scholarly journals Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians

2020 ◽  
Vol 152 (9) ◽  
pp. 094108
Author(s):  
Pavel Pokhilko ◽  
Anna I. Krylov
Keyword(s):  
Equation Of Motion ◽  
Wave Functions ◽  
Coupled Cluster ◽  
Effective Hamiltonians

scholarly journals Effective Hamiltonians Derived from Equation-of-Motion Coupled-Cluster Wave-Functions: Theory and Application to the Hubbard and Heisenberg Hamiltonians

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Anna I. Krylov
Keyword(s):  
Electronic Structure Calculations ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Coarse Grained ◽  
Coupled Cluster ◽  
Many Body ◽  
Quantum Chemistry Calculations ◽  
Structure Calculations ◽  
Effective Hamiltonians

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’s forms. We report the key equations and illustrate the theory by examples of systems with electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians are extracted directly from the so-obtained effective Hamiltonians. By making quantitative connections between many-body states and simple models, the approach also facilitates the analysis of the correlated wave functions. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.<br>

scholarly journals Effective Hamiltonians Derived from Equation-of-Motion Coupled-Cluster Wave-Functions: Theory and Application to the Hubbard and Heisenberg Hamiltonians

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Anna I. Krylov
Keyword(s):  
Electronic Structure Calculations ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Coarse Grained ◽  
Coupled Cluster ◽  
Many Body ◽  
Quantum Chemistry Calculations ◽  
Structure Calculations ◽  
Effective Hamiltonians

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’s forms. We report the key equations and illustrate the theory by examples of systems with electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians are extracted directly from the so-obtained effective Hamiltonians. By making quantitative connections between many-body states and simple models, the approach also facilitates the analysis of the correlated wave functions. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.<br>

scholarly journals General Framework for Calculating Spin–orbit Couplings Using Spinless One-Particle Density Matrices: Theory and Application to the Equation-of-Motion Coupled-Cluster Wave Functions

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Evgeny Epifanovsky ◽  
Anna I. Krylov
Keyword(s):  
Degrees Of Freedom ◽  
Particle Density ◽  
Mean Field ◽  
Transition Density ◽  
Open Shell ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Coupled Cluster ◽  
Spin Orbit ◽  
Matrix Elements

Standard implementations of non-relativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms =0 triplets), however, matrix elements for all components are necessary for calculations of experimentally relevant spin-dependent quantities. To circumvent explicit calculations of all multiplet components, we employ Wigner–Eckart’s theorem. Applied to a reduced one-particle transition density matrix computed for a single multiplet component, Wigner–Eckart’s theorem generates all other spin–orbit matrix elements. In addition to computational efficiency, this approach also resolves the phase issue arising within Born–Oppenheimer’s separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculations of spin–orbit couplings using equation-of-motion coupled-cluster wave functions is presented. The two-electron contributions are included via the mean-field spin–orbit treatment. Intrinsic issues of constructing spin–orbit mean-field operators for open-shell references are discussed and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

scholarly journals Equation-of-Motion Coupled-Cluster Theory to Model L-edge X-Ray Absorption and Photoelectron Spectra

2020 ◽  
Author(s):  
Marta Lopez Vidal ◽  
Pavel Pokhilko ◽  
Anna Krylov ◽  
Sonia Coriani
Keyword(s):  
Small Molecules ◽  
Particle Density ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Model Systems ◽  
Photoelectron Spectra ◽  
Coupled Cluster ◽  
Coupled Cluster Theory ◽  
X Ray ◽  
X Ray Absorption

We present an extension of the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory for computing x-ray L-edge spectra, both in the absorption (XAS) and photoelectron (XPS) regimes. The approach is based on the perturbative evaluation of spin-orbit couplings using the Breit-Pauli Hamiltonian and nonrelativistic wave-functions described by the fc-CVS-EOM-CCSD ansatz (EOM-CCSD within the frozen-core core-valence separated (fc-CVS) scheme). The formalism is based on spinless one-particle density matrices. The approach is illustrated by modeling XAS and XPS of several model systems ranging from argon atoms to small molecules containing sulfur and silicon.

Equation-of-Motion Coupled-Cluster Method with Double Electron-Attaching Operators: Theory, Implementation, and Benchmarks

2020 ◽  
Author(s):  
Sahil Gulania ◽  
Eirik Fadum Kjønstad ◽  
John F. Stanton ◽  
Henrik Koch ◽  
Anna Krylov
Keyword(s):  
Particle Density ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Bond Breaking ◽  
Coupled Cluster Method ◽  
Density Matrices ◽  
Double Electron ◽  
Structure Patterns

<div> <div> <div> <p>We report a production-level implementation of equation-of-motion coupled-cluster method with double electron- attaching EOM operators of 2p and 3p1h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we can compare EOM-DEA- CCSD wave-functions with wave-functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD capable of treating diradicals, bond-breaking, and some types of conical intersection. </p> </div> </div> </div>

scholarly journals Equation-of-Motion Coupled-Cluster Theory to Model L-edge X-Ray Absorption and Photoelectron Spectra

2020 ◽  
Author(s):  
Marta Lopez Vidal ◽  
Pavel Pokhilko ◽  
Anna Krylov ◽  
Sonia Coriani
Keyword(s):  
Small Molecules ◽  
Particle Density ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Model Systems ◽  
Photoelectron Spectra ◽  
Coupled Cluster ◽  
Coupled Cluster Theory ◽  
X Ray ◽  
X Ray Absorption

We present an extension of the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory for computing x-ray L-edge spectra, both in the absorption (XAS) and photoelectron (XPS) regimes. The approach is based on the perturbative evaluation of spin-orbit couplings using the Breit-Pauli Hamiltonian and nonrelativistic wave-functions described by the fc-CVS-EOM-CCSD ansatz (EOM-CCSD within the frozen-core core-valence separated (fc-CVS) scheme). The formalism is based on spinless one-particle density matrices. The approach is illustrated by modeling XAS and XPS of several model systems ranging from argon atoms to small molecules containing sulfur and silicon.

scholarly journals General Framework for Calculating Spin–orbit Couplings Using Spinless One-Particle Density Matrices: Theory and Application to the Equation-of-Motion Coupled-Cluster Wave Functions

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Evgeny Epifanovsky ◽  
Anna I. Krylov
Keyword(s):  
Degrees Of Freedom ◽  
Particle Density ◽  
Mean Field ◽  
Transition Density ◽  
Open Shell ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Coupled Cluster ◽  
Spin Orbit ◽  
Matrix Elements

Standard implementations of non-relativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms =0 triplets), however, matrix elements for all components are necessary for calculations of experimentally relevant spin-dependent quantities. To circumvent explicit calculations of all multiplet components, we employ Wigner–Eckart’s theorem. Applied to a reduced one-particle transition density matrix computed for a single multiplet component, Wigner–Eckart’s theorem generates all other spin–orbit matrix elements. In addition to computational efficiency, this approach also resolves the phase issue arising within Born–Oppenheimer’s separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculations of spin–orbit couplings using equation-of-motion coupled-cluster wave functions is presented. The two-electron contributions are included via the mean-field spin–orbit treatment. Intrinsic issues of constructing spin–orbit mean-field operators for open-shell references are discussed and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

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