AB initio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular wavefunctions

Ermler, Walter C.; Lee, Yoon S.; Christiansen, P. A.; Pitzer, Kenneth S.

doi:10.1016/0009-2614(81)85329-8

Cited by 147 publications

(51 citation statements)

References 23 publications

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“…Since the potentials are generated from Dirac-Fock atomic orbitals and eigenvalues, they account for the effects of relativity on valence electron spatial distribution and energetics. While spin-orbit dependencies have been averaged out during the generation of the potentials, these effects may be reintroduced via effective spin-orbit operators (17) or by scaling the usual spinorbit integrals over valence orbitals (21).…”

Section: Discussionmentioning

confidence: 99%

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Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms

Stevens¹,

Krauß²,

Basch³

et al. 1992

Can. J. Chem.

2,107

1,289

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. Can. J. Chem. 70, 6 12 (1992). Relativistic compact effective potentials (RCEP), which replace the atomic core electrons in molecular calculations, have been derived from numerical Dirac-Fock atomic wavefunctions using shape-consistent valence pseudo-orbitals and an optimizing procedure based on an energy-overlap functional. Potentials are presented for the third-, fourth-, and fifthrow atoms of the Periodic Table (excluding the lanthanide series). The efficiency of molecular calculations is enhanced by using compact Gaussian expansions (no more than three terms) to represent the radial components of the potentials, and energy-optimized, shared-exponent, contracted-Gaussian atomic orbital basis sets. Transferability of the potentials has been tested by comparing calculated atomic excitation energies and ionization potentials with values obtained from numerical relativistic Hartree-Fock calculations. For the alkali and alkaline earth atoms, core polarization potentials (CPP) have been derived which may be added to the RCEP to make possible accurate molecular calculations without explicitly including core-valence correlating configurations in the wavefunction. Introduction two rows (Li-Ar) of the Periodic Table ( 5 ) . We designatedThe use of atomic effective core potentials (ECP) and model potentials (MP) to eliminate chemically inactive atomic core electrons from quantum mechanical calculations has become routine in the past decade. The development of such potentials in the early 1970's and applications through the mid-1980's have been reviewed previously (1). The use of such potentials in molecular calculations has gained widespread acceptance, and sets of effective potentials are included in widely distributed quantum chemistry programs such as HONDO ( 2 ) , GAMESS (3), and GAUSSIAN (4). We previously published accurate compact effective potentials (CEP) and matching basis sets for the atoms of the first '~u t h o r to whom correspondence may be addressed. 'NRC-NAS Postdoctoral Fellow, NIST, 1984NIST, -1986. Current address: California State University, San Marcos, CA 92096, U.S.A.Primed in Canada -the potentials "compact" because they are represented analytically by small Gaussian expansions and, therefore, offer significant economy in molecular calculations where the computer time required to construct the electronic integrals is proportional to the complexity of the potentials. In this report, we present effective potentials and basis sets of similar quality for the third, fourth, and fifth rows of the Periodic Table derived from numerical, relativistic, Dirac-Fock atomic wavefunctions. The analytic expansions of these POtentials are also limited to a few Gaussian terms (three or less), so we have designated them as "relativistic compact effective potentials" (RCEP).Recently, several compilations of model potentials and effective core potentials for use in molecular calculations have appeared in the literature. For the heavier atoms, relativistic effects have been incorporated by deriving the potentials ...

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Section: Discussionmentioning

confidence: 99%

“…This was first proposed by Ermler et al (21), and used by Stevens and Krauss (22) to calculate spin-orbit splittings for several diatomic molecules. The form of the spin-orbit coupling operator is where the difference potential is defined by…”

mentioning

confidence: 99%

Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms

Stevens¹,

Krauß²,

Basch³

et al. 1992

Can. J. Chem.

2,107

1,289

View full text Add to dashboard Cite

show abstract

“…The relativistic effective potential can be written in a different form that separates the relativistic effects into scalar relativistic and spin-orbit 24 , namely…”

Section: −3mentioning

confidence: 99%

Quantum Monte Carlo with variable spins

Melton

Bennett

Mitáš

2016

The Journal of Chemical Physics

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We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC), we thoroughly discuss the details of the method and elaborate upon its technicalities. We present a proof for an upper-bound property for complex nonlocal operators, which allows for the implementation of T-moves to ensure the variational property. We discuss the time step biases associated with our particular choice of spin representation. Applications of the method are also presented for atomic and molecular systems. We calculate the binding energies and geometry of the PbH and Sn 2 molecules, as well as the electron affinities of the 6p row elements in close agreement with experiments.

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“…The molecular spinor (MS), an eigenfunctions of a two-component Fock matrix at the SCF convergence is given by (7) where ϕ i denotes the i-th spinor, μ denotes the AO basis, σ denotes the associated spin functions, and is the corresponding HF coefficients. The integral transformation from the AO to MS basis is performed prior to a post-HF stage in order to generate the one-and two-electron MS integrals defined by (8) . ( 9 ) The nonrelativistic eight-fold permutational symmetry of electron repulsion integrals is no longer valid due to the complex coefficients, yet the Hermitian symmetry is retained and can be exploited to reduce the number of integrals to be evaluated.…”

Section: -28mentioning

confidence: 99%

“…4 Instead, quasirelativistic two-component approaches are often employed, and among a few available, the two-component SO relativistic effective core potential (SOREP) in particular has been demonstrated as an efficient alternative, for which only the valence (and semi-core) electrons are explicitly considered and the one-electron effective SO operators are provided. [6][7][8] During the last two decades, our group had developed several relativistic quantum chemistry computer codes in the framework of the two-component SOREP, ranging from a simple SCF program to highly correlated methods. [9][10][11][12][13][14][15][16] The development began with a focus on the self-consistent treatment of SO-coupling, and initially delivered a computer code for Kramers restricted Hartree-Fock (KRHF) method, 9 in which time-reversal (or Kramers) symmetry was imposed on the one-electron functions, working in conjunction with the atomic orbital (AO) integral program ARGOS 17 for the evaluation of SOREP integrals.…”

Section: Introductionmentioning

confidence: 99%

KPACK: Relativistic Two-component Ab Initio Electronic Structure Program Package

Kim¹,

Lee²

2013

Bulletin of the Korean Chemical Society

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We describe newly developed software named KPACK for relativistic electronic structure computation of molecules containing heavy elements that enables the two-component ab initio calculations in Kramers restricted and unrestricted formalisms in the framework of the relativistic effective core potential (RECP). The spin-orbit coupling as relativistic effect enters into the calculation at the Hartree-Fock (HF) stage and hence, is treated in a variational manner to generate two-component molecular spinors as one-electron wavefunctions for use in the correlated methods. As correlated methods, KPACK currently provides the two-component second-order Møller-Plesset perturbation theory (MP2), configuration interaction (CI) and complete-activespace self-consistent field (CASSCF) methods. Test calculations were performed for the ground states of group-14 elements, for which the spin-orbit coupling greatly influences the determination of term symbols. A categorization of three procedures is suggested for the two-component methods on the basis of spin-orbit coupling manifested in the HF level.

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AB initio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular wavefunctions

Cited by 147 publications

References 23 publications

Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms

Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms

Quantum Monte Carlo with variable spins

KPACK: Relativistic Two-component Ab Initio Electronic Structure Program Package

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