A spin–free approach for valence bond theory and its applications

Wu, Wei; Mo, Yirong; Cao, Zexing; Zhang, Qianer

doi:10.1016/s1380-7323(02)80007-3

Cited by 41 publications

(33 citation statements)

References 55 publications

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“…A many-electron system wave function Y in VB theory is expressed as a linear combination of Heitler-London-Slater-Pauling (HLSP) functions, F K in Equation (2): [22] Y ¼ X…”

Section: Theory and Methodologymentioning

confidence: 99%

“…[19] Note however that an analysis of the same CASSCF wave function in terms of VB structures yields weights of 34 % for 1 and 14 % for 2 in S 2 N 2 . This latter analysis, which implies that diradical structures account to almost 50 % of the CAS (22,16) wave function of S 2 N 2 , shows that the index B in Equation (1) does not give us much information about the description of the ground state in terms of VB structures. We return to this point below.…”

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confidence: 98%

“…[19,20] This implies that symmetry-broken solutions UHF should have lower energies than RHF ones, which suggests that all molecules have significant singlet diradical character. These authors also estimated the diradical character of E 2 N 2 by means of the index B in Equation (1), introduced long ago by Laidig and Schaefer, [21] where C 2 is the coefficient of the most important diexcitation in a CI or MCSCF calculation, here a CAS (22,16) one:…”

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confidence: 99%

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Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S₂N₂ and Related 6π‐Electron Four‐Membered Rings E₂N₂ and E₄²⁺ (E=S, Se, Te)

Braı̈da

Hiberty

2012

ChemPhysChem

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A series of 6π-electron 4-center species, E(2)N(2) and E(4)(2+) (E=S, Se, Te) is studied by means of ab initio valence bond methods with the aims of settling some controversies on 1) the diradical character of these molecules and 2) the radical sites, E or N, of the preferred diradical structure. It was found that for all molecules, the cumulated weights of the two possible diradical structures are always important and close to 50 %, making these molecules comparable to ozone in terms of diradical character. While the two diradical structures are degenerate in the E(4)(2+) dications, they have on the contrary strongly unequal weights in the E(2)N(2) neutral molecules. In these three molecules, the electronic structure is dominated by one diradical structure, in which the radical sites are the two nitrogen atoms, while the other diradical structure is much less important. The ordering of the various VB structures in terms of their calculated weights is confirmed by the relative energies of individual VB structures. In all cases, the major diradical structure (or both diradical structures when they are degenerate) is (are) the lowest one(s), while the covalent VB structures lie higher in energy. The vertical resonance energies are considerable in S(2)N(2) and S(4)(2+), about 80 % of the estimated value for benzene, and diminish as one goes down the periodic table (S→Se→Te). This confirms the aromatic character of these species, as already demonstrated for S(2)N(2) on the basis of magnetic criteria. This and the high weights and stabilities of one or both diradical structures in all systems indicates that aromaticity and diradical character do not exclude each other, contrary to what is usually claimed. Furthermore, it is shown that the diradical structures find their place in a collective electron flow responsible for the ring currents in the π system of these species.

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“…A many-electron system wave function Y in VB theory is expressed as a linear combination of Heitler-London-Slater-Pauling (HLSP) functions, F K in Equation (2): [22] Y ¼ X…”

Section: Theory and Methodologymentioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S₂N₂ and Related 6π‐Electron Four‐Membered Rings E₂N₂ and E₄²⁺ (E=S, Se, Te)

Braı̈da

Hiberty

2012

ChemPhysChem

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“…The procedure of the evaluation of Hamiltonian and overlap matrices is described in detail elsewhere [15][16][17] and will not be addressed further in this paper.…”

Section: Methodsmentioning

confidence: 99%

Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types

Zhang

Ying

et al. 2009

Chemistry A European J

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104

118

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To characterize the nature of bonding we derive the topological properties of the electron charge density of a variety of bonds based on ab initio valence bond methods. The electron density and its associated Laplacian are partitioned into covalent, ionic, and resonance components in the valence bond spirit. The analysis provides a density-based signature of bonding types and reveals, along with the classical covalent and ionic bonds, the existence of two-electron bonds in which most of the bonding arises from the covalent-ionic resonance energy, so-called charge-shift bonds. As expected, the covalent component of the Laplacian at the bond critical point is found to be largely negative for classical covalent bonds. In contrast, for charge-shift bonds, the covalent part of the Laplacian is small or positive, in agreement with the weakly attractive or repulsive character of the covalent interaction in these bonds. On the other hand, the resonance component of the Laplacian is always negative or nearly zero, and it increases in absolute value with the charge-shift character of the bond, in agreement with the decrease of kinetic energy associated with covalent-ionic mixing. A new interpretation of the topology of the total density at the bond critical point is proposed to characterize covalent, ionic, and charge-shift bonding from the density point of view.

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“…The related scheme by Sarma and Rettrup [10] also gives a useful technique. Against the background of these and other commonly acknowledged achievements of the group-theoretic approaches (e.g., see [11][12][13][14][15][16][17][18][19] and references therein), the Fock approach might be regarded as interesting and fundamental but somewhat old-fashioned. Arguably, such a verdict would be premature (see, e.g., [20]) and deserves more scrutiny.…”

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confidence: 99%

Spin‐free quantum chemistry: What one can gain from fock's cyclic symmetry

Luzanov

2010

Int J of Quantum Chemistry

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ABSTRACT:The spin-free wave function due to Fock (Zh Eksp Teor Fiz, 1940, 10, 961) is re-examined with a stress on the reduced density matrix (RDM) theory. The key notion of the Fock approach is the cyclic symmetry of wave functions. It is a specific algebraic identity involving transpositions of numbers taken from two different columns of the corresponding Young tableau. We show first how to construct symmetry adapted states by accounting for high-order cyclic symmetry conditions. For Young's projectors, it gives a new expression including nothing but antisymmetrizers. Next, transforming the Fock spin-free state by a duality operator (the star operator in exterior algebra), we arrive at the representation closely related to spin-flip models. In such spin-flip models, a coupling operator is the basic object for which we show that the cyclic symmetry is transformed into a tracelessness of the coupling operator. The main results are related to the spin-free theory of spin properties. In particular, the theorem previously stated (Luzanov and Whyman, Int J Quantum Chem, 1981, 20, 1179) is refined by an explicit general representation of spin density operators through spin-free (charge) RDMs. Some applications implicating high-order RDMs (collectivity numbers, the unpaired electron problem, cumulant spin RDMs, spin correlators, etc.) are also considered. For spin-free RDM components, a new projection procedure without constructing any symmetry adapted state is proposed. An unsolved problem of constructing orthogonal representation matrices within the Fock theory is raised.

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A spin–free approach for valence bond theory and its applications

Cited by 41 publications

References 55 publications

Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S₂N₂ and Related 6π‐Electron Four‐Membered Rings E₂N₂ and E₄²⁺ (E=S, Se, Te)

Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S₂N₂ and Related 6π‐Electron Four‐Membered Rings E₂N₂ and E₄²⁺ (E=S, Se, Te)

Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types

Spin‐free quantum chemistry: What one can gain from fock's cyclic symmetry

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A spin–free approach for valence bond theory and its applications

Cited by 41 publications

References 55 publications

Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S2N2 and Related 6π‐Electron Four‐Membered Rings E2N2 and E42+ (E=S, Se, Te)

Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S2N2 and Related 6π‐Electron Four‐Membered Rings E2N2 and E42+ (E=S, Se, Te)

Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types

Spin‐free quantum chemistry: What one can gain from fock's cyclic symmetry

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Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S₂N₂ and Related 6π‐Electron Four‐Membered Rings E₂N₂ and E₄²⁺ (E=S, Se, Te)

Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S₂N₂ and Related 6π‐Electron Four‐Membered Rings E₂N₂ and E₄²⁺ (E=S, Se, Te)