Academic literature on the topic 'Moller-Plesset Perturbation'

We carry out ab initio calculations, based on finite-field scheme, of the longitudinal polarizabilities (αL) and second hyperpolarizabilities (γL) of conjugated polyenes, and study the effects of electron correlation, with second-order Moller-Plesset perturbation theory and coupled cluster with singles and doubles method. Calculations with density functional theory are also made to compare with wave-function based methods. Our study shows that electron correlation reduces linear longitudinal polarizability and enhances longitudinal second hyperpolarizability for short polyenes, but the effects decrease as the chain increases; choosing appropriate basis sets is important when quantitative results are required.

The ab initio SCF method was applied to a conformation study of thiocarbamic acid. The 3-21 G calculations revealed that the trans isomer with the O-H···S intramolecular hydrogen bond is more stable than the cis isomer. The calculated rotational barrier for the rotation about the central C-N bond is very high, 125.5 kJ mol-1; this value, however, decreased to 106.2 kJ mol-1 by electron correlation determined at the 2nd order Moller-Plesset perturbation level. Proton affinities for the protonation of the electronegative atoms in the acid increase in the order of the atoms N, O and S. Changes in the Mulliken gross atomic populations are examined in dependence on the configuration and protonation of the acid.

A method to perform full quantum mechanical (ab initio) calculation of interaction energy involving a macromolecule like protein has recently been developed. This new scheme, named molecular fractionation with conjugate caps (MFCC), decomposes a protein molecule into amino acid-based fragments. These individual fragments are properly treated to preserve the chemical property of the bonds that are cut. Through proper combination of interaction energies between the molecule and individual fragments and their conjugate caps, the full protein-molecule interaction energy can be obtained to a high degree-of-accuracy by full ab initio calculations. Here we report a benchmark full ab initio calculation of interaction energy between a HIV-1 gp41 protein (with 982 atoms) and a water molecule at various geometries using HF (Hartree Fock), DFT (density functional theory) and MP2 (second-order Moller-Plesset perturbation theory) methods on a standard workstation.

The ab initio SCF method was applied to the protonation of the carbonyl group in carbamic acid and its methyl derivatives, viz. methyl carbamate and methyl N-methylcarbamate. Complete geometry optimization was accomplished for these compounds and their protonated species using the MINI-1, 3-21 G, and 6-31 G* bases and the proton affinities were calculated at the MINI-1, 3-21 G, 6-31 G*, and 6-31 G** levels. 2nd and 3rd order Moller-Plesset perturbation calculations were also performed for examining the effect of the correlation energy on the calculated protonation energies. The carbonyl protonation energies were found to increase in order carbamic acid < methyl carbamate < methyl N-methylcarbamate. The absolute values of calculated gas phase proton affinities depend on the basis used and way of evaluating the correlation energy. The results are discussed with respect to the theoretical proton affinities of structurally related amides and to related available theoretical gas phase proton affinities.

Low energy isomers of [Formula: see text] and Au4 were reexamined using the hybrid density functional B3LYP method and the couple-cluster method with the aug-cc-pVDZ-PP and aug-cc-pVTZ-PP basis sets. For [Formula: see text], the B3LYP method favors the zigzag isomer and the second order Moller–Plesset perturbation (MP2) total energy calculation favors the D2h rhombus isomer, whereas the couple-cluster singles and doubles with perturbative triples [CCSD(T)] level of theory favors the Y-shaped C2v isomer. The pyramid isomer is much higher in energy and could be easily excluded. The Gibbs free energy correction based on harmonic approximation suggests that the zigzag isomer is lower in free energy than the D2h rhombus isomer at 298.15 K. These results confirm that the Y-shaped C2v isomer is the global minimum at both 0 K and room temperature and is thus the major isomer to account for the experimental photoelectron spectrum. The zigzag isomer is suggested, as a minor isomer, to account for the weak second peak at 3.40 eV in the experimental photoelectron spectrum. For neutral Au4 , the zigzag isomer is more stable than D2h rhombus isomer at the B3LYP level and the D2h rhombus isomer is the global minimum on basis of all post Hartree–Fock levels of theory.

The work presented in this thesis is dedicated to developing inexpensive quantum-chemical models that are able to produce smooth and physically correct potential energy curves for the dissociation of single covalent bonds. It is well known that the energies produced by many ab initio theories scaling as the fifth order with the system size (for instance, second-order Moller-Plesset (MP2) and Epstein-Nesbet perturbation theories) diverge at large interatomic separations. We show that the divergent behavior of such perturbation schemes is due to a small number of terms in the energy expressions. Then, we demonstrate that the self-consistent replacement of these terms by their analogs from the coupled cluster theory (such as CCSD) allows one to redress the erroneous behavior of the perturbation theories without the damage to the overall scaling. We also investigate the accuracy of these hybrid perturbation theory-coupled cluster theories near equilibrium geometry. Judging from the computed spectroscopic constants and shapes of the potential energy curves, one such model, denoted MP2-CCSD(II) in this work, performs consistently better than the MP2 theory at essentially the same computational cost.

The first part of this work focuses on the characterization of systems which complex electronic structures require the application of multi-reference methods. The anti-tumor efficacy of the natural product Neocarzinostatin is based on the formation of diradicals and causes DNA cleavage and finally cytolysis. Computations on model systems performed in the present work show the influence of structural features on the mode of action and the efficacy of this antitumor-antibiotic. The cyclization of systems related to the enyne-cumulene framework like the enyne-allenes was investigated earlier and relations to the more unusual class of enyne-ketenes are analyzed. The class of enyne-ketenes (and also the enyne-allenes) show a broad spectrum of possible intermediates (diradicals, zwitterions, allenes). The electronic structures of these intermediates are also possible for the (heteroatom substituted) 1,2,4-cyclohexatriene and a model for their energetic sequence based on high-level multi-reference computations is proposed. In all three projects the application of multi-reference approaches is necessary to obtain a comprehensive picture of the reactivity and electronic structure but also shows up the limits inherently existing in the currently available programs with respect to the size of the molecules. In the second part, algorithms for a multi-reference Moller-Plesset perturbation theory (MR-MP2) program, designed to perform large-scale computations, were developed and implemented. The MR-MP2 approach represents the most cost-effective multireference ansatz and requires an efficient evaluation of the Hamilton matrix for which an algorithm is designed to instantly recognize only non-vanishing matrix elements and to employ the recurring interaction patterns of the Hamilton matrix. The direct construction of the Hamilton matrix is additionally parallelized to work on cluster environments
Der erste Teil der vorliegenden Arbeit beschäftigt sich mit der Charakterisierung von Systemen, deren komplexe elektronische Struktur die Anwendung von Multireferenz-Methoden erfordert. Die Antitumor-Wirkung des Naturstoffes Neocarzinostatin beruht auf der Bildung von Diradikalen und führt zur Spaltung der DNS und löst den Zelltod aus. Berechnungen an Modellsystemen zeigen den Einfluss der Strukturmotive auf die Wirkungsweise und die Wirksamkeit des Antitumor-Antibiotikums. Die Cyclisierung von Systemen, wie die Eninallene, die dem Enincumulen-Grundgerüst des aktivierten Neocarzinostatin-Chromophors verwandt sind, wurden schon in früheren Arbeiten untersucht und die Verwandtschaft zur ungewöhnlicheren Substanzklasse der Eninketene wird in dieser Arbeit analysiert. Diese Verbindungsklasse und die der Eninallene zeigen ein breites Spektrum an möglichen Intermediaten, wie Diradikale, Carbene, Zwitterionen und Allene, deren elektronische Strukturen auch bei (heterosubstituierten) 1,2,4 Cyclohexatrienen auftreten. Für diese Verbindungen wird ein Modell für die energetische Abfolge der elektronischen Strukturen auf Basis von hochwertigen Multireferenz-Rechnungen vorgeschlagen. In den drei aufgeführten Projekten ist die Anwendung von Multireferenz-Ansätzen notwendig um ein umfassendes Bild der Reaktivitäten und elektronischen Strukturen zu erhalten, zeigen im Hinblick auf große Moleküle aber auch die inhärenten Grenzen in den zur Zeit verfügbaren Programme auf. Im zweiten Teil der Arbeit wurden Algorithmen für ein Multireferenz-Moller-Plesset-Störungstheorie-Programmes (MR-MP2) entwickelt und implementiert. Der MR-MP2-Ansatz stellt den effizientesten Multireferenz-Ansatz dar und setzt eine geschickte und schnelle Berechnung der Hamilton-Matrix voraus. Hierfür ist ein Algorithmus konzipiert worden, der zum einen verschwindende Matrixelemente sofort erkennt und die sich wiederholenden Muster innerhalb der Hamilton-Matrix zu Nutze macht. Die Konstruktion der Hamilton-Matrix für das direkte Verfahren ist zudem für Clusterumgebungen parallelisiert

Perturbation theory (PT) is a method by which the energies and wavefunctions of a system of interest are expressed in terms of the known solutions of a presumably simpler reference system. The Rayleigh-Schrodinger expressions for the wavefunctions and energies of exact states are derived up to 3rd and 4th order, respectively. A simple application deals with substitution effects on the absorption color of organic chromophores. The Moller-Plesset correlation energy is derived in 2nd order (MP2). It is then shown how bi-linear perturbations associated with the electric and magnetic field operators of chapter 21 define properties such as polarizability, magnetizability or susceptibility, nuclear magnetic resonance shielding and spin-spin coupling, harmonic nuclear vibrational frequencies, and many other properties. The bi-linear magnetic perturbation energy is derived for paramagnetic systems with low-energy thermally populated degenerate states. The chapter concludes with a description of derivative techniques for approximate quantum chemical methods.

Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient determination of the exact exchange energy. When going beyond mean field approaches, e.g. for Moller-Plesset perturbation theory, RPA and Coupled-Cluster methods, or the GW methods, it becomes necessary to manipulate higher-order sparse tensors. Very similar problems are also encountered in other domains, like signal processing, data mining, computer vision, and machine learning. With the idea that the most of the tensor operations can be mapped to matrices, we have implemented sparse tensor algebra functionalities in the frames of the sparse matrix linear algebra library DBCSR (Distributed Block Compressed Sparse Row). DBCSR has been specifically designed to efficiently perform blocked-sparse matrix operations, so it becomes natural to extend its functionality to include tensor operations. We describe the newly developed tensor interface and algorithms. In particular, we introduce the tensor contraction based on a fast rectangular sparse matrix multiplication algorithm.