awomir M. Cybulski

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...

Calculations of magnetic properties. IV. Electron‐correlated magnetizabilities and rotational g factors for nine small molecules

Calculations of the magnetizabilities and the rotational g factors at the self‐consistent‐field (SCF) and second‐order Mo/ller–Plesset perturbation theory (MP2) levels of theory are reported for H2, N2, F2, HF, CO, HCN, HNC, H2O, and NH3. The sums rules, that verify the reliability of the calculations, are shown to be well satisfied. The second‐order correlation corrections to the magnetizabilities are found to be small, thus substantiating the generally observed good agreement between the experimental and SCF results. Vibrational corrections to the properties of the diatomic molecules are given. Very good agreement is found between the experimental and vibrationally corrected MP2 rotational g factors for the diatomic molecules.

Calculations of magnetic properties. II. Electron‐correlated nuclear shielding constants for nine small molecules

Calculations of the nuclear magnetic shielding constants at the self‐consistent‐field (SCF) and second‐order Mo/ller–Plesset (MP2) levels of theory are reported for H2, N2, F2, HF, CO, HCN, HNC, H2O, and NH3. The reliability of the calculations is verified by the high degree of satisfaction of the appropriate sum rule. The second‐order correlation corrections to the shielding constants are found to be particularly important for the multiply bonded atoms in molecules such as N2, CO, HCN, and HNC. Vibrational corrections to the shielding constants for the diatomic molecules are shown to be significant.

Calculation of magnetic properties. VI. Electron correlated nuclear shielding constants and magnetizabilities for thirteen small molecules

The theory of relaxed density matrices has been developed for the calculation of second-order response properties at third-order Mo/ller–Plesset (MP3) and linearized coupled cluster double excitation (L-CCD) levels of theory. The ensuing algorithm is applied to the determination of the isotropic and anisotropic nuclear magnetic shielding constants and magnetizabilities for thirteen molecules (H2, N2, F2, HF, CO, HCN, HNC, H2O, NH3, H2O2, HCHO, CH4, and HCCH). The method uses conventional gauge-variant orbitals but, by using large basis sets, produces results which are equivalent to those found with gauge-including orbitals. In general the L-CCD values of the magnetizabilities are consistent with those obtained with multiconfigurational self-consistent-field (MCSCF) methods for molecules which have been treated by this method. For the nuclear shieldings, when there is a difference between L-CCD and MP3, the former gives results closer to the coupled-cluster singles and doubles level treatment augmented with a perturbation correction for connected triple excitations [CCSD(T)] which is our reference point. Again the results for the shieldings at the L-CCD level are quite good. We also use the paramagnetic components of the shieldings and magnetizabilities to determine the spin-rotation constants and rotational g tensors, respectively. These quantities are important since they may be compared more directly with experiment than the magnetizabilities and shieldings.

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...

Ab initio potential energy surfaces for He–Cl2, Ne–Cl2, and Ar–Cl2

The three-dimensional ground state potential energy surfaces for He–Cl2, Ne–Cl2, and Ar–Cl2 have been calculated using the single and double excitation coupled-cluster approach with noniterative perturbational treatment of triple excitations [CCSD(T)]. Calculations have been performed with the augmented correlation consistent triple zeta basis sets supplemented with an additional set of bond functions. Single point calculations for approximate minima have also been performed with several other basis sets including the quadruple zeta basis set (aug-cc-pVQZ) with bond functions. For He–Cl2 and Ar–Cl2 the CCSD(T) results show that the linear configuration is lower in energy than the T-shaped one. For Ne–Cl2 the CCSD(T) approach predicts the T-shaped configuration to be lower in energy. The linear configuration has been found to be more sensitive than the T-shaped one to the changes of the Cl–Cl bond length with the interaction becoming weaker when the Cl–Cl bond length is shortened from its equilibrium value...

Vibrational corrections for some electric and magnetic properties of H2, N2, HF, and CO

The effects of vibration on certain electric and magnetic properties of H2, N2, HF, and CO are reported. These properties include electric field gradients, generalized Sternheimer shielding constants, electric‐field‐gradient polarizabilities, nuclear shielding constants, and shielding polarizabilities. The calculations were based on both electron correlated and uncorrelated methods. Pure vibrational effects, where appropriate, were investigated as well as conventional vibrational averaging. It is found that in many cases vibration plays a very significant role.

Calculations of magnetic properties. V. Electron‐correlated hypermagnetizabilities (Cotton–Mouton effect) for H2, N2, HF, and CO

Calculations of the hypermagnetizabilities (η) at the self‐consistent‐field (SCF) and second‐order Mo/ller–Plesset perturbation theory (MP2) levels of theory are reported for H2, N2, HF, and CO. Electron correlation is found to be unimportant for H2, but very important for the other three molecules. The individual components of η are more affected by correlation effects than the hypermagnetizability anisotropy (Δη) which mediates the birefringence of a material in the presence of a magnetic field (the Cotton–Mouton effect). The zero‐point‐vibrational averaging, pure vibrational corrections, and frequency dependence are important for the individual components, but are less important for Δη due to cancellation between the various contributions. Excellent agreement is found with the previous theoretical results for H2, but only fair agreement with the experimental results for N2 and CO.

Magnetic optical rotation in H2 and D2

Results are reported of the first definitive calculation of the Verdet constant for H2 and D2. This constant governs the Faraday effect. A new and compact formalism is introduced and applied with the aid of explicitly electron correlated wave functions. After ro‐vibrational and thermal averaging (factors which affect the results by about 10%), our values are in good agreement with the experimental ones, which, at best, are probably only accurate to 1%. Approximations and an appropriate dispersion formula are also discussed. Our results show that for H2 and D2 the exact constant is almost exactly proportional to the so‐called normal Verdet constant for the experimentally accessible frequencies. The recommended dispersion formula for H2 is V≂2.0701 (ℏω/Eh)2/[0.2435−(ℏω/Eh)2]2×10−7 rad e a0 ℏ−1.

HYPERMAGNETIZABILITY ANISOTROPY (COTTON-MOUTON EFFECT) FOR H2 AND D2

Explicitly electron‐correlated wave functions have been used to calculate the hypermagnetizability anisotropy (Δη) for H2 and D2. This property is the essential feature of the birefringence of a material in the presence of a magnetic field (the Cotton–Mouton effect). The calculations were carried out in the framework of perturbation theory and both dispersion and vibrational effects were fully taken into account. A detailed analysis of our results is made and it is concluded that electron correlation and ‘‘pure’’ vibrational effects are less important than vibrational averaging and dispersion. The experimental results are only in fair agreement with our theoretical ones.