Yirong Mo

Efficient algorithm for the spin-free valence bond theory. I. New strategy and primary expressions

A new algorithm for nonorthogonal valence bond (VB) method is presented by using symmetric group approach. In the present algorithm, a new function, called paired-permanent-determinant (PPD), is defined, which is an algebrant and has the same symmetry of a corresponding VB structure. The evaluation of a PPD is carried out by using a recursion formula similar to the Laplace expansion method for determinants. An overlap matrix element in the spin-free VB method may be obtained by evaluating a corresponding PPD, while the Hamiltonian matrix element is expressed in terms of the products of electronic integrals and sub-PPDs. In the present work, some important properties of PPDs are discussed, and the primary procedure for the evaluation of PPD is deduced. Furthermore, the expressions for evaluating both the overlap and Hamiltonian matrix elements are also given in details, which are essential to develop an efficient algorithm for nonorthogonal VB calculations. In the present study, some further effective technical considerations will be adopted, and a new ab initio VB program will be introduced.xa0© 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 287–297, 1998

ON THE RESONANCE THEORY

Abstract In the present paper, the mathematical formulation of resonance theory is discussed. In fact, resonance theory is a representative form of the unitary group approach. Using the standard projection operator of the symmetric group, a new basis for an irreducible representation of the unitary group, called bonded tableau, can be constructed to describe a resonance structure correspondingly. The relationships between bonded tableau and Weyl tableaux and between valence bond and molecular orbital approaches are revealed. Finally, test calculations on ozone and benzene are performed.

Theoretical study of conjugation, hyperconjugation, and steric effect in B2D4 (D=H, F, OH, NH2, and CH3)

The rotational barriers of BD2 in B2D4 (D=H, F, OH, NH2, and CH3) are examined in terms of conjugation, hyperconjugation, and steric effect at the level of HF/6‐31G*. By deleting or keeping the π orbitals on the boron atoms in the HFSCF calculations, for the first time we are able to analyze the hyperconjugation effect on molecular structures and stabilities quantitatively. In the perpendicular structure of B2H4, hyperconjugation results in the shortening of B–B bond from 1.705 to 1.679 A and stabilizes the system by 3.1 kcal/mol. For B2D4 systems in which D are π donors, there is a competition between the steric effect and π electronic delocalization. The former prefers a perpendicular conformation while the latter prefers a planar one. For B2F4 and B2(NH2)4, these two factors are comparable and therefore, the rotational barrier is close to zero. For B2(OH)4, the intramolecular hydrogen bonds stabilize the planar structure significantly. For B2(CH3)4, however, steric effect dominates and consequently perpendicular structures are overwhelmingly preferred.

Quantitative evaluation of hyperconjugation in the cyclopropylcarbinyl cation and in cyclopropylborane

Abstract An orbital deletion procedure (ODP) at HF/6-311G** have been used to evaluate the hyperconjugation effects in the cyclopropylcarbinyl cation ( 1 ) and in cyclopropylborane ( 2 ), as well as the conjugation effects in the allyl cation ( 3 ) and in vinylborane ( 4 ). The hyperconjugation (or conjugation) energies have been quantified by ODP in which the critical “vacant” carbocation (or boron) p orbital is “deactivated”. Comparisons between the bisected conformations of 1 with 3 , and 2 with 4 demonstrate that cyclopropane can be just as effective as a π-electron donor as a Cue605C double bond.

Application of the orbital deletion procedure (ODP) to planar carbocations

Abstract An orbital deletion procedure (ODP), which inactivates a critical π orbital and therefore interrupts cyclic conjugation, and the nucleus independent chemical shifts (NICS) have been employed to evaluate the aromaticity of the tropylium, cyclopropenyl and benzyl cations, as well as the antiaromaticity of the singlet cyclopentadienyl cation, compared with their reference cations: 1,3,5-heptatrienyl, allyl, 1,3,5-hexatrienyl-3-carbinyl and 1,3,5-pentadienyl. The aromatic stabilization energies, defined as the difference in the delocalization energies (deduced from ODP) between the cyclic and the acyclic reference cation, are in general agreement with the values from appropriate isodesmic equations.

Valence bond description for the ground state and several low-lying excited states of LiH

Of these three bonded tableaux, the first two consist of the covalent bond between the atomic orbital Hls and the hybrid atomic orbitals of Li 2s and Li 2p,, while the last one corresponds to the ionic structure Li+H-. Further analyses showed that, compared with the covalent structures, the ionic structure Li+H- contributes less to the binding energy and the dipole moment of the ground state of LiH. This result differs from that based on MO theory. Our results clearly indicate that an electron will transfer from lithium to hydrogen in the range 5.0-7.0 a.u., which explains the so-called “harpoon” mechanism in the molecular-beam dynamics. A detailed and successful valence bond explanation for the variation curve of the dipole moment ~1 with respect to the distance R for the first excited state is also presented. There are two opposite effects, namely the contribution from the ionic structure Li+H- and the non-equivalent sp hybridization of the atomic orbitals on lithium, which make the dipole moment of the first excited state vary with R and lead the direction of ~1 to reverse at approximately 6.0a.u. A brief discussion of the other three excited states is given.

Internal conrotation and disrotation in H2BCH2BH2 and diborylmethane 1,3 H exchange

The paths of correlated internal disrotation (barrier less than 0.4 kcal/mol) and conrotation (barrier around 1.9 kcal/mol) of the two BH2 groups in H2BCH2BH2 have been computed employing ab initio [MP2(full)/6–31G**] and density functional theory (Becke3LYP/6–311+G**) methods. Two B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative interactions stabilize the Cs symmetric H2BCH2BH2 isomer (1). The B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative stabilization, evaluated by homodesmotic reactions and using the orbital deletion procedure (which “deactivates” the “vacant” born p orbital), is less than 6 kcal/mol in diborylmethane. The B(SINGLE BOND)C(DOTTED BOND)B(p) stabilization is shown to be remarkably large in C4B6H10 (Td). At MP2(fu)/6–31G**, disproportionation into 1 and methane is only 5.6 kcal/mol exothermic. The 1,3 H exchange in diborylmethane is an asynchronous process and proceeds via a doubly bridged cyclic intermediate with 9.3 kcal/mol barrier. Structures with “planar tetracoordinate” carbon are stabilized considerably by BH2 substituents, but they are still high in energy.u2003© 1997 John Wiley & Sons, Inc.u2003J Comput Chem 18: 1792–1803, 1997

Paired-permanent approach for VB theory (II) - An ab initio spin-free VB program

Paired-permanent approach for VB theory is extensively developed. Canonical expansion of a paired-permanent is deduced. Furthermore, it is shown that a paired-permanent may be expressed in terms of the products of sub-paired-permanents of any given order and their corresponding minors. An ab initio spin-free valence bond program, called Xiamen, is implemented by using paired-permanent approach. Test calculation shows that Xiamen package is more efficient than some other programs based on the traditional VB algorithm, and it provides a new practical tool for quantum chemistry.Paired-permanent approach for VB theory is extensively developed. Canonical expansion of a paired-permanent is deduced. Furthermore, it is shown that a paired-permanent may be expressed in terms of the products of sub-paired-permanents of any given order and their corresponding minors. Anab initio spin-free valence bond program, called Xiamen, is implemented by using paired-permanent approach. Test calculation shows that Xiamen package is more efficient than some other programs based on the traditional VB algorithm, and it provides a new practical tool for quantum chemistry.

The correlation between theoretical and experimentally estimated resonance energies

Abstract In this paper we have discussed the relationship between theoretical and experimentally estimated resonance energies, and in particular we have reviewed the discrepancies in the above two kinds of resonance energies for butadiene and benzene. Unfortunately, at present there are some difficulties in determining the resonance stabilization by using the prevailing calculation programs at the ab initio level. In contrast, experimentally estimated resonance energies can be well-defined and are discussed routinely. However, as we have pointed out in this paper, the π-electronic delocalization ability is somewhat underestimated by the experimentally deduced data.

VALENCE-BOND STUDIES OF N2O4

Abstract A non-empirical valence bond method is used to investigate the conformation of N2O4. Calculations of the planar conformer shows that the π resonance energy between the two NO2 fragments is only 3.60 kJ mol−1, so that the planarity cannot result primarily from the presence of N-N π bonding in accordance with previous results. We also present a technique for studying the origin of the rotation barrier for N2O4. Our results indicate that the variations of the oneelectron orbital energies of the N2Pπ and O2Pπ atomic orbitals as well as their electron populations are responsible for the stability of the planar conformer compared with the skew conformer.