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The present study further explores the concept of the seniority number (Ω) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of Ω in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of Ω in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyond minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G), N2 (6-31G), C2 (6-31G), and Be2 (cc-pVTZ). We find that the potential energy profile for H2O dissociation can be reasonably well described using only the Ω = 0 sector of the CI wave function. For the Be2 case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either Ω-based (including configurations having up to Ω = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valence-reference function. Finally, in dissociation cases of N2 and C2, we shall also consider novel hybrid wave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths. [ABSTRACT FROM AUTHOR]

The present study further explores the concept of the seniority number (Ω) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of Ω in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of Ω in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyond minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G), N2 (6-31G), C2 (6-31G), and Be2 (cc-pVTZ). We find that the potential energy profile for H2O dissociation can be reasonably well described using only the Ω = 0 sector of the CI wave function. For the Be2 case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either Ω-based (including configurations having up to Ω = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valence-reference function. Finally, in dissociation cases of N2 and C2, we shall also consider novel hybrid wave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths. [ABSTRACT FROM AUTHOR]

The present study further explores the concept of the seniority number (O) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of O in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of O in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyond minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G),N2 (6-31G), C2 (6-31G), and Be2 (cc-pVTZ).We find that the potential energy profile for H2O dissociation can be reasonably well described using only the O = 0 sector of the CI wave function. For the Be2 case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either O-based (including configurations having up to O = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valencereference function. Finally, in dissociation cases of N2 and C2, we shall also consider novel hybridwave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths. [ABSTRACT FROM AUTHOR]

The present study further explores the concept of the seniority number (O) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of O in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of O in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyond minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G),N2 (6-31G), C2 (6-31G), and Be2 (cc-pVTZ).We find that the potential energy profile for H2O dissociation can be reasonably well described using only the O = 0 sector of the CI wave function. For the Be2 case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either O-based (including configurations having up to O = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valencereference function. Finally, in dissociation cases of N2 and C2, we shall also consider novel hybridwave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths. [ABSTRACT FROM AUTHOR]

We explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electron correlation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N2 and CO2 molecules, as well as the symmetric dissociation of an H8 hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction. [ABSTRACT FROM AUTHOR]

The recently introduced method of correlation energy extrapolation by intrinsic scaling is used to calculate the nonrelativistic electron correlations in the valence shell of the O2 molecule at 24 internuclear distances along the ground state 3Σg- potential energy curve from 0.9 to 6 Å, the equilibrium distance being 1.207 52 Å. Using Dunning’s correlation-consistent triple- and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to sextuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. [ABSTRACT FROM AUTHOR]

In the first paper of this series, a very accurate ab initio potential energy curve of the 3Σg- ground state of O2 has been determined in the approximation that all valence shell electron correlations were calculated at the complete basis set limit. In the present study, the corrections arising from core electron correlations and relativity effects, viz., spin-orbit coupling and scalar relativity, are determined and added to the potential energy curve. From the 24 points calculated on this curve, an analytical expression in terms of even-tempered Gaussian functions is determined and, from it, the vibrational and rotational energy levels are calculated by means of the discrete variable representation. We find 42 vibrational levels. Experimental data (from the Schumann–Runge band system) only yield the lowest 36 levels due to significant reduction in the transition intensities of higher levels. For the 35 term values G(v), the mean absolute deviation between theoretical and experimental data is 12.8 cm-1. The dissociation energy with respect to the lowest vibrational energy is calculated within 25 cm-1 of the experimental value of 41 268.2±3 cm-1. The theoretical crossing between the 3Σg- state and the 1Σg+ state is found to occur at 2.22 Å and the spin-orbit coupling in this region is analyzed. [ABSTRACT FROM AUTHOR]

The potential energy curve of the fluorine molecule in the ground electronic state 1Σg+ is determined and analyzed in the long-range region. The analysis is based on expressing the potential as the sum of the potential energy curve of the uncorrelated, but properly dissociating wave function and the correlation energy contribution. It is shown that, in the long-range region, the former becomes identical with the interaction between the quadrupoles of the fluorine atoms and the latter becomes the London dispersion interaction. The former is repulsive because of the coaxial quadrupole alignments in the 1Σg+ ground state and proportional to 1/R5. The latter is attractive and proportional to 1/R6. There moreover exists an additional repulsive force due to the loss of spin-orbit coupling upon the bond formation. As a result of these antagonistic interactions, the potential energy curve has a barrier at about 4 Å, with a value about +0.04 mhartree. The descent of the potential toward the minimum, when the atoms approach each other from infinity, begins therefore only at internuclear distances less than about twice the equilibrium distance and is then very steep. [ABSTRACT FROM AUTHOR]

A close approximation to the empirical potential energy curve of the neon dimer is obtained by coupled-cluster singles plus doubles plus noniterative triples calculations by using nonaugmented correlation-consistent basis sets without counterpoise corrections and complementing them by three-term extrapolations to the complete basis set limit. The potential energy is resolved into a self-consistent-field Hartree–Fock contribution and a correlation contribution. The latter is shown to decay in the long-range region in accordance with the empirical dispersion expansion. [ABSTRACT FROM AUTHOR]

The recently introduced method of correlation energy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F2 molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 Å to 8 Å, the equilibrium distance being 1.412 Å. Using Dunning’s correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail. [ABSTRACT FROM AUTHOR]

The method of correlation energy extrapolation by intrinsic scaling, recently introduced to obtain accurate molecular electronic energies, is used to calculate the total nonrelativistic electronic ground state energy of the water molecule. Accurate approximations to the full configuration interaction energies are determined for Dunning’s [J. Chem. Phys. 90, 1007 (1989)] correlation-consistent double-, triple- and quadruple-zeta basis sets and then extrapolated to the complete basis set limit. The approach yields the total nonrelativistic energy -76.4390±0.0004 hartree, which compares very well with the value of -76.4389 hartree derived from experiment. The energy of atomization is recovered within 0.1 mh. The enthalpy of formation, which is obtained in conjunction with our previous calculation of the dissociation energy of the oxygen molecule, is recovered within 0.05 mh. [ABSTRACT FROM AUTHOR]

The method of extrapolation by intrinsic scaling, recently introduced to obtain correlation energies, is generalized to multiconfigurational reference functions and used to calculate the binding energies of the diatomic molecules C2, N2, O2, and F2. First, accurate approximations to the full configuration interaction energies of the individual molecules and their constituent atoms are determined, employing Dunning’s correlation consistent double-, triple- and quadruple ζ basis sets. Then, these energies are extrapolated to their full basis set limits. Chemical accuracy is attained for the binding energies of all molecules. [ABSTRACT FROM AUTHOR]

The information gained in the context of extrapolating the correlation energy by intrinsic scaling is used to shorten the full configurational expansions of electronic wave function without compromising their chemical accuracy. The truncations are accomplished by judiciously limiting the participation of the ranges of predetermined approximate sets of natural orbitals in the various excitation categories. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Remarkably accurate scaling relations are shown to exist between the correlation energy contributions from various excitation levels of the configuration interaction approach, considered as functions of the size of the correlating orbital space. These relationships are used to develop a method for extrapolating a sequence of smaller configuration interaction calculations to the full configuration-interaction energy. Calculations of the neon atom ground state with the Dunning’s quadruple ζ basis set demonstrate the ability of the method to obtain benchmark quality results. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The convergence of configuration interaction (CI) expansions depends upon the orbitals from which the configurations are formed. Since their introduction half a century ago, natural orbitals have gained an increasing popularity for generating rapidly converging CI expansions and the notion has become widespread that they always yield the fastest CI convergence. It is shown here that, in fact, certain localized orbitals often yield a better CI convergence than natural orbitals, as measured by a wave function criterion as well as by an energy criterion. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The molybdenum dimer is an example of a transition metal system with a formal sextuple bond that constitutes a challenging case forab initioquantum chemistry methods. In particular, the complex binding pattern in the Mo2molecule requires a high-quality description of non-dynamic and dynamic electron correlation in order to yield the correct shape of the potential energy curve. The present study examines the performance of a recently implemented multi-component symmetry projected Hartree–Fock (HF) approach. In this work, the spin and spatial symmetries of a trial wavefunction written in terms of non-orthogonal Slater determinants are deliberately broken and then restored in a variation-after-projection framework. The resulting symmetry-projected HF wavefunctions, which possess well-defined quantum numbers, can account for static and some dynamic correlations. A single symmetry-projected configuration in aD∞hS-UHF or aD∞hKS-UHF framework offers a reasonable description of the potential energy curve of Mo2, though the binding energy is too small for the former. Our multi-component strategy offers a way to improve on the single configuration result in a systematic way towards the exact wavefunction: in the def2-TZVP basis set considered in this study, a 7-determinant multi-componentD∞hS-UHF approach yields a bond length of 2.01 Å, in good agreement with experimental results, while the predicted binding energy is 39.2 mhartree. The results of this exploratory study suggest that a multi-component symmetry-projected HF stategy is a promising alternative in a high-accuracy description of the electronic structure of challenging systems. We also present and discuss some benchmark calculations based on the CEEIS-FCI (correlation energy extrapolation by intrinsic scaling – full configuration interaction) method for selected geometries. [ABSTRACT FROM PUBLISHER]

In the first paper of this series, a very accurate ab initio potential energy curve of the (3)Sigma(g)(-) ground state of O(2) has been determined in the approximation that all valence shell electron correlations were calculated at the complete basis set limit. In the present study, the corrections arising from core electron correlations and relativity effects, viz., spin-orbit coupling and scalar relativity, are determined and added to the potential energy curve. From the 24 points calculated on this curve, an analytical expression in terms of even-tempered Gaussian functions is determined and, from it, the vibrational and rotational energy levels are calculated by means of the discrete variable representation. We find 42 vibrational levels. Experimental data (from the Schumann-Runge band system) only yield the lowest 36 levels due to significant reduction in the transition intensities of higher levels. For the 35 term values G(v), the mean absolute deviation between theoretical and experimental data is 12.8 cm(-1). The dissociation energy with respect to the lowest vibrational energy is calculated within 25 cm(-1) of the experimental value of 41,268.2+/-3 cm(-1). The theoretical crossing between the (3)Sigma(g)(-) state and the (1)Sigma(g)(+) state is found to occur at 2.22 A and the spin-orbit coupling in this region is analyzed.