Robert Moszynski

On decomposition of second‐order Mo/ller–Plesset supermolecular interaction energy and basis set effects

The basis set effects on the total self‐consistent field (SCF) and second‐order Mo/ller–Plesset (MP2) interaction energies in the HF dimer (in the equilibrium geometry) are investigated in relation to their components: electrostatic, exchange, induction, and dispersion, calculated within the framework of intermolecular Mo/ller–Plesset perturbation theory (IMPPT). The basis set dependence of the SCF interaction energy in the HF dimer is almost exactly determined by the electrostatic contribution. The exchange, induction, and the SCF‐deformation terms are found substantially less sensitive. The MP2 correlation contribution reflects primarily the basis set dependence of dispersion. However, an accurate image of the basis set dependence is reproduced only if the electrostatic‐correlation term is considered as well. Other correlation contributions: the deformation‐ correlation and exchange terms are found to be much less sensitive to basis set effects. All these conclusions are valid only under the condition t...

Symmetry‐adapted perturbation theory calculation of the Ar–H2 intermolecular potential energy surface

The many‐body symmetry adapted perturbation theory has been applied to compute the Ar–H2 potential energy surface. Large basis sets containing spdfgh‐symmetry orbitals optimized for intermolecular interactions have been used to achieve converged results. For a broad range of the configuration space the theoretical potential energy surface agrees to almost two significant digits with the empirical potential extracted from scattering and infrared spectroscopy data by Le Roy and Hutson. The minimum of our theoretical potential is em=−164.7 cal/mol and is reached at the linear geometry for the Ar–H2 distance Rm=6.79 bohr. These values agree very well with corresponding empirical results em=−161.9 cal/mol and Rm=6.82 bohr. For the first time such a quantitative agreement has been reached between theory and experiment for a van der Waals system that large. Despite such excellent agreement in the overall potential, the exponential and the inverse R components of it agree to only about 20%.

Symmetry-adapted perturbation theory for the calculation of Hartree-Fock interaction energies

A symmetry-adapted perturbation theory is formulated for the calculation of Hartree-Fock interaction energies of closed-shell dimers. The proposed scheme leads to a basis-set-independent interpretation of the Hartree-Fock interaction energy in terms of basic concepts of the theory of intermolecular forces: electrostatics, exchange and induction. Numerical results for different geometries of HE2, Ne2, He-C2H2, He-CO, Ar-HF, (HF)2 and (H2O)2 complexes show that in the region of the van der Waals minimum the proposed perturbation theory reproduces accurately the Hartree-Fock interaction energy. This fast convergence and relatively small computational cost of the proposed perturbation scheme suggest that this method is a practical alternative for the standard supermolecular approach.

Many‐body theory of exchange effects in intermolecular interactions. Density matrix approach and applications to He–F−, He–HF, H2–HF, and Ar–H2 dimers

The first‐order exchange energy for the interactions of closed‐shell many‐electron systems is expanded as a perturbation series with respect to the Mo/ller–Plesset correlation potentials of the monomers. Explicit orbital formulas for the leading perturbation corrections are derived applying a suitable density matrix formalism. The numerical results obtained using the Mo/ller–Plesset perturbation expansion, as well as nonperturbative, coupled‐cluster type procedure, are presented for the interactions of He–F−, He–HF, H2–HF, and Ar–H2. It is shown that the correlation part of the first‐order exchange energy increases the uncorrelated results by 10% to 30% for the investigated range of configurations. The analysis of the total interaction energies for selected geometries of these systems shows that at the present level of theory the symmetry‐adapted perturbation approach correctly accounts for major intramonomer correlation effects and is capable to accurately reproduce the empirical potential energy surfaces.

Many‐body theory of exchange effects in intermolecular interactions. Second‐quantization approach and comparison with full configuration interaction results

Explicitly connected many‐body perturbation expansion for the energy of the first‐order exchange interaction between closed‐shell atoms or molecules is derived. The influence of the intramonomer electron correlation is accounted for by a perturbation expansion in terms of the Mo/ller–Plesset fluctuation potentials WA and WB of the monomers or by a nonperturbative coupled‐cluster type procedure. Detailed orbital expressions for the intramonomer correlation corrections of the first and second order in WA+WB are given. Our method leads to novel expressions for the exchange energies in which the exchange and hybrid integrals do not appear. These expressions, involving only the Coulomb and overlap integrals, are structurally similar to the standard many‐body perturbation theory expressions for the polarization energies. Thus, the exchange corrections can be easily coded by suitably modifying the existing induction and dispersion energy codes. As a test of our method we have performed calculations of the first‐...

BASECOL2012: A collisional database repository and web service within the Virtual Atomic and Molecular Data Centre (VAMDC)

The BASECOL2012 database is a repository of collisional data and a web service within the Virtual Atomic and Molecular Data Centre (VAMDC, http://www.vamdc.eu). It contains rate coefficients for the collisional excitation of rotational, ro-vibrational, vibrational, fine, and hyperfine levels of molecules by atoms, molecules, and electrons, as well as fine-structure excitation of some atoms that are relevant to interstellar and circumstellar astrophysical applications. Submissions of new published collisional rate coefficients sets are welcome, and they will be critically evaluated before inclusion in the database. In addition, BASECOL2012 provides spectroscopic data queried dynamically from various spectroscopic databases using the VAMDC technology. These spectroscopic data are conveniently matched to the in-house collisional excitation rate coefficients using the SPECTCOL sofware package (http:// vamdc.eu/software), and the combined sets of data can be downloaded from the BASECOL2012 website. As a partner of the VAMDC, BASECOL2012 is accessible from the general VAMDC portal (http://portal.vamdc.eu) and from user tools such as SPECTCOL.

A new He–CO interaction energy surface with vibrational coordinate dependence. I. Ab initio potential and infrared spectrum

The intermolecular potential energy surface of the He–CO complex including the CO bond length dependence has been calculated using symmetry-adapted perturbation theory (SAPT). The potential has a minimum of em=−23.734 cm−1 with Rm=6.53 bohr at a skew geometry (ϑm=48.4°) if the molecular bond length is fixed at the equilibrium value of 2.132 bohr. We have applied the potential in the calculation of bound state levels and the infrared spectrum for the 3He–CO and 4He–CO complexes. The computed ab initio transition frequencies are found to agree within 0.1 cm−1 with experiment. In paper II [J. P. Reid, H. M. Quiney, and C. J. S. M. Simpson, J. Chem. Phys. 107, 9929 (1997)], the potential surface is used to calculate vibrational relaxation cross sections and rate constants.

Many‐body perturbation theory of electrostatic interactions between molecules: Comparison with full configuration interaction for four‐electron dimers

Many‐body perturbation theory for a direct calculation of the electrostatic interaction energy is developed. Since no multipole expansion is used, the obtained electrostatic energy includes the short‐range contributions resulting from the overlap (penetration) of monomers’ charge distributions. The influence of intramonomer electronic correlation is accounted for by the perturbation expansion in terms of the Mo/ller–Plesset type fluctuation potentials for the interacting molecules. Two types of expansions are introduced: one based on the standard Mo/ller–Plesset expansion of the electron density, and the second accounting for the perturbation induced modifications of the monomer’s Fock operators, i.e., for the so‐called response or orbital relaxation effects. Explicit orbital expressions for the terms through the fourth order in the intramonomer fluctuation potentials are derived. In this way the leading three‐particle correlation contribution to the electrostatic energy is taken into account. Numerical r...

Many‐body theory of intermolecular induction interactions

The second‐order induction energy in the symmetry‐adapted perturbation theory is expressed in terms of electron densities and polarization propagators at zero frequency of the isolated monomers. This expression is used to derive many‐body perturbation series with respect to the Mo/ller–Plesset type correlation potentials of the monomers. Two expansions are introduced—one based on the standard Mo/ller–Plesset expansion of electron densities and polarization propagators, and the second accounting for the so‐called response or orbital relaxation effects, i.e., for the perturbation induced modification of the monomer’s Fock operators. Explicit orbital formulas for the leading perturbation corrections that correctly account for the response effects are derived through the second order in the correlation potential. Numerical results are presented for several representative van der Waals complexes—a rare gas atom and an ion Ar–Na+, Ar–Cl−, and He–F−; a polar molecule and an ion H2O–Na+ and H2O–Cl−; two polar mol...

Symmetry‐adapted perturbation theory of nonadditive three‐body interactions in van der Waals molecules. I. General theory

Symmetry‐adapted perturbation theory of pairwise nonadditive interactions in trimers is formulated, and pure three‐body polarization and exchange components are explicitly separated out. It is shown that the three‐body polarization contributions through the third order of perturbation theory naturally separate into terms describing the pure induction, mixed induction–dispersion, and pure dispersion interactions. Working equations for these components in terms of molecular integrals and linear and quadratic response functions are derived. These formulas have a clear, partly classical, partly quantum mechanical, physical interpretation. The asymptotic expressions for the second‐ and third‐order three‐body polarization contributions through the multipole moments and (hyper)polarizabilities of the isolated monomers are reported. Finally, assuming the random phase approximation for the response functions, explicit orbital formulas for the three‐body polarization terms are derived. The exchange terms are also c...