The generalized valence bond π orbitals of ethylene and allyl cation

Using a fixed sigma core obtained from full electron ab initio Hartree-Fock calculations, the spatially projected GVB orbitals for the pi electron systems of ethylene and allyl cation are reported. The GVB(SP) method generates wavefunctions possessing the correct spatial and spin symmetry without restricting the nature of the individual orbitals. The GVB(SP) wavefunction provides a simple interpretation of the molecule in terms of orbitals each containing a single electron. The resulting total energies and excitation energies agree very well with full configuration interaction calculations.     

Paired-permanent approach to valence bond theory

A new function called paired-permanent is defined and widely discussed, and a practicable procedure for evaluations of paired-permanents is proposed, which is similar to the Laplace method for determinants. Using the concept of paired-permanents, an efficient algorithm is presented for evaluating the Hamiltonian and overlap matrix elements in the spin-free form of valence bond (VB) theory. With the new algorithm, a spin-free wavefunction is simply written as a paired-permanent, and an overlap matrix element may be obtained by evaluating a corresponding paired-permanent. Meanwhile, the Hamiltonian matrix element is expressed in terms of the summation of the products of electronic integrals and the corresponding sub-paired-permanents     

The application of cholesky decomposition in valence bond calculation

The Cholesky decomposition (CD) technique, used to approximate the two‐electron repulsion integrals (ERIs), is applied to the valence bond self‐consistent field (VBSCF) method. Test calculations on ethylene, C_2nH_2n+2, and C_2nH_4n?2 molecules (n = 1–7) show that the performance of the VBSCF method is much improved using the CD technique, and thus, the integral transformation from basis functions to VB orbitals is no longer the bottleneck in VBSCF calculations. The errors of the CD‐based ERIs and of the total energy are controlled by the CD threshold, for which a value of 10^?6 ensures to control the total energy error within 10^?6 Hartree. © 2016 Wiley Periodicals, Inc.     

A valence bond analysis of electronic degeneracies in Jahn-Teller systems: low-lying states of the cyclopentadienyl radical and cation

The lowest doublet electronic state of the cyclopentadienyl radical (CPDR) and the lowest singlet state of the cyclopentadienyl cation (CPDC) are distorted from the highly symmetric D(5h) structure due to the Jahn-Teller effect. A valence bond analysis based on the phase-change rule of Longuet-Higgins reveals that in both cases the distortion is due to the first-order Jahn-Teller effect. It is shown that, while for the radical an isolated Jahn-Teller degeneracy is expected, in the case of the cation the main Jahn-Teller degeneracy is accompanied by five satellite degeneracies. The method offers a chemically oriented way for identifying the distortive coordinates.     

VB2000: Pushing valence bond theory to new limits

Full valence bond (VB) calculations for a system of N electrons have always been hindered by the rapidly growing value of N!, which effectively imposes a limit N < 20. Often, however, not all electrons in a molecule are of interest; if we focus on a “group” G of N_G electrons (e.g., in an “active” region), then it is N_G! that sets the limit. In this work, group function (GF) theory is used to represent a molecule as a collection of interacting electron groups, each with a many‐electron wave function of any chosen form (e.g., VB, MO‐SCF, MCSCF), and each GF is optimized individually in a step‐by‐step process. An efficient VB algorithm allows for up to 14 electrons in any VB group and this combination of GF and VB methods greatly extends the range of feasibility of molecular calculations with VB‐type wave functions: Thus, (1) a large system can be divided into any number of smaller subsystems (groups); (2) each group may contain any chosen number of electrons; (3) the form of any group function (including its level of accuracy) may be chosen at will by the program user. A number of sample calculations are briefly presented. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Hydrogen-abstraction reactivity patterns from A to Y: the valence bond way

"Give us insight, not numbers" was Coulson's admonition to theoretical chemists. This Review shows that the valence bond (VB)-model provides insights and some good numbers for one of the fundamental reactions in nature, the hydrogen-atom transfer (HAT). The VB model is applied to over 50 reactions from the simplest H + H(2) process, to P450 hydroxylations and H-transfers among closed-shell molecules; for each system the barriers are estimated from raw data. The model creates a bridge to the Marcus equation and shows that H-atom abstraction by a closed-shell molecule requires a higher barrier owing to the additional promotion energy needed to prepare the abstractor for H-abstraction. Under certain conditions, a closed-shell abstractor can bypass this penalty through a proton-coupled electron transfer (PCET) mechanism. The VB model links the HAT and PCET mechanisms conceptually and shows the consequences that this linking has for H-abstraction reactivity.     

Resonance effect in the allyl cation and anion: a revisit

The interest over the magnitude of the conjugation effect in the allyl cation (1) and anion (2) has been revived recently by Barbour and Karty (J. Org. Chem. 2004, 69, 648-654), who derived the resonance energies of 20-22 and 17-18 kcal/mol for 1 and 2, respectively, using an empirical extrapolation approximation. This paper revisits the case by explicitly calculating the Pauling-Wheland resonance energy, which measures the stabilization from the most stable resonance structure to the delocalized energy-minimum state of a conjugated system, using our newly developed block-localized wave function (BLW) method. This BLW method has the geometrical optimization capability. The computations result in adiabatic resonance energies of 37 kcal/mol for 1 and 38 kcal/mol for 2. The significant disagreement between these values and Barbour and Karty's results originates from the neglect of structural and electronic variations in their derivation which are energy costing.     

Gradients in valence bond theory

A gradient method for very general valence bond (VB) wavefunctions is presented. This method introduces the electronic energy as a Lagrange multiplier, and evaluates the contributions of the derivatives of the normalisation and of the first- and second-order cofactors present in the VB energy expression. The correctness of the method is illustrated with classic and breathing-orbital VB calculations on the HF molecule.     

A unique coordination environment for an ion: EXAFS studies and bond valence model approach of the encapsulated cation in the Preyssler anion

X-Ray absorption spectroscopy was used to probe the coordination of different encrypted cations in the Preyssler anions [M(n+)P5W(30)O(110)]((15-n)-)(M(n+)= Sr2+, Am3+, Eu3+, Sm3+, Y3+, Th4+, U4+ in decreasing order of ionic radius, IR), hereafter abbreviated [M(n+)PA](15-n)-. The increase of the M-W distance and the decrease of the M-P distance with increasing M ionic radius reveal that the M cation is displaced along the C5 axis within the Preyssler cavity. The slight change (0.07 A) of the M-O distance that does not correspond to the IR difference of 0.27 A confirms that the cavity retains its rigidity upon cation substitution. Geometric modeling of the encapsulated cation in the channel was performed for comparison to the EXAFS results. The position of the cation in the cavity was calculated as well as the M-O10, -W5 and -P5 distances. This modeling confirms the cation displacement toward the center of the Preyssler anion as the cation size increases, which is understood in terms of the non-homogenous electrostatic potential present within the cavity. The bond valence model approach was applied to obtain experimental bond valences. Only the bond valence sum (BVS) of Am3+ is close to its actual charge. Sums smaller than the actual valences of the +3 and +4 ions (2.39-2.63 for +3 cations, Y, Sm, Eu; 3.17 and 3.38 for +4 cations, U and Th, respectively) were obtained, and a larger sum (2.89) was obtained for Sr2+. The deviations from the formal M sums of the encapsulated ions are attributed to the rigidity of the Preyssler framework. The tendency toward coordinative unsaturation for electroactive cations, such as Eu3+, is thought to be the driving force for facile reduction. Unlike other inorganic chelating ligands, the Preyssler anion provides a unique redox system to stabilize an electroactive cation in a low oxidation state.     

A variational biorthogonal valence bond method

The details of a simple and efficient scheme for performing variational biorthogonal valence bond calculations are presented. A variational bound on the energy functional is obtained through the use of a complete configuration expansion in a well-chosen subset of orbitals. The resultant wave functions are clearly dominated by the covalent (spin-coupled) structures, with a negligible contribution from ionic structures. The orbitals obtained compare favorably with overlap enhanced atomic orbitals obtained by other valence bond approaches. The method is illustrated by calculations on water and dioxygen difluoride. © 1994 by John Wiley & Sons, Inc.     

Wheland intermediates: an ab initio valence bond study

The traditional resonance model for electrophilic attacks on substituted aromatic rings is revisited using high level valence bond (VB) calculations. A large π-donation is found in the X = NH(2) case and a weaker one for the X = Cl case, not only for ortho and para isomers but also for the meta case, which can be explained by considering five (not three) fundamental VB structures. No substantial π-effect is found in the X = NO(2) case, generally viewed as π-attractive.     

A valence bond study of the oxygen molecule

Ab initio valence bond calculations are performed for the three lowest states of the oxygen molecule (³Σ⁻_g, ¹Δ_g, and ¹Σ⁺_g). One objective of the present study was to make a contribution to previous valence bond discussions about the oxygen “double” bond. Further, we study the origin of a small barrier in the potential energy surface of the ground state. Two compact models are employed to maintain the clear picture that can be offered by the valence bond method. The first model has only the Rumer structures that are essential for bonding and a proper dissociation. The second model, in addition, has structures which represent excited atoms. These prove to be important for the dissociation energies. For both models, the orbitals are fully optimized. The spectroscopic data obtained are significantly better than are the (few) valence bond results on O₂ that have been published and have the quality of multiconfiguration self-consistent field calculations in which the same valence space is used. The “hump” in the potential energy surface of the ground state is shown to arise from a spin recoupling. The free atoms correspond to a spin coupling that is incapable of describing the formation of bonds. Only at short distances, an alternative spin coupling provides bonding and the repulsive curve is converted into an attractive one. Our results on this subject support a valence bond explanation previously given by McWeeny [R. McWeeny, Int. J. Quantum Chem. Symp. 24 , 733 (1990)]. © 1996 John Wiley & Sons, Inc.     

The valence bond description of xylylenes

The ground states or ortho-, meta- and para-xylylenes and low lying excited states of meta-xylylenes are investigated by the valence-bond approach. Weights of structural formulas are calculated. A criterion for biradical character is defined as the sum of the weights of biradical structures. It is found that meta-xylylene is best described as a benzene ring relatively unperturbed by the two adjacent méthylène radicals, and that ortho- and para-xylylene are unequal mixtures of localized Kékulé structures and aromatic biradical structures. Surprisingly, low lying excited states of meta-xylylene deviate from the zwitterionic picture expected for singlet excited states of biradicals.