Grzegorz Chal

Critical evaluation of some computational approaches to the problem of basis set superposition error

The basis set extension (BSE) effects such as primary and secondary basis set superposition errors (BSSE) are discussed on the formal and numerical ground. The symmetry‐adapted perturbation theory of intermolecular forces offers an independent reference point to determine efficacy of some computational approaches aiming at elimination of BSSE. The formal and numerical results support the credibility of the function counterpoise method which dictates that the dimer energy calculated within a supermolecular approach decomposes into monomer energies reproduced with the dimer centered basis set and the interaction energy term which also takes advantage of the full dimer basis. Another consistent approach was found to be Cullen’s ‘‘strictly monomer molecular orbital’’ SCF method [J. M. Cullen, Int. J. Quantum Chem. Symp. 25, 193 (1991)] in which all BSE effects are a priori eliminated. This approach misses, however, the charge transfer component of the interaction energy. The SCF and MP2 results obtained withi...

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...

Ab initio study of the potential energy surface of CH4‐H2O

The potential energy surface of CH4‐H2O is calculated through the fourth‐order Mo/ller–Plesset perturbation theory. In an attempt to obtain basis‐set saturated values of interaction energies the extended basis sets are augmented by bond functions which simulate the effects of high‐symmetry polarization functions. The absolute minimum occurs for the configuration involving the C–H‐O hydrogen‐bond in which O‐H points toward one of the faces of the CH4 tetrahedron. The equilibrium C–O separation is equal to 6.8 a0 which corresponds to the bond energy of 0.83 kcal/mol. Due to basis set unsaturation of the dispersion energy the bond energy may still be underestimated by about 0.05 kcal/mol. The secondary minimum involving the C‐H–O hydrogen‐bond is some 0.2 kcal/mol less stable, and the corresponding C–O distance is longer by 0.6 a0. The anisotropy of the potential energy surface is analyzed via the perturbation theory of intermolecular forces. The binding in CH4‐H2O is chiefly due to the dispersion energy whi...

Structure and energetics of van der Waals complexes of carbon monoxide with rare gases. He–CO and Ar–CO

The potential energy surfaces for Ar–CO and He–CO were calculated at the fourth order Mo/ller–Plesset perturbation theory and analyzed using perturbation theory of intermolecular forces. Both the complexes reveal only one minimum related to the approximately T‐shaped geometry. For Ar–CO, our best ab initio estimates of Re and De are 3.70 A and 496 μhartrees, respectively, and the optimal angle Rg–com–O is about 80°. For He–CO, our best Re and De are 3.4 A and 100 μhartrees, respectively, at the optimal angle Rg–com–O of 70°. Our geometrical parameters agree very well with the experimental data. Our ab initio well depths are estimated to be within ±5% in error and are expected to be the most accurate in the literature so far. The De values were obtained with extended basis sets which included bond functions. Basis set effects on the dispersion and electrostatic correlation terms that are caused by bond functions were also analyzed. Both complexes are bound by dispersion forces, but the anisotropy of the in...

Analysis of the potential energy surface of Ar–NH3

The combination of supermolecular Mo/ller–Plesset treatment with the perturbation theory of intermolecular forces is applied in the analysis of the potential energy surface of Ar–NH3. Anisotropy of the self‐consistent field (SCF) potential is determined by the first‐order exchange repulsion. Second‐order dispersion energy, the dominating attractive contribution, is anisotropic in the reciprocal sense to the first‐order exchange, i.e., minima in one nearly coincide with maxima in the other. The estimated second‐order correlation correction to the exchange effect is nearly as large as a half ΔESCF in the minimum and has a ‘‘smoothing’’ effect on the anisotropy of e(20)disp. The model which combines ΔESCF with dispersion energy (SCF+D) is not accurate enough to quantitatively describe both radial and angular dependence of interaction energy. Comparison is also made between Ar–NH3 and Ar–PH3, as well as with the Ar dimer.

On the role of bond functions in interaction energy calculations: Ar⋅⋅⋅HCl, Ar⋅⋅⋅H2O, (HF)2

We analyze the effect of an extended set of bond functions on the SCF and MP2 interaction energies, and their SAPT perturbation components; electrostatic, induction, dispersion, and exchange. The electrostatic, induction, and exchange terms at the SCF level prove to be largely independent. The dispersion energy is substantially improved and the improvement did not depend much on the bond‐function location. In contrast, the electrostatic‐correlation term is usually seriously distorted and the distortion strongly dependent on the bond‐function location. It was also shown that the distortion may be significantly reduced by appropriate shifting of the location. Only then the interaction energies obtained with bond functions may be considered reliable. It is strongly recommended to control the electrostatic‐correlation term. We also present samples of accurate results (within 5% error bar) for the Ar–HCl, Ar–H2O, and (HF)2 complexes.

Intermolecular Potential of the Methane Dimer and Trimer

The Heitler–London (HL) exchange energy is responsible for the anisotropy of the pair potential in methane. The equilibrium dimer structure is that which minimizes steric repulsion between hydrogens belonging to opposite subsystems. Dispersion energy, which represents a dominating attractive contribution, displays an orientation dependence which is the mirror image of that for HL exchange. The three‐body correction to the pair potential is a superposition of HL and second‐order exchange nonadditivities combined with the Axilrod–Teller dispersion nonadditivity. A great deal of cancellation between these terms results in near additivity of methane interactions in the long and intermediate regions.

The nonadditive interactions in the Ar2HF and Ar2HCl clusters: An ab initio study

The three‐body effects in the Ar2HX (X=F, Cl) are studied by means of the supermolecular Mo/ller–Plesset perturbation theory in conjunction with the perturbation theory of intermolecular forces. In both systems the nonadditive interactions are large and repulsive around the equilibrium geometry. The in‐plane bending potential of H–F in the Ar2HF cluster reveals a double minimum with the barrier of ca. 2–3 cm−1. The barrier is due to the three‐body interactions. In Ar2HCl the analogous potential has a single minimum, and the three‐body effects make it shallower. The three‐body interaction energy is dissected into its components such as exchange, polarization, and dispersion. The anisotropy of the total nonadditvity in Ar2HF is dominated by polarization and exchange effects, and, consequently, it can be well reproduced at the self‐consistent field level of theory. The overall nonadditivity in Ar2HCl is quite similar in magnitude, but it displays a different composition. The most anisotropic is polarization ...

Partitioning of interaction energy in van der Waals complexes involving excited state species: The He(1S)+Cl2(B 3Πu) interaction

The partitioning of interaction energy between a closed‐shell and an open‐shell system is proposed. This allows us to describe the unrestricted Mo/ller–Plesset interaction energy as a sum of fundamental contributions: electrostatic, exchange, induction and dispersion. The supermolecular energies derived within unrestricted Mo/ller–Plesset perturbation theory are analyzed in terms of perturbation theory of intermolecular forces. The latter has been generalized to allow for the description of monomer wave functions within the unrestricted Hartree–Fock approach. The method is applied to the potential energy surfaces for the first excited triplet states, 3A′ and 3A″, of the He+Cl2(3Πu) complex. The 3A′ and 3A″ potential energy surfaces have different shapes. The lower one, 3A′, has a single minimum for the T‐shaped structure. The higher one, 3A″, has the global minimum for the T‐shaped structure and the secondary minimum for a linear orientation. The calculated well depth for the 3A′ state is 31.1 cm−1 at the...

Analysis of the intermolecular potential of Ar-CH4 : an ab initio study

The perturbation theory of intermolecular forces in conjunction with the supermolecular Mo/ller–Plesset treatment is applied in the analysis of the potential energy surface of Ar–CH4. The anisotropy of the Ar–CH4 potential energy surface is chiefly due to exchange repulsion. In the equilibrium structure, Ar approaches the face of CH4 tetrahedron thus avoiding contacts with C–H bonds. The equilibrium Ar–C separation was found equal to 7.5 a0 and the De energy to 113 cm−1. We estimate that our De may be too small by up to 25% with respect to the accurate value. The properties of Ar–CH4 are also compared with other Ar‐molecule systems, such as Ar–NH3, Ar–H2O, and Ar–HCl. We find that the equilibrium structures of weak proton donors bound to Ar (CH4, NH3) are determined by the exchange repulsion, while those of efficient proton donors, such as HCl (and to a lesser extent H2O), result from the strong polarization of Ar in the field of a molecule.