding to the ion-pair structure H,O'...OH-as g increases in value (Figure 2). A potential barrier against the proton displacement from H30+toward OH-can thus be calculated but was seen to depend on the magnitude of g. 41 S. Kato K. Kato.and K. Fukui J. Amer. Chem. SOC.,1977,99,684. 42 J. H.Busch and J. R. de la Vega J. Amer. Chem. SOC.,1977,99,2397. O3 0.Tapia and E. Poulain Internat. J. Quantum Chem. 1977,11,473. G. Klopman and P. Andreozzi Figure 2 Proton potential curves for the water dimer model as a function of the orientation and reaction field strength (Reproducedby permission from Internat. J. Quantum Chem. 1977 11,473) 4 Other Molecular Associations Quantum mechanical calculations have been used to investigate van der Waals charge-transfer and ionic associations. For example Lochmann et aE.44used the PCILO method to analyse the individual energy contributions responsible for the stabilization of van der Waals hydrogen-bonding and charge-transfer complexes. The nonane dimer representing a van der Waals type interaction was found to be stabilized by -0.85 kcal mol-' while the water dimer and a Li'-cis-but-2-ene complex were stabilized by -4.15 and -3.60 kcal mol-' respectively.The zeroth- order energy involving an electrostatic interaction was destabilizing for all systems. Stabilization of the nonane dimer was seen to arise from inter-bond correlation as well as delocalization but the delocalization contribution was significantly more important in the other two complexes considered. In a second paper Lochmann calculated intermolecular interactions again using the supermolecule approach within the PCILO method but this time using fixed polaritie~.~~ By employing fixed 44 R. Lochmann and T. Weller InternaF. J.Quantum Chem. 1976 10,909. 45 R.Lochmann Internat. J. Quantum Chem.. 1977 11,293. Theoretical Chemistry 57 polarities determined by minimization of the polarization energy of the isolated subsystems of the complex for all distances between them his PCILO calculations were without any iteration cycle. Both the stabilization energies and equilibrium distances for the nonane dimer water dimer and a benzene-tetracyanoethylene complex were in good agreement with the calculated values using optimized wave- functions. A more sophisticated analysis of non-covalent interactions was presented by K~llman,~~ using a STO 4-31G basis set and the Morokuma energy-decomposition scheme. The interaction energies and equilibrium structures for a wide variety of intermolecular complexes were presented including van der Waals molecules hydrogen-bonded complexes charge-transfer complexes radical complexes and three-body interactions.It was found that the electrostatic energy and electrostatic potential are the most useful guides to qualitative and semi-quantitative predictions of the energies of non-covalent interactions. The electrostatic energy also correctly predicts the directionality of many inter.actions including (C12)2 (HF), (HClh F--.H20 and C1-. -H20. Consequently it was suggested that a general equation can be used to calculate the interaction energy for many non-covalent interactions involving Lewis acids and bases. The procedure was found to be successful in a host of test cases including (C12)2 C02.-.H20 S02-.NH3 Li'. -OH2 F--H20 NH4+.-.F- and F-. -HF. In a related paper Kollman et al.47 calculated the proton affinities Li' affinities and hydrogen-bond affinities for some simple bases. As before they found that the electrostatic potential is a good guide to predicting the relative H+ HF and Li' affinity for basic sites. However the order of the basicities of various compounds varied significantly depending on the nature of the acid and on the substituent on the basic site. Specifically the methyl substituent effect was found to be quite different for fluoro and amine bases. In the case of fluoro bases electrostatic and charge- redistribution effects reinforce each other; in amine bases they oppose each other. STO-3G and 4-31G calculations have been used to determine the relative proton affinities of pyridine and the diazine~.~~ The experimentally observed order (pyridine > 1,2-diazine> 1,3-diazine> 1,4-diazine) was reproduced only at the 4-31G level.In the protonated ions increasing stability correlated with increasing an orbital energy of the base. This contrasts with the behaviour of the hydrogen- bonded complexes where increasing stability correlated with increasing p-character of the nitrogen lone-pair orbital. A series of electron donor-acceptor complexes of halogens was studied by Umeyama et al.49 Based on the energy components essential for binding the complexes were qualitatively classified as weak electrostatic-charge-transfer complexes intermediate electrostatic complexes weak electrostatic complexes and very weak dispersion-charge-transfer complexes.N-Methyl substituent effects were studied in a number of donor-NH2R systems. It was found that methyl substitution in H2N-ClF resulted in a small destabilization due to cancellation of 46 P. Kollman J. Amer. Chem. SOC.,1977,99 4875. '' P. Kollman and S. Rothenberg J. Amer. Chem. SOC., 1977,99 1333. J. E. Del Bene J. Amer. Chem. SOC.,1977,99 3617. 49 H. Umeyama K. Morokuma and S. Yamabe J. Amer. Chem. SOC.,1977,99,330. G. Klopman and P. Andreozzi exchange repulsion and charge-transfer terms (see Table). This contrasted with a small stabilization effect for H3N-BH3 due to polarization-exchange repulsion stabilization and large stabilization for H3N-..H’ which was found to result from a polarization effect. Table Comparisonof interaction energy components and N-methyl substituent effects between various complexes at equilibrium geometry in kcal mol-’ HSN-CIF H3N-BH3 H3N-H’ RIA 2.717 1.705 1.02 Total interaction energy Electrostatic Exchange repulsion Polarization Charge transfer Coupling AE ES EX PL CT MIX -8.23 (0.29) -1 1.18 (0.32) 7.41 (0.53) -1.05 (0.02) -3.59 (-0.57) 0.19 (-0.01) -44.7 (-0.8) -92.9 (-1.2) 86.9 (4.4) -17.2 (-5.0) -27.1 (-1.4) 5.6 (2.4) -221.9 (-8.5) -99.8 (3.3) -27.4 (-12.8) -88.3 (-3.4) -6.5 (4.4) 0.0(0.0) The numbers in parentheses are the difference between the value for the CH3H2N complex and that for the H3N complex. A negative number indicates that the CH3N2N complex is more stable and oice uersa.LaGrange and co-workerssO studied a similar series of charge-transfer complexes with a 4-31G basis set. For the complexes studied H3N-C12 HZO-C12 and HF-CI2 it was found that the intermolecular distance is smaller than the sum of the van der Waals radii. It was also found that the energy of formation of the complexes diminished regularly as the eIectronegativity of the donor atom increased. Finally SCF studies have been carried out on a novel class of molecular complexes involving neutral alkali-metal and halogen atoms with dipolar molecules in particular interactions between Li Na or F with NH3 H20 HF PH3 H2S or HC1.” The minimum-energy structures for the alkali-metal atom-dipolar mole- cule interactions are M-BH, where the negatively charged end of the hydride approaches the neutral atom.There is transfer of charge from the hydrides to the metal and this leads to a rather substantial dipole moment for the complexes. It was found that the interaction energies of a lithium atom with different hydrides decrease in the order NH3 >H20>HF> PH3>H2S> HCl. The interaction of Na with the hydrides follows the same relative order as the Li complexes but the interaction energies are smaller. J. LaGrange G. Leroy and G. Louterman-Leloup Bull. SOC.chim. belges. 1976,86 241. ’’ M. Trenary H. F. Shaefer and P. Kollman J. Amer. Chem. Sac. 1977,99 3885.