Nondiagonal second order intermolecular forces for interactions involving molecules

Very often only “diagonal” second order energies, varying as an even power of R^?1, occur in the multipole expansion of the interaction energy. However for many molecular interactions important “nondiagonal” second order energies, varying as an odd or even power of R^?1 can arise. This point is emphasized by a general discussion and by a detailed specific example, the interaction of an ionized dipolar molecule with a nondegenerate atom. Also some useful theorems, on the orientation average of various types of second order energies, are derived.     

Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers

A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.     

Long range intermolecular forces between conjugated systems

The long range intermolecular forces in terms of the interaction energies between two conjugated molecules are computed and discussed for the cases: (a) a point charge and ethylene, (b) two ethylene molecules, (c) two hexatriene molecules, (d) two benzene molecules, (e) two naphthalene molecules, and (f) two polar merocyanine molecules. The calculations are based on Buckingham's theory of long range intermolecular forces and the author's values for multipole moments and polarizabilities presented previously. The advantage of the treatment is: asymmetric molecules are correctly described and the intermolecular potential is better approximated than by the usual dipole approximation.     

Modeling intermolecular interactions of physisorbed organic molecules using pair potential calculations

The understanding and control of epitaxial growth of organic thin films is of crucial importance in order to optimize the performance of future electronic devices. In particular, the start of the submonolayer growth plays an important role since it often determines the structure of the first layer and subsequently of the entire molecular film. We have investigated the structure formation of 3,4,9,10-perylene-tetracarboxylic dianhydride and copper-phthalocyanine molecules on Au(111) using pair-potential calculations based on van der Waals and electrostatic intermolecular interactions. The results are compared with the fundamental lateral structures known from experiment and an excellent agreement was found for these weakly interacting systems. Furthermore, the calculations are even suitable for chemisorptive adsorption as demonstrated for copper-phthalocyanine/Cu(111), if the influence of charge transfer between substrate and molecules is known and the corresponding charge redistribution in the molecules can be estimated. The calculations are of general applicability for molecular adsorbate systems which are dominated by electrostatic and van der Waals interaction.     

On the theory of intermolecular forces between inert gas atoms

The method described by Gordon and Kim and modified by Rae has been further modified to restrict the self-exchange correction to an electron gas composed of the outer shell electrons. Revised results are presented for the interaction potentials between various pairs of inert gas atoms.     

On calculations of intermolecular potentials

Ab initio MO calculations of intermolecular potentials using conventional Gaussian basis set have a tendency to over emphasize binding due to underestimation of exchange repulsion. A modified semi-empirical method has been suggested and results are found to be reliable at medium- and long-range separation.     

Hardness of intermolecular forces and thermal diffusion

An approximate momentum transfer theorem leads to a direct relation between the thermal diffusion ratio and the logarithmic derivative of the potential. The correlation with exact results is excellent.     

Spherical tensor theory of long-range intermolecular forces

General expressions are given for the electrostatic, induction and dispersion energies of a pair of interacting, molecules in terms of spherical tensor components of the molecular multipole moments and polarizabilities. The orientation dependence is given in terms of the scalar expansion functions S_l1l2l^k1k2.     

High order correlation effects in intermolecular forces

A new approach to the calculation of intermolecular forces is presented. The total hamiltonian is used and no arbitrary separation into “orders” is made. The approach allows the interaction to be calculated, including intraatomic electron correction, to various degrees of approximation, the ultimate being full configuration interaction. The approximations are guided by the choice of wave function and the partitioning of the variational form. In this paper the method is applied to the long range interactions of helium, and in more approximate forms to HHe and LiHe. For He₂, studies are made of two- and three-electron excitations. Three-electron excitations contribute almost 9% to the value of the C₆ coefficient. Our final C₆ coefficient is 1.457 (in atomic units) versus the best semi-empirical value of 1.4618 ≠ 0.0004. The results are compared with other calculations in a formal way so as to demonstrate the value of our alternative expressions.     

Orbital-shell density functional in calculations on the intramolecular and intermolecular potentials for chromium atoms and benzene molecules

Calculations have been performed in the orbital-shell density-functional approximation from the nonempirical approximating quasiparticle density function, which show that the total potential energy surface for the CrBz complex is described by a two-well interaction potential. The minimum in the short-range part of the potential corresponds to an intramolecular bond in a bisarenechromium charge-transfer complex, while the minimum in the long-range part describes the molecular interaction between those components in atomically dispersed solutions of chromium in arene matrices. Good agreement with experiment is obtained.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 2, pp. 218–220, March–April, 1990.     

Axial force fluctuations in long-chain molecules

The fluctuations Δf in the axial force f acting on a long-chain molecule whose end-to-end displacement r is fixed are computed for a freely jointed model in which the covalent bonds are represented by stiff linear springs. It is found that the relative fluctuation Δf/f remains large regardless of the length of the chain. A time-dependent computer simulation of the model serves both to verify the theoretical calculation of Delta;f and to provide physical insight. The result helps to clarify the difference in behavior of the strain ensemble (r is fixed and f fluctuates) and the stress ensemble (f is fixed and r fluctuates) for which, in the absence of excluded volume, the strain ensemble predicts that f = 0 for r = 0, while for the stress ensemble with f = 0 it is found that 〈r²〉₀ > 0.     

Retarded intermolecular interactions involving diamagnetic molecules

Second‐ and third‐order time‐dependent perturbation theory within the multipolar framework of nonrelativistic quantum electrodynamics is used to calculate the retarded dispersion interaction between two diamagnetic molecules, a diamagnetic molecule and a magnetic‐dipole susceptible molecule, and a diamagnetic molecule and an electric‐quadrupole polarizable molecule. New expressions for the energy shift valid for all intermolecular separation distances, R, beyond the region of overlap of molecular electronic wave functions and applicable to a pair of randomly oriented molecules in the ground electronic state are given. The R‐dependent behavior of the far‐zone limit of the interaction energies is also examined. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 437–442, 2000     

Comparisons between crystallographic results and theoretical calculations on phenol molecules

The internal angles in the benzene ring and the external C-C-O angles have been determined by the MNDO method for phenol, the three cresols and 4-nitrophenol. Despite the fact they are supposed to be related to the isolated molecules, the results are in very good agreement with crystal structure determinations.     

On the theory for closed shell intermolecular forces

The electron gas model of Gordon and Kim is applied to the interaction of inert gases with a hydrogen molecule. Comparison of the isotropic potential wells with available experimental data shows clearly that modification of the exchange potential along the lines suggested by Rae produces greatly improved agreement when simple power series representations of the dispersion energy are included.     

Thomas-Fermi-Dirac calculations for molecules

The electrostatic potential derived from a solution to the molecular Thomas-Fermi-Dirac equation for F₂ is combined with the exchange potential and modified to give the correct behavior far from the nuclei. One-electron energy levels in this potential are calculated and are in qualitative agreement with SCF orbital energies. Similar computations are carried through for F and Ar, which correspond to the separated and united atoms for F₂. To compensate for errors in the potential, we subtract from molecular orbital energies the difference of TFD and SCF orbital energies for the separated atoms. Now all the orbital energies are correct to a few electron volts.

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Zusammenfassung Das elektrostatische Potential, das sich für F₂ aus der Thomas-Fermi-Dirac Theorie ergibt, wird mit dem Austauschpotential kombiniert und so modifiziert, daß sich das richtige Verhalten in Kernnähe ergibt. Die berechneten Einelektronenenergien sind in qualitativer Übereinstimmung mit SCF-Werten. Analoge Rechnungen für F und Ar werden ausgeführt und als Grenzfälle für Korrekturen verwendet. Dann ergeben sich alle Orbitalenergien bis auf wenige eV richtig.

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Supported by the National Science Foundation under Grant GP-20718.     

Gaussian representations of charge overlap effects in intermolecular forces

The ground state H? H⁺ and H? H interactions are used as model interactions for investigating the feasibility of using Gaussian basis sets for representing charge overlap effects in intermolecular forces. The non-expanded charge-induced dipole energy and the non-expanded dipole-dipole dispersion energy, respectively, for these interactions are calculated using two types of Gaussian basis functions to represent the first order wave function, Ψ⁽¹⁾. Very good results for these interaction energies, which include charge overlap effects, are obtained for all interatomic separations by using small Gaussian basis sets to represent the interaction, that is Ψ⁽¹⁾, and/or the isolated atoms (the zeroth order wave function).     

AB initio calculations on intermolecular forces. The systems He…HF and He…H2O

The interaction energy between a He atom and a polar molecule (HF, H₂O) is calculated with a gaussian basis set both in the SCF approximation and with the inclusion of the intersystem correlation energy. The long range behaviour of the interaction energy is compared with results from perturbation theory.     

Quantum-Chemical and semiclassical calculations of intermolecular interactions of phospholipids

By use of empirical 0–1–6–12 atom–atom potential functions and the PCILOCC method intra- and intermolecular interactions of glycero–phosphoryl–ethanolamine model head groups in a planar layer crystal were calculated. Starting from investigations of the two-dimensional energy-contour diagrams the minima of energy as a function of all head group torsion angles were calculated using a gradient procedure. Within an interval of 15 kcal/mol above the energy of the global minimum we obtained about 30 local minima. These results demonstrate a high flexibility of the investigated phosphorylethanolamine head group in agreement with experiment. The ethanolamine moiety exists in enantiomeric conformations. With the torsion angles of the 0–1–6–12 energy minimization procedure PCILOCC calculations were carried out. These calculations yield the x-ray conformation as the most stable one (unit-cell stabilization energy = ?36.3 kcal/mol). The PCILOCC as well as the potential function calculations show that the conformation of phospholipid head groups in layer crystals is determined by intramolecular as well as by intermolecular interactions with neighboring phospholipid molecules.