Denis Bokhan

Exact-exchange density functional theory for hyperpolarizabilities

Time-dependent density functional theory (TDDFT) employing the exact-exchange functional (TDDFTx) has been formulated using the optimized effective potential method for the beta static hyperpolarizabilities, where it reduces to coupled-perturbed Kohn-Sham theory. A diagrammatic technique is used to take the functional derivatives for the derivation of the adiabatic second kernel, which is required for the analytical calculation of the beta static hyperpolarizabilities with DFT. The derived formulas have been implemented using Gaussian basis sets. The structure of the adiabatic exact-exchange second kernel is described and numerical examples are presented. It is shown that no current DFT functional satisfies the correct properties of the second kernel. Not surprisingly, TDDFTx, which corrects the self-interaction error in standard DFT methods and has the correct long-range behavior, provides results close to those of time-dependent Hartree-Fock in the static limit.

Explicitly correlated similarity transformed equation-of-motion coupled-cluster method

Similarity transformed equation-of-motion method, based on linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] model, has been formulated and implemented. An extension of similarity transformation operator is introduced in order to treat short-range correlation effects for excited states. Additionally, effective reduction of the number of active virtuals can be obtained by such modification. Numerical tests for sets of valence and Rydberg excited states of several molecules are conducted. Statistical measures of errors in excitation energies show that explicitly correlated results are accurate up to 0.1 e.V already at a double-ζ level compared to those in the complete basis set limit, if the excitation energy is not too close to an ionization threshold. An example of long-range charge transfer excitation is also considered and highly accurate results are obtained.

Interconnection between functional derivative and effective operator approaches to ab initio density functional theory

In the recent implementation of the second-order Optimized Effective Potential method (R.J. Bartlett, I. Grabowski, S. Hirata, S. Ivanov, J. chem. Phys. (submitted).), the effective potential is determined by requiring that the perturbative contribution to the reference density vanishes through second order. We show that in general, such a density condition for any finite order leads to an OEP equation equivalent to that obtained via the functional derivative of the corresponding order energy. We develop diagrammatic tools for functional differentiation to facilitate the transition between many-body diagrammatic expressions and those of density functional theory.

Electric multipole moments calculation with explicitly correlated coupled-cluster wavefunctions

A method of calculation of expectation values of dipole and quadrupole moments with wavefunctions, corresponding to linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] model has been formulated and implemented. As a part of algorithm, explicitly correlated version of Λ equations has also been derived and implemented. Numerical tests, conducted for sets of molecules, show that explicitly correlated results for expectation values of dipole moment are accurate up to 0.01 a.u. already at a double-ζ level compared to those in the complete basis set limit. The corresponding results for quadrupole moments at double-ζ level are accurate up to 0.1 a.u., while for the triple-ζ bases errors do not exceed 0.01 a.u.

Explicitly correlated coupled-cluster theory for static polarizabilities

A method of calculation of static polarizabilities with wavefunctions, corresponding to linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] model, has been formulated and implemented. For the proper description of the response of system on applied electric field, modified ansatz is introduced for geminal part of cluster operators. Such extension of CCSD(F12) model provides balanced description of both perturbed and unperturbed wave functions, what leads to the increase of the accuracy of target polarizabilities. As a part of algorithm, explicitly correlated version of coupled-perturbed CCSD equations has also been derived and implemented. Numerical tests conducted for the set of eight molecules show good agreement between static polarizabilities, calculated with developed explicitly correlated approach and corresponding complete basis set results in regular CCSD already at triple-ζ level.

Explicitly correlated second-order Møller-Plesset perturbation theory employing pseudospectral numerical quadratures.

We implemented explicitly correlated second-order Møller-Plesset perturbation theory with numerical quadratures using pseudospectral construction of grids. Introduction of pseudospectral approach for the calculation of many-electron integrals gives a possibility to use coarse grids without significant loss of precision in correlation energies, while the number of points in the grid is reduced about nine times. The use of complementary auxiliary basis sets as the sets of dealiasing functions is justified at both theoretical and computational levels. Benchmark calculations for a set of 16 molecules have shown the possibility to keep an error of second-order correlation energies within 1 milihartree (mH) with respect to MP2-F12 method with dense grids. Numerical tests for a set of 13 isogyric reactions are also performed.

Excitation energies with spin-orbit couplings using equation-of-motion coupled-cluster singles and doubles eigenvectors

A method of calculation of excited states with spin-orbit couplings, which utilizes left and right eigenvectors of equation-of-motion coupled-cluster singles and doubles model has been formulated and implemented. The spin-orbit interactions are introduced by using the spin-orbit mean field approximation of the Briet-Pauli Hamiltonian. In order to evaluate all the necessary matrix elements, a scheme based on the diagrammatic representation of the second-quantized form of the spin-orbit interaction operator and the standard rules of second-quantized algebra is presented. We posit that this scheme is general and much simpler to use than the often used rules derived for the configuration state functions by using the Wigner-Eckart theorem. We show that the spin-orbit coupled states (i.e., target relativistic states) must satisfy specific conditions in order to classify them according to the double group symmetry. This interrelation between the structure of the target relativistic states and its double group symmetry is discussed in detail. An algorithm to classify the target states according to the irreducible representation of the double group symmetry is offered and implemented. Numerical tests for several atoms and molecules show good agreement of predicted and experimental spin-orbit splittings of the target excited states.

Long-range dispersion C6 coefficient for SF6 dimer: Experimental and theoretical study

The long-range dispersion C6 coefficient for the SF6 dimer is experimentally measured using a technique that uses the expansion of a supersonic pulse jet into a vacuum. A dynamic model of the jet enables us to correlate the position of the maximal peak in the time-of-flight spectrum with the initial conditions of the experiment and the parameters of the intermolecular interaction potential. Due to the low temperature of the jet target, the C6 coefficient can be extracted directly from the experimental results. Theoretical calculation of the C6 dispersion coefficient is also performed by using linearly approximated explicitly correlated coupled-cluster singles and doubles (CCSD(F12)) method with the subsequent utilization of the Casimir-Polder formula. Good agreement of experimental and theoretical results confirms the reliability of results.