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Takeshi Nagata - One of the best experts on this subject based on the ideXlab platform.
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Perturbation Expansion theory corrected from basis set superposition error ii charge transfer pair correlation and dispersion terms
Theoretical Chemistry Accounts, 2006Co-Authors: Suehiro Iwata, Takeshi NagataAbstract:The second-order Perturbation theory based on the locally projected molecular orbitals is developed. A few test calculations with cc-pVDZ and aug-cc-pVDZ basis sets are carried out for the dimers, (H2O)2 and (HF)2. The charge transfer terms remove the deficiency of the locally projected self-consistent field method for molecular interaction (LP SCF MO MI), and the potential energy curves calculated with aug-cc-pVDZ are very close to the corresponding curves of the counterpoise-corrected SCF energy. Only after adding the spin-exchanged dispersion type to the dispersion and intra-molecular pair correlation terms, the calculated potential energy curves become close to those of the counterpoise-corrected second-order Moller–Plesset (MP2). Pragmatic approaches for reducing the influence of the basis set superposition error are proposed.
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Perturbation Expansion theory corrected from basis set superposition error i locally projected excited orbitals and single excitations
Journal of Chemical Physics, 2004Co-Authors: Takeshi Nagata, Suehiro IwataAbstract:The locally projected self-consistent field molecular orbital method for molecular interaction (LP SCF MI) is reformulated for multifragment systems. For the Perturbation Expansion, two types of the local excited orbitals are defined; one is fully local in the basis set on a fragment, and the other has to be partially delocalized to the basis sets on the other fragments. The Perturbation Expansion calculations only within single excitations (LP SE MP2) are tested for water dimer, hydrogen fluoride dimer, and colinear symmetric ArM+Ar (M=Na and K). The calculated binding energies of LP SE MP2 are all close to the corresponding counterpoise corrected SCF binding energy. By adding the single excitations, the deficiency in LP SCF MI is thus removed. The results suggest that the exclusion of the charge-transfer effects in LP SCF MI might indeed be the cause of the underestimation for the binding energy.
Suehiro Iwata - One of the best experts on this subject based on the ideXlab platform.
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Perturbation Expansion theory corrected from basis set superposition error ii charge transfer pair correlation and dispersion terms
Theoretical Chemistry Accounts, 2006Co-Authors: Suehiro Iwata, Takeshi NagataAbstract:The second-order Perturbation theory based on the locally projected molecular orbitals is developed. A few test calculations with cc-pVDZ and aug-cc-pVDZ basis sets are carried out for the dimers, (H2O)2 and (HF)2. The charge transfer terms remove the deficiency of the locally projected self-consistent field method for molecular interaction (LP SCF MO MI), and the potential energy curves calculated with aug-cc-pVDZ are very close to the corresponding curves of the counterpoise-corrected SCF energy. Only after adding the spin-exchanged dispersion type to the dispersion and intra-molecular pair correlation terms, the calculated potential energy curves become close to those of the counterpoise-corrected second-order Moller–Plesset (MP2). Pragmatic approaches for reducing the influence of the basis set superposition error are proposed.
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Perturbation Expansion theory corrected from basis set superposition error i locally projected excited orbitals and single excitations
Journal of Chemical Physics, 2004Co-Authors: Takeshi Nagata, Suehiro IwataAbstract:The locally projected self-consistent field molecular orbital method for molecular interaction (LP SCF MI) is reformulated for multifragment systems. For the Perturbation Expansion, two types of the local excited orbitals are defined; one is fully local in the basis set on a fragment, and the other has to be partially delocalized to the basis sets on the other fragments. The Perturbation Expansion calculations only within single excitations (LP SE MP2) are tested for water dimer, hydrogen fluoride dimer, and colinear symmetric ArM+Ar (M=Na and K). The calculated binding energies of LP SE MP2 are all close to the corresponding counterpoise corrected SCF binding energy. By adding the single excitations, the deficiency in LP SCF MI is thus removed. The results suggest that the exclusion of the charge-transfer effects in LP SCF MI might indeed be the cause of the underestimation for the binding energy.
Jacques K Desmarais - One of the best experts on this subject based on the ideXlab platform.
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Perturbation theory treatment of spin orbit coupling part i double Perturbation theory based on a single reference initial approximation
Journal of Chemical Theory and Computation, 2021Co-Authors: Jacques K Desmarais, Alessandro Erba, Jeanpierre Flament, Bernard KirtmanAbstract:We develop a Perturbation theory for solving the many-body Dirac equation within a given relativistic effective-core potential approximation. Starting from a scalar-relativistic unrestricted Hartree-Fock (SR UHF) solution, we carry out a double Perturbation Expansion in terms of spin-orbit coupling (SOC) and the electron fluctuation potential. Computationally convenient energy expressions are derived through fourth order in SOC, second order in the electron fluctuation potential, and a total of third order in the coupling between the two. Illustrative calculations on the halogen series of neutral and singly positive diatomic molecules show that the Perturbation Expansion is well-converged by taking into account only the leading (nonvanishing) term at each order of the electron fluctuation potential. Our Perturbation theory approach provides a computationally attractive alternative to a two-component self-consistent field treatment of SOC. In addition, it includes coupling with the fluctuation potential through third order and can be extended (in principle) to multireference calculations, when necessary for both closed- and open-shell cases, using quasi-degenerate Perturbation theory.
Francesco Petruccione - One of the best experts on this subject based on the ideXlab platform.
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Projection operator based Expansion of the evolution operator
Journal of Physics A, 2016Co-Authors: Vitalii Semin, Francesco PetruccioneAbstract:The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schrodinger equation allows the derivation of an alternative expression for the evolution operator, which differs from the traditional chronological exponent. An appropriate choice of projection operators results in the possibility of studying the diagonal and non-diagonal elements of the evolution operator separately. The suggested expression implies a particular form of Perturbation Expansion, which leads to a new formula for the short time dynamics. The new kind of Perturbation Expansion can be used to improve the accuracy of the usual chronological exponent significantly. The evolution operator for any arbitrary time can be efficiently recovered using the semigroup properties. The method is illustrated by two examples, namely the dynamics of a three-level system in two nonresonant laser fields and the calculation of the partition function of a finite XY-spin chain.
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the time convolutionless projection operator technique in the quantum theory of dissipation and decoherence
Annals of Physics, 2001Co-Authors: Heinzpeter Breuer, Bernd Kappler, Francesco PetruccioneAbstract:Abstract The time-convolutionless projection operator method is used to investigate the non-Markovian dynamics of open quantum systems. On the basis of this method a systematic Perturbation Expansion for the reduced density matrix equation is obtained involving a time-dependent generator which is local in time. This formalism is generalized to enable the treatment of system-environment correlations in the initial state, which arise in the computation of equilibrium correlation functions or from the preparation of the system by a quantum measurement. The general method is illustrated by means of the damped harmonic oscillator and of the spin-boson model. The Perturbation Expansion of the equation of motion is applied to a study of relaxation and dephasing processes and to the determination of the stationary state and of equilibrium correlation functions. Special emphasis is laid on the construction of general, computable error estimates which allow the explicit validation of the obtained results. In particular, the parameter regime for which an Expansion of the equation of motion to fourth order yields reliable results is determined. The results clearly reveal that a large range of physically relevant parameters, in particular those that might be interesting for experiments on macroscopic quantum coherence phenomena, can already be treated using the Expansion to fourth order. It is thus demonstrated that the time-convolutionless projection operator technique provides a transparent and technically feasible method to go beyond the Markovian approximation in the study of open quantum systems.
Bernard Kirtman - One of the best experts on this subject based on the ideXlab platform.
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Perturbation theory treatment of spin orbit coupling part i double Perturbation theory based on a single reference initial approximation
Journal of Chemical Theory and Computation, 2021Co-Authors: Jacques K Desmarais, Alessandro Erba, Jeanpierre Flament, Bernard KirtmanAbstract:We develop a Perturbation theory for solving the many-body Dirac equation within a given relativistic effective-core potential approximation. Starting from a scalar-relativistic unrestricted Hartree-Fock (SR UHF) solution, we carry out a double Perturbation Expansion in terms of spin-orbit coupling (SOC) and the electron fluctuation potential. Computationally convenient energy expressions are derived through fourth order in SOC, second order in the electron fluctuation potential, and a total of third order in the coupling between the two. Illustrative calculations on the halogen series of neutral and singly positive diatomic molecules show that the Perturbation Expansion is well-converged by taking into account only the leading (nonvanishing) term at each order of the electron fluctuation potential. Our Perturbation theory approach provides a computationally attractive alternative to a two-component self-consistent field treatment of SOC. In addition, it includes coupling with the fluctuation potential through third order and can be extended (in principle) to multireference calculations, when necessary for both closed- and open-shell cases, using quasi-degenerate Perturbation theory.