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A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves.

ABSTRACT: The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the Appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double, and triple bond breaking together with an excited state calculation. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

SUBMITTER: Giner E

PROVIDER: S-EPMC5469683 | biostudies-other | 2017 Jun

REPOSITORIES: biostudies-other

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A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves.

Giner Emmanuel E Angeli Celestino C Garniron Yann Y Scemama Anthony A Malrieu Jean-Paul JP

The Journal of chemical physics 20170601 22

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definiti ...[more]

PMID: 29166052

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Project description:This paper contributes to the environmental literature by (i) demonstrating that the estimated coefficients and the statistical significance of the non-leading terms in quadratic, cubic, and quartic logarithmic environmental Kuznets curve (EKC) specifications are arbitrary and should therefore not be used to choose the preferred specification and (ii) detailing a proposed general-to-specific type methodology for choosing the appropriate specifications when attempting to estimate higher-order polynomials such as cubic and quartic logarithmic EKC relationships. Testing for the existence and shape of the well-known EKC phenomenon is a hot topic in the environmental economics literature. The conventional approach widely employs quadratic and cubic specifications and more recently also the quartic specification, where the variables are in logarithmic form. However, it is important that researchers understand whether the estimated EKC coefficients, turning points, and elasticities are statistically acceptable, economically interpretable, and comparable. In addition, it is vital that researchers have a clear structured non-arbitrary methodology for determining the preferred specification and hence shape of the estimated EKC. We therefore show mathematically and empirically the arbitrary nature of estimated non-leading coefficients in quadratic, cubic, and quartic logarithmic EKC specifications, being dependent upon the units of measurement chosen for the independent variables (e.g. dependent upon a rescaling of the variables such as moving from $m to $bn). Consequently, the practice followed in many previously papers, whereby the estimates of the non-leading terms are used in the decision to choose the preferred specification of an estimated EKC relationship, is incorrect and should not be followed since it potentially could lead to misleading conclusions. Instead, it should be based upon the sign and statistical significance of the estimated coefficients of the leading terms, the location of turning point(s), and the sign and statistical significance of the estimated elasticities. Furthermore, we suggest that researchers should follow a proposed general-to-specific type methodology for choosing the appropriate order of polynomials when attempting to estimate higher-order polynomial logarithmic EKCs.

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A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves.

Publications

A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves.

Similar Datasets

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