Atomic Many-Body Theory

Lindgren, Ingvar; Morrison, John C.

doi:10.1007/978-3-642-96614-9

Cited by 700 publications

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“…Similarly to the extended Wick theorem for the MR case, 24 a normal ordered operator for two nonorthogonal determinants can be expressed by subtracting the expectation values order-by-order in the operator rank. The fact that the expectation value for the nonorthogonal Slater-determinants is factrizable into one-body transition density matrices may allow us to express the normal ordered operator in exactly the same manner as the single-reference one 25 in an orthogonal basis, ,…”

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confidence: 99%

Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

Tsuchimochi

Ten‐no

2016

The Journal of Chemical Physics

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We present single and double particle-hole excitations in the recently revived spin-projected Hartree-Fock. Our motivation is to treat static correlation with spin-projection and recover the residual correlation, mostly dynamic in nature, with simple configuration interaction (CI). To this end, we introduce the Wick theorem for nonorthogonal determinants, which enables an efficient implementation in conjunction with the direct CI scheme. The proposed approach, termed spin-extended CI with singles and doubles, achieves a balanced treatment between dynamic and static correlations. To approximately account for the quadruple excitations, we also modify the well-known Davidson correction. We report that our approaches yield surprisingly accurate potential curves for HF, H 2 O, N 2 , and a hydrogen lattice, compared to traditional single reference wave function methods at the same computational scaling as regular CI. C 2016 AIP Publishing LLC. [http://dx

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confidence: 99%

Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

Tsuchimochi

Ten‐no

2016

The Journal of Chemical Physics

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“…Thus, the magnetic HFS is the sum of one body interactions from the point of view of electronic structure theory [2]. The magnetic vector potential ( A) at a distance r is given by…”

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Implementation of theZ-vector method in the relativistic-coupled-cluster framework to calculate first-order energy derivatives: Application to the SrF molecule

et al. 2015

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The molecular dipole moment and magnetic hyperfine structure constant demand an accurate wavefunction far from the nucleus and in near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of relativistic coupled cluster theory to calculate the first order property of molecular systems in their open-shell ground state configuration. The implemented method is applied to calculate molecular dipole moment and parallel component of the magnetic hyperfine structure constant of SrF molecule. The results of our calculation are compared with the experimental and other available theoretically calculated values. We are successful in achieving good accordance with the experimental results. The result of our calculation of molecular dipole moment is in the accuracy of ∼ 0.5 %, which is clearly an improvement over the previous calculation based on the expectation value method in the four component coupled cluster framework [V. S. Prasannaa et al, Phys. Rev. A 90, 052507 (2014)] and it is the best calculated value till date. Thus, it can be inferred that the Z-vector method can provide an accurate wavefunction in both near and far nuclear region, which is evident from our calculated results.PACS numbers: 31.15.bw, 31.15.vn, 32.10.Fn Theoretical physicists find it very challenging to calculate the spectroscopic properties of atoms and molecules. The precise description of the spectroscopic properties demands the wavefunction to be accurate both in the nuclear region and the region far from the nucleus. The calculation of an accurate wavefunction involving heavy atoms and molecules needs to include the relativistic and electron correlation effects simultaneously, as these two effects are non-additive in nature [1,2]. The best possible way to include the effects of relativity in a single determinantal theory is to solve the Dirac-Hartree-Fock (DHF) Hamiltonian in its four component formalism. The DHF Hamiltonian converts the complicated many electron problem into a sum of many one-electron problems by assuming an average electron-electron interaction. Therefore, the DHF Hamiltonian lacks the correlation of opposite spin electrons. The missing electron correlation can be included by adding orthogonal space to the DHF wavefunction. On the other hand, normal coupled cluster (NCC) [3][4][5] method is known to be the most elegant many-body theory to effectuate the dynamic part of the electron correlation.The calculations of one electron response properties in the NCC framework, can either be done by taking expectation value of the desired property operator or as a derivative of energy. These two approaches are not same as the NCC is by nature non-variational. In fact, the first order derivative of energy is the corresponding expectation value plus some additional terms, which makes the derivative approach closer to the full configuration * sk.sasmal@ncl.res.in interaction (FCI) property value. It is worth to mention that the expectation value approach in the NCC leads to a nonterminating ...

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“…Here (µ ↔ ν) indicates that µ must be interchanged with ν. Notice, that when examining the atomic perturbation theory expansion terms or coupled cluster (CC) approach equation ones, they can be considered as the matrix elements of some effective operator (γ) γ [6]. Then the factor (α β µ ν; γ γ ) can be associated with the matrix element αβ (γ) γ µν .…”

Section: Coupling Schemes Of Ranks For a Two-particle Operatormentioning

confidence: 99%

“…For example, large-scale configuration interaction (CI) calculations [1][2][3][4][5] use a massive matrix for the atomic Hamiltonian. A large fraction of expansion terms of perturbation theory (PT) recently applied in atomic calculations [6][7][8][9][10][11] are considered as * E-mail: jursenas@itpa.lt matrix elements of some effective two-particle operators with complex tensorial structures. In all the above mentioned studies, a significant fraction of computations are devoted to the calculation of N-electron angular parts of the matrix elements of a two-electron operator.…”

Section: Introductionmentioning

confidence: 99%

Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

Jursenas

Merkelis

2010

Open Physics

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Atomic Many-Body Theory

Cited by 700 publications

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Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

Implementation of theZ-vector method in the relativistic-coupled-cluster framework to calculate first-order energy derivatives: Application to the SrF molecule

Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

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