n-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants

2002 ◽  
Vol 117 (20) ◽  
pp. 9138-9153 ◽  
Author(s):  
Celestino Angeli ◽  
Renzo Cimiraglia ◽  
Jean-Paul Malrieu
Keyword(s):  
Perturbation Theory ◽  
Valence State ◽  
Efficient Implementation

Nonlinear impedance boundary condition for 2D BEM

2018 ◽  
Vol 37 (2) ◽  
pp. 772-783 ◽  
Author(s):  
Carlo de Falco ◽  
Luca Di Rienzo ◽  
Nathan Ida ◽  
Sergey Yuferev
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Diffusion Equation ◽  
Efficient Implementation ◽  
Impedance Boundary Condition ◽  
Computational Domain ◽  
Impedance Boundary ◽  
Content Type ◽  
The Magnetic Field ◽  
Element Method

PurposeThe purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors. Design/methodology/approachAn approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields. FindingsThe results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost. Research limitations/implicationsLimitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor. Originality/valueThe efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant

2001 ◽  
Vol 350 (3-4) ◽  
pp. 297-305 ◽  
Author(s):  
Celestino Angeli ◽  
Renzo Cimiraglia ◽  
Jean-Paul Malrieu
Keyword(s):  
Perturbation Theory ◽  
Valence State ◽  
Fast Implementation

Analytic First-Order Derivatives of Partially Contracted N-Electron Valence State Second-Order Perturbation Theory (PC-NEVPT2)

2019 ◽  
Author(s):  
Yoshio Nishimoto
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Valence State ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Transition Energies ◽  
First Order ◽  
Static Electron ◽  
Second Order Perturbation Theory

A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, speci cally gradients and dipole moments, are developed for a particular MRPT method, state-specific partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. Comparison of the calculated results with experimental geometrical parameters of O<sub>3</sub> indicates excellent agreement, although the calculated results for O<sub>3</sub><sup>-</sup> are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.

Explicitly correlated N-electron valence state perturbation theory (NEVPT2-F12)

2017 ◽  
Vol 147 (6) ◽  
pp. 064110 ◽  
Author(s):  
Yang Guo ◽  
Kantharuban Sivalingam ◽  
Edward F. Valeev ◽  
Frank Neese
Keyword(s):  
Perturbation Theory ◽  
Valence State ◽  
Explicitly Correlated
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