Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

Datta, Dipayan; Gauß, Jürgen

doi:10.1063/1.4923436

Cited by 16 publications

(25 citation statements)

References 48 publications

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“…Here,τ xy is a permutation operator. For states in their highest spin projection (m s = S ), the spin-density matrices (γ (1s) ) can be expressed in terms of the spin-free density matrices as (in the MO representation) 12,29,30 γ (1s)…”

Section: Theorymentioning

confidence: 99%

“…5 For instance, the methods based on single-reference manybody perturbation and coupled-cluster theories have been studied in the past few decades. [6][7][8][9][10][11][12] In general, the coupled cluster approaches provide benchmark accuracy when the wave function is well described by a single Slater determinant. The methods based on the complete active space selfconsistent field (CASSCF) and (uncontracted) multiconfiguration interaction (MRCI) methods have been reported as well.…”

Section: Introductionmentioning

confidence: 99%

“…Though the work by Lan et al 27,28 has clearly shown that the DMRG-CASSCF method provides benchmark accuracy for small systems, the use of such large active spaces severely limits the scope of applications; the necessity of such large active spaces originates from the fact that the DMRG-CASSCF model is not designed to efficiently capture dynamical electron correlation, the importance of which has been emphasized in the previous studies based on the coupled cluster theory. 8,9,11,12 To overcome this problem, a method based on CASPT2 is developed in this work to efficiently and accurately describe the contributions to HFCCs from both static and dynamical electron correlation.…”

Section: Introductionmentioning

confidence: 99%

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Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

Shiozaki

Yanai

2016

J. Chem. Theory Comput.

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We present an accurate method for calculating hyperfine coupling constants (HFCCs) based on the complete active space second-order perturbation theory (CASPT2) with full internal contraction. The HFCCs are computed as a first-order property using the relaxed CASPT2 spin-density matrix that takes into account orbital and configurational relaxation due to dynamical electron correlation. The first-order unrelaxed spin-density matrix is calculated from one-and two-body spin-free counterparts that are readily available in the CASPT2 nuclear gradient program [M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 051103 (2015)], whereas the second-order part is computed directly using the newly extended automatic code generator. The relaxation contribution is then calculated from the so-called Z-vectors that are available in the CASPT2 nuclear gradient program. Numerical results are presented for the CN and AlO radicals, for which the CASPT2 values are comparable (or, even superior in some cases) to the ones computed by the coupled-cluster and density matrix renormalization group methods. The HFCCs for the hexaaqua complexes with V II , Cr III , and Mn II are also presented to demonstrate the accuracy and efficiency of our code.

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

Shiozaki

Yanai

2016

J. Chem. Theory Comput.

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“…While the assumed normal ordering of the wave operator removes a lot of complexity from the theory (mainly by avoiding internal T contractions), its effects on the quality of the CC wave function are unknown. One of the latest developments in spin-adapted CC theory is the combinatoric open-shell CC (COSCC) approach [31][32][33][34][35][36][37]. Here, the wave operator is assumed to be normal-ordered while contractions among the cluster operators are reintroduced following a combinatoric cluster expansion.…”

Section: Introductionmentioning

confidence: 99%

A correctly scaling rigorously spin-adapted and spin-complete open-shell CCSD implementation for arbitrary high-spin states

Herrmann,

Hanrath

2021

Preprint

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“…In their recent paper on the formulation of spin densities for the spin‐adapted open‐shell coupled‐cluster method, Datta and Gauss suggested that formulae by Gould et al were rather too complicated and indeed no implementation has been reported so far . (However, note that Battle has published an implementation of the Gould formalism in his PhD thesis …”

Section: Introductionmentioning

confidence: 99%

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S² eigenfunctions

Polyak

Bearpark

Robb

2017

Int J of Quantum Chemistry

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We present an implementation of the spin-dependent unitary group approach to calculate spin densities for configuration interaction calculations in a basis of spin symmetry-adapted functions.Using S 2 eigenfunctions helps to reduce the size of configuration space and is beneficial in studies of the systems where selection of states of specific spin symmetry is crucial. To achieve this, we combine the method to calculate U(n) generator matrix elements developed by Downward and Robb (Theor. Chim. Acta 1977, 46, 129) with the approach of Battle and Gould to calculate U(2n) generator matrix elements (Chem. Phys. Lett. 1993, 201, 284). We also compare and contrast the spin density formulated in terms of the spin-independent unitary generators arising from the group theory formalism and equivalent formulation of the spin density representation in terms of the one-and two-electron charge densities. K E Y W O R D S configuration interaction, configuration state function, quantum chemistry, spin density, unitary group approach 1 | I N TR ODU C TI ONThe unitary group approach (UGA) in quantum chemistry was pioneered by Paldus in 1974, [1] with practical algorithms including the most famous graphical approach by Shavitt, [2,3] having been developed in the following years. It offered a simple and straightforward way of evaluating the spinless generator matrix elements (ME) using implicit Gelfand-Tsetlin basis [4,5] and was suitable for calculating many-electron wavefunction expectation values for spin-independent Hamiltonians. [6] The growing demand for relativisitc corrections and other spin dependent properties in wavefunction methods inspired the subsequent development of spin-dependent generator ME in 80-90s by the several groups of authors [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the latest work in this field is actually quite recent. [24] In particular, a theory for spin dependent operators formulated entirely within the unitary group formalism has been developed by Gould, Chandler, Paldus, and Battle. [7][8][9][10][11][12][13][14][15] As we shall discuss, the final formulae are easy to implement and are based on spin-independent U(n) and well-known U(2) generator ME in terms of the Gelfand-Tsetlin implicit basis. As a special, zero-order case, this theory provides a rather simple way for calculating spin density. [13,15,25] An obvious approach to spin density calculation with configuration interaction (CI) wavefunction would be to use the precomputed spindependent generator ME. The general single-particle reduced density operator (in a 2 3 2 matrix form) is given by [13] : qðr; r 0 Þ lm 5 X n i;j51

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Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

Abstract: Analytic energy derivatives for the calculation of the first-order molecular properties using the domain-based local pair-natural orbital coupled-cluster theory The Journal of Chemical Physics 145, 114101 (2016)

Cited by 16 publications

References 48 publications

Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

A correctly scaling rigorously spin-adapted and spin-complete open-shell CCSD implementation for arbitrary high-spin states

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S² eigenfunctions

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Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

Abstract: Analytic energy derivatives for the calculation of the first-order molecular properties using the domain-based local pair-natural orbital coupled-cluster theory The Journal of Chemical Physics 145, 114101 (2016)

Cited by 16 publications

References 48 publications

Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory

A correctly scaling rigorously spin-adapted and spin-complete open-shell CCSD implementation for arbitrary high-spin states

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S2 eigenfunctions

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Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S² eigenfunctions