Tables of Integrals Useful for the Calculations of Molecular Energies. IV

Kotani, Masao; Ishiguro, Eiichi; Hijikata, Katsunori

doi:10.1143/jpsj.9.553

Cited by 22 publications

(13 citation statements)

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“…39 (The full GVB wave function and the spin-coupled valence bond (SCVB) wave function 40,41 are identical.) In general, the only constraint placed on the wave function was that orbitals of different symmetries (a′, a″) were forced to be orthogonal.…”

Section: Methodsmentioning

confidence: 99%

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Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O₃ and SO₂

2015

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There are many well-known differences in the physical and chemical properties of ozone (O3) and sulfur dioxide (SO2). O3 has longer and weaker bonds than O2, whereas SO2 has shorter and stronger bonds than SO. The O-O2 bond is dramatically weaker than the O-SO bond, and the singlet-triplet gap in SO2 is more than double that in O3. In addition, O3 is a very reactive species, while SO2 is far less so. These disparities have been attributed to variations in the amount of diradical character in the two molecules. In this work, we use generalized valence bond (GVB) theory to characterize the electronic structure of ozone and sulfur dioxide, showing O3 does indeed possess significant diradical character, whereas SO2 is effectively a closed shell molecule. The GVB results provide critical insights into the genesis of the observed difference in these two isoelectronic species. SO2 possesses a recoupled pair bond dyad in the a"(π) system, resulting in SO double bonds. The π system of O3, on the other hand, has a lone pair on the central oxygen atom plus a pair of electrons in orbitals on the terminal oxygen atoms that give rise to a relatively weak π interaction.

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Section: Methodsmentioning

confidence: 99%

“…The GVB calculations were performed with the fully variational CASVB program written by Cooper, Thorsteinsson, and co-workers − with the Kotani spin basis . (The full GVB wave function and the spin-coupled valence bond (SCVB) wave function , are identical.)…”

Section: Methodsmentioning

confidence: 99%

Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O₃ and SO₂

2015

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“…In addition, it is sometimes necessary to switch between different types of spin functions. The three main types of spin functions employed in SCGVB theory were introduced by Rumer, Kotani, and Serber: , The Rumer spin functions are products of singlet pairs, 1 / √2 ( αβ – βα ), and 2 S α spin functions, where S is the total spin. Although straightforward construction of spin functions in this way leads to more than f S n a spin functions, the diagrammatic techniques developed by Rumer and extended to nonsinglet states by Simonetta et al can be used to determine a set of the linearly dependent spin functions.…”

Section: Overview Of Scgvb Theorymentioning

confidence: 99%

“…In fact, VB theory, which is the foundation for SCGVB theory, is the basis for many of the concepts used every day by chemistshybrid orbitals, covalent bond pairs, lone pairs, resonance, and more. Although computational considerations favored the use of MO methods over VB methods in the early decades of computational quantum chemistry, this is no longer the case and, over the past couple of decades, applications of VB theory, including modern VB theories such as SCGVB theory, have blossomed (see several recent reviews; − see also Olsen).…”

Section: Insights Into the Electronic Structure Of Moleculesmentioning

confidence: 99%

Spin-Coupled Generalized Valence Bond Theory: New Perspectives on the Electronic Structure of Molecules and Chemical Bonds

Dunning

Cooper

et al. 2021

J. Phys. Chem. A

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Spin-Coupled Generalized Valence Bond (SCGVB) theory provides the foundation for a comprehensive theory of the electronic structure of molecules. SCGVB theory offers a compelling orbital description of the electronic structure of molecules as well as an efficient and effective zero-order wave function for calculations striving for quantitative predictions of molecular structures, energetics and other properties. The orbitals in the SCGVB wave function are usually semi-localized and, for most molecules, can be interpreted using concepts familiar to all chemists (hybrid orbitals, localized bond pair, lone pairs, etc.). SCGVB theory also provides new perspectives on the nature of the bonds in molecules such as C2, Be2 and SF4/SF6. SCGVB theory contributes unparalleled insights into the underlying cause of the first-row anomaly in inorganic chemistry as well as the electronic structure of organic molecules and the electronic mechanisms of organic reactions. The SCGVB wave function accounts for nondynamical correlation effects and, thus, corrects the most serious deficiency in molecular orbital (RHF) wave functions. Dynamical correlation effects, which are critical for quantitative predictions, can be taken into account using the SCGVB wave function as the zero-order wave function for multireference configuration interaction or coupled cluster calculations.* In prior articles in the literature the Spin-Coupled Generalized Valence Bond wave function has usually been referred to as the Spin-Coupled Valence Bond (SCVB) wave function or the full Generalized Valence Bond (full GVB) wave function. These wave functions are identical; to prevent confusion, the authors have adopted the allencompassing SCGVB name. Spin-Coupled Generalized Valence Bond Theory: New Perspectives on the Electronic Structure of Molecules and Chemical Bonds3 and recoupled pair bond dyad. 36 The SCGVB wave function describes molecules in terms of orbitals that are optimized at each geometry, allowing the atomic orbitals to change as a result of molecule formation. In addition to the changes in the orbitals, optimization of the general spin function used in the SCGVB wave function allows the spin function to change from that appropriate for the separated atoms or fragments to that appropriate for the molecule. SCGVB theory addresses a major limitation of RHF theory, providing an excellent zero-order description of molecules that require multiconfiguration descriptions, the making/breaking of bonds, and many chemical reactions and excited states. For most molecules, the SCGVB wave function captures the essential features of the FORS/CASSCF wave functions, with much reduced complexity compared to these latter wave functions.

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“…Extensive efforts by Kotani et al [3], Roothaan [4], and Ruedenberg [ 5 ] among others pushed elliptical coordinate methods for STOs to a high level for two-center integrals but these methods could not solve the general cases for three-and four-center integrals. The use of a single center (the origin of the coordinate system) for the expansion of orbitals in spherical harmonics was introduced by Coolidge 161 to perform all cases of molecular integrals.…”

Section: Introductionmentioning

confidence: 99%

Formulas for three-center exchange integrals by computer implementation of the L�wdin ?-function method

Jones

1984

Int. J. Quantum Chem.

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By use of computer algebra and expansions of orbitals about a single center in spherical harmonics with a matrix representation for the a-function coefficients it is possible to produce formulas for each term of an infinite series that represents the value of a three-center exchange integral. Only seven terms are required to get six decimal digits for triatomic hydrogen. This method is readily generalized to solve all three-center exchange integrals over Slater-type orbitals.

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Tables of Integrals Useful for the Calculations of Molecular Energies. IV

Cited by 22 publications

References 1 publication

Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O₃ and SO₂

Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O₃ and SO₂

Spin-Coupled Generalized Valence Bond Theory: New Perspectives on the Electronic Structure of Molecules and Chemical Bonds

Formulas for three-center exchange integrals by computer implementation of the L�wdin ?-function method

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Tables of Integrals Useful for the Calculations of Molecular Energies. IV

Cited by 22 publications

References 1 publication

Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O3 and SO2

Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O3 and SO2

Spin-Coupled Generalized Valence Bond Theory: New Perspectives on the Electronic Structure of Molecules and Chemical Bonds

Formulas for three-center exchange integrals by computer implementation of the L�wdin ?-function method

Contact Info

Product

Resources

About

Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O₃ and SO₂

Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O₃ and SO₂