Modellek a kvantumkémiában = Models in Quantum Chemistry

Lineárisan skálázódó módszert fejlesztettünk ki abból a célból, hogy elkerüljük az egyelektron Hamilton-mátrixok diagonalizálását, amely köbösen skálázódó procedúra. A multikonfigurációs perturbációszámítás több változátát dolgoztuk ki, teszteltük, és hasonlítottuk össze más perturbációs sémákkal. Bevezettük a hiper-hartree-Fock módszert, ami magasabb rangú (több, mint kételektron-kölcsönhatást tartalmazó) operátorok speciális átlagolási szisztémája. A full-CI probléma skálázódási tulajdonságait ritka-mátrixos technikák alkalmazásával javítottuk. A lokális kémiai kölcsönhatások leírása céljából javasoltuk az ún. FLMO (Frozen Localized Molecular Orbitals) eljárást, amely a Hartree-Fock megoldást a molekulapályák explicit megkonstruálása nélkül szolgáltatja az egész nagy molekulára a sűrűségmátrixon keresztül, a korralációt azonban csak az aktív molekularészletre szám1tja ki. Kimutattuk, hogy a korrelációs energia explicit funkcionálja a Hartree-Fock sűrűségmátrixnak, és a levezettük másodrendű energiaképlet funkcionálját. A kutatás során 21 tudományos közleményt publikáltunk nemzetközi folyóiratokban. | A linear-scaling algorithm was developed for avoiding the diagonalization of large one-electron Hamiltonian matrices, which is a cubicly scaling procedure. Several versions of the multi-configuration perturbation theory was developed, tested, and compared to other methods. The so-called hyper Hartree-Fock methods was introduced, which is a special averaging scheme for high-rank Hamiltonians, i.e., those describing higher than two-particle interactions. To describe local interactions in chemical systems, the FLMO (Frozen Localized Molecular Orbitals) model was developed, which avoids constructing molecular orbitals but solves the Hartree-Fock problem via the density matrix, then computes electron correlation for the active site only. It was proven that the correlation energy is an explicit functional of the Hartree-Fock density matrix, and this functional was constructed at the second order. Te project resulted 21 publications in international journals

A general-order local coupled-cluster method based on the cluster-in-molecule approach

A general-order local coupled-cluster (CC) method is presented which has the potential to provide accurate correlation energies for extended systems. Our method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with the frozen natural orbital (NO) techniques widely used for the cost reduction of correlation methods. The occupied molecular orbitals (MOs) are localized, and for each occupied MO a local subspace of occupied and virtual orbitals is constructed using approximate Moller-Plesset NOs. The CC equations are solved and the correlation energies are calculated in the local subspace for each occupied MO, while the total correlation energy is evaluated as the sum of the individual contributions. The size of the local subspaces and the accuracy of the results can be controlled by varying only one parameter, the threshold for the occupation number of NOs which are included in the subspaces. Though our local CC method in its present form scales as the fifth power of the system size, our benchmark calculations show that it is still competitive for the CC singles and doubles (CCSD) and the CCSD with perturbative triples [CCSD(T)] approaches. For higher order CC methods, the reduction in computation time is more pronounced, and the new method enables calculations for considerably bigger molecules than before with a reasonable loss in accuracy. We also demonstrate that the independent calculation of the correlation contributions allows for a higher order description of the chemically more important segments of the molecule and a lower level treatment of the rest delivering further significant savings in computer time. (C) 2011 American Institute of Physics. [doi:10.1063/1.3632085

High-Accuracy Thermochemistry of Atmospherically Important Fluorinated and Chlorinated Methane Derivatives

High-precision quantum chemical calculations have been performed for atmospherically important halomethane derivatives including CF, CF3, CHF2, CH2F, CF2, CF4, CHF, CHF3, CH3F, CH2F2, CCl, CCl3, CHCl2, CH2Cl, CCl2, CCl4, CHCl, CHCl3, CH3Cl, CH2Cl2, CHFCl, CF2Cl, CFCl2, CFCl, CFCl3, CF2Cl2, CF3Cl, CHFCl2, CHF2Cl, and CH2FCl. Theoretical estimates for the standard enthalpy of formation at 0 and 298.15 K as well as for the entropy at 298.15 K are presented. The determined values are mostly within the experimental uncertainty where accurate experimental results are available, while for the majority of the considered heat of formation and entropy values the present results represent the best available estimates

An efficient linear-scaling CCSD(T) method based on local natural orbitals

An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kallay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Moller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets. (C) 2013 AIP Publishing LLC