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Journal ArticleDOI

Quadratic configuration interaction. A general technique for determining electron correlation energies

15 Nov 1987-Journal of Chemical Physics (American Institute of Physics)-Vol. 87, Iss: 10, pp 5968-5975
TL;DR: In this article, a general procedure for calculation of the electron correlation energy, starting from a single Hartree-Fock determinant, is introduced, and the relation of this method to coupled-cluster (CCSD) theory is discussed.
Abstract: A general procedure is introduced for calculation of the electron correlation energy, starting from a single Hartree–Fock determinant. The normal equations of (linear) configuration interaction theory are modified by introducing new terms which are quadratic in the configuration coefficients and which ensure size consistency in the resulting total energy. When used in the truncated configuration space of single and double substitutions, the method, termed QCISD, leads to a tractable set of quadratic equations. The relation of this method to coupled‐cluster (CCSD) theory is discussed. A simplified method of adding corrections for triple substitutions is outlined, leading to a method termed QCISD(T). Both of these new procedures are tested (and compared with other procedures) by application to some small systems for which full configuration interaction results are available.
Citations
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Journal ArticleDOI
TL;DR: The M06-2X meta-exchange correlation function is proposed in this paper, which is parametrized including both transition metals and nonmetals, and is a high-non-locality functional with double the amount of nonlocal exchange.
Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

22,326 citations

Journal ArticleDOI
TL;DR: In this paper, a new augmented version of coupled-cluster theory, denoted as CCSD(T), is proposed to remedy some of the deficiencies of previous augmented coupledcluster models.

7,249 citations

Journal ArticleDOI
TL;DR: The new local density functional, called M06-L, is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit.
Abstract: We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993

4,154 citations

Journal ArticleDOI
TL;DR: This chapter discusses the development of DFT as a tool for Calculating Atomic andMolecular Properties and its applications, as well as some of the fundamental and Computational aspects.
Abstract: I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

3,890 citations

Journal ArticleDOI
TL;DR: The M05-2X functional has the best performance for thermochemical kinetics, noncovalent interactions (especially weak interaction, hydrogen bonding, π···π stacking, and interactions energies of nucleobases), and alkyl bond dissociation energies and the best composite results for energetics, excluding metals.
Abstract: We present a new hybrid meta exchange-correlation functional, called M05-2X, for thermochemistry, thermochemical kinetics, and noncovalent interactions. We also provide a full discussion of the new M05 functional, previously presented in a short communication. The M05 functional was parametrized including both metals and nonmetals, whereas M05-2X is a high-nonlocality functional with double the amount of nonlocal exchange (2X) that is parametrized only for nonmetals. In particular, M05 was parametrized against 35 data values, and M05-2X is parametrized against 34 data values. Both functionals, along with 28 other functionals, have been comparatively assessed against 234 data values: the MGAE109/3 main-group atomization energy database, the IP13/3 ionization potential database, the EA13/3 electron affinity database, the HTBH38/4 database of barrier height for hydrogen-transfer reactions, five noncovalent databases, two databases involving metal−metal and metal−ligand bond energies, a dipole moment databas...

3,246 citations

References
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Journal ArticleDOI
TL;DR: In this article, a perturbation theory for treating a system of n electrons in which the Hartree-Fock solution appears as the zero-order approximation was developed, and it was shown by this development that the first order correction for the energy and the charge density of the system is zero.
Abstract: A perturbation theory is developed for treating a system of n electrons in which the Hartree-Fock solution appears as the zero-order approximation. It is shown by this development that the first order correction for the energy and the charge density of the system is zero. The expression for the second-order correction for the energy greatly simplifies because of the special property of the zero-order solution. It is pointed out that the development of the higher approximation involves only calculations based on a definite one-body problem.

12,067 citations

Journal ArticleDOI
TL;DR: The coupled cluster singles and doubles model (CCSD) as discussed by the authors is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin-orbital form, and the computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are compared with full CI calculations for H2O and BeH2.
Abstract: The coupled‐cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher‐order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth‐order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low‐order models provide estimates of the effect of the higher‐order terms T1T2, T21T2, T31, and T41 on the correlation energy.

5,603 citations

Journal ArticleDOI
TL;DR: In this article, a method for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation is proposed.
Abstract: A method is suggested for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one‐electron approximation. The method is based on the use of the creation and annihilation operators, hole—particle formalism, Wick's theorem, and the technique of Feynman‐like diagrams. The connection of this method with the configuration‐interaction method as well as with the perturbation theory in the quantum‐field theoretical form is discussed. The method is applied to the simple models of nitrogen and benzene molecules. The results are compared with those obtained with the configuration‐interaction method considering all possible configurations within the chosen basis of one‐electron functions.

2,676 citations

Journal ArticleDOI
TL;DR: In this article, a contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation, and second-order perturbation theory overestimated the correlated energy by 23-50% depending on how H0 was chosen.
Abstract: A contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation. Second-order perturbation theory overestimated the correlation energy by 23–50% depending on how H0 was chosen. Pair-pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.

2,374 citations