Włodzimierz Kołos

Possible improvements of the interaction energy calculated using minimal basis sets

Interaction energies for H2O·H2O, H2O·F− and H2O·CH4 have been calculated using the LCAO MO SCF method with minimal basis sets, and employing the counterpoise method to eliminate the basis set superposition error. The results compare favourably with those obtained using extended basis sets. It is shown that for H2O·H2O and for the benzene-carbonyl cyanide complex a large part of the dispersion energy can easily be obtained as a sum of bond-bond dispersion energies calculated from a London-type formula using experimental values of the bond polarizability tensors. By considering the interaction between a water and a glycine molecule it is also shown that the dispersion energy plays an important role in the hydration of organic molecules.

Non-additivity in water-ion-water interactions

The three-body system Li+(H2O)2 was analyzed to study that non-additive part of the interaction potential which can be obtained by the Hartree-Fock approximation.For long and intermediate distances the three-body correction was found to be well represented by the induction energy, where bond dipoles are induced on each water molecule by point charges located on the (unpolarizable) lithium ion and on the other molecule respectively: for shorter distances this approximation was corrected by means of an exponential repulsive term. Such a potential model for non-additive interactions was extended to the more general situation Li+(H2O)n, and Monte-Carlo calculations were carried out on clusters containing up to six water molecules; comparison with other simulation results and with available data showed a significantly improved agreement with experiment. Tentative values for ΔH are presented for n =7, 8,..., 20, where experimental data are not available.

Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH4 and H2O. Improved basis sets developed for these molecules have been extended to NH3 and HF and employed to H2CO and CH3OH. Interaction energies between XHn molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.

Convergence properties and large-order behavior of the polarization expansion for the interaction energy of hydrogen atoms

Abstract High-order corrections in the polarization expansion for the interaction energy of two ground-state hydrogen atoms are computed for a wide range of interatomic distances R . At large R , the convergence radius ρ of the expansion is found to be only slightly greater than unity, e.g. ρ = 1.0000000031 at the van der Waals minimum for the triplet state. The branch points determining ρ are calculated and used in a convergence acceleration procedure, which shows that the polarization expansion is a sum of two series — one converging quickly to the Coulomb energy and the other also converging , although extremely slowly for large R , to the negative of the exchange energy. The total series converges to the energy of the ground state of the hydrogen molecule. A simple formula describing the large-order behavior of the polarization series at large R is derived and used to show that the exchange energy can be accurately calculated from the knowledge of three consecutive large-order polarization energies.

Adiabatic potential energy curves for the b and e3Σu+ states of the hydrogen molecule

Abstract Calculations of the Born-Oppenheimer (BO) potential energy curves and adiabatic corrections for the b and e 3 Σ u + states of the hydrogen molecule have been performed using explicitly correlated wavefunctions in elliptic coordinates. The calculated potential energy curves are more accurate than any previous results for the above-mentioned states. The energies of the vibrational levels and rotational constants for the e 3 Σ u + state have been computed and very good agreement with experimental data has been found. It is shown that the homogeneous nonadiabatic corrections, estimated in this work, if taken into account, improve the agreement between theory and experiment. If, in addition, the small convergence error in the BO calculation, estimated as 0.3 cm −1 in the vicinity of the equilibrium, is added to the theoretical dissociation energy, D 0 , perfect agreement for the lowest vibrational levels of H 2 and D 2 is obtained.

Symmetry-adapted perturbation theory of potential-energy surfaces for weakly bound molecular complexes

Abstract The symmetry-adapted perturbation theory (SAPT) expansions for the intermolecular interaction energies can provide potential energy surfaces for weakly bound complexes such as van der Waals molecules or systems forming hydrogen bonds. The convergence properties of SAPT expansions are discussed. New results are presented for the Hirschfelder-Silbey (HS) method applied through high order to the interaction of two ground-state hydrogen atoms. As has been shown for the case of the interaction of a hydrogen atom with a proton, the HS theory converges very well. At low order this theory provides results very close to those of the symmetrized Rayleigh-Schrodinger (SRS) approach. In particular, the differences are negligible at the second order, i.e. at the level which can be practically applied to larger systems. Our results indicate that these two SAPT methods properly account for the electron exchange effects. The singlet-triplet splitting at the van der Waals minimum, obtained from the SRS exchange energy through second order, is considerably more accurate than that obtained from the asymptotically exact Herring and Flicker formula. The many-body version of the SRS theory is briefly discussed and the results of its applications to several many-electron systems (He 2 , He-K + , Ar-H 2 , He-HF and Ar-HF) are presented. In all cases a very good agreement, generally within a few per cent or less, between theoretical and experimental binding energies was found.

Unusual double-minimum potential energy curves: The h and g 3Σg+ states of the hydrogen molecule

Abstract Born-Oppenheimer potential energy curves and adiabatic corrections for the h and g 3 Σ g + states of the hydrogen molecule have been computed using explicitly correlated wavefunctions in elliptic coordinates. The calculated potential energy curves are more accurate than any previous results for the above states. It is shown that, in contrast to the Born-Oppenheimer results, the adiabatic potential energy curves for the h and g states are characterized by double-minimum functions. The energies of the vibrational levels and rotational constants for both states have been computed. Large differences have been found between theoretical and experimental results. It is, however, possible that the irregular changes of the rotational constant with increasing vibrational excitation, found in the present work, if taken into account, may change the assignment of the experimental term values.

Ab initio potential energy curve for the J1Δg state of the hydrogen molecule

Abstract The Born-Oppenheimer potential energy curve for the J 1 Δ g state of the hydrogen molecule was computed using highly flexible wavefunction in the form of a 60-term expansion in elliptic coordinates. The vibrational Schrodinger equation for the J state was solved for H 2 , HD, and D 2 . For H 2 the resulting energies are compared with the experimental values and it is shown that the adiabatic effects are likely to be responsible for the main part of the existing discrepancy between theoretical and experimental values. For HD the disagreement is too great to be attributable to approximations in the present work and therefore it is suggested that the J state of HD was incorrectly determined.

On the ionization potential of H2

Abstract The relativistic and radiative corrections to the ground state energy of H + 2 have been calculated and employed to get the theoretical value of the ionization potential of the hydrogen molecule IP = 124416.8 cm −1 .

AB-Initio Methods in Calculations of Intermolecular Interaction Energies

A general formulation of the perturbation theory approach to intermolecular interactions is presented and recent progress in computations of various interaction energy components, mostly for model systems, is discussed. In the second part a review is given of the recent work on the nonadditivity of interactions between closed-shell systems.