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.     

On the origin of energy barriers in the excited states of He2

The A ¹Σ⁺_u and C ¹Σ⁺_g states of He₂ have been examined using self-consistent (spatially projected) generalized valence bond (GVB) wavefunctions. We find both states to have humps (0.06 and 0.22 eV, respectively) at large R (3.1 Å and 2.1 Å, respectively). The repulsive nature of these states at large R results from non-bonding interactions between the singlet pairs of orbitals located on different centers. For R smaller than the size of the excited He orbital (2s or 2p), the state becomes attractive if the symmetry is such that the wavefunction can build in attractive He⁺₂(²Σ⁺_u) character.     

SCF wavefunctions and energies for valence states and excited states of carbon and nitrogen

Wavefunctions and energies are reported for the (2s)ⁿ(2p)^m states of neutral carbon and nitrogen using the fixed double-zeta bases employed by Clementi to describe the ground state of these atoms. In addition, the wavefunctions and energies for a number of valence states are given, including the so-called sp³ valence state of carbon. Calculated energies of the valence states agree well with those obtained from experiment. The corresponding valence-state orbitals are useful in semi-empirical quatum-mechanical calculators, such as the maximum overlap method.     

The orbital description of the potential energy curves and properties of the lower excited states of the BH molecule

The electronic wavefunctions for the ground (X¹ Σ⁺) and the low-lying excited states (a³Π, A¹Π, ³Σ⁺) of the BH molecule have been calculated as a function of internuclear distance using the ab initio generalized valence bond method (GVB) with optimization of spin coupling (SOGI). The potential curve of the A¹Π state in the zero rotational level is found to have a hump of 0.150 eV at R = 3.8₉a_o (experimentally a hump of unknown size is found at 3.9 ± 0.4 a₀); a smaller hump at larger R (0.02 eV at R = 4.9₂a₀) is also found for the calculated a³Π state. The presence of such humps is found to result from the recoupling of orbitals that must occur as R is decreased from ∞ to R_e and is comparable in origin to the activation barrier in a radical exchange reaction (e.g., H₂ + D ? HD + H). The calculated binding energies of the BH states are 3.272 eV (X¹ Σ⁺), 2.216 eV (a³ Π), and 0.502 eV (A¹ Π). The ³Σ⁺ state is unbound although it does exhibit a small unbound minimum. The dipole moment, quadrupole moment, and electric field gradient are calculated as a funtion of R. The shapes of the potential curves and the properties are interpreted in terms of simple qualitative considerations of the GVB orbitals.     

The valence electronic excited states of trans-1,3-butadiene and trans,trans-1,3,5-hexatriene from generalized valence bond and configuration interact

Self-consistent ab initio generalized valence bond (GVB) and configuration interaction (Cl) calculations are presented for the ground and valence electronic excited states of trans-1,3-butadine and all trans-1,3,5-hexatrine. Previous workers have suggested that (all trans) polyenes exhibit a parity-forbidden valence excited state (2¹ A_g at an energy just below that of the first dipole-allowed (1¹ B_u) state. We find such valence excited electronic states for butadiene (ΔE = 7.06 eV) and hexatriene (ΔE = 5.87 eV), but in both cases the excitation energy is considerably higher than the dipole-allowed transitions (zero-zero transitions at 5.95 eV and 4.95 eV, respectively). The lower two triplet states are found at 3.35 eV and 5.08 eV for butadie and at 2.71 eV and 4.32 eV in hexatrine, in good agreement with experimental values (3.2–3.3 eV and 4.92 eV for butadiene and 2.66 eV and 4.1–4.2 eV for hexatrine). Considering the states formed by removing one electron from the π space we found ion states at 8.95 eV and 11.40 eV for butadiene and at 8.33 eV, 10.53 eV, and 11.60 eV for hexatriene, in godo agreement with experimental results (9.0 eV and 11.5 eV for butadiene and 8.45 eV, 10.43 eV and 11.6 eV for hexatriene).     

Variational wavefunctions for low-lying excited states

The multiconfiguration method based on the generalized Brillouin theorem is well suited to optimize orbitals in variational wavefunctions for low-lying excited states of a given symmetry. Such wavefunctions are constrained to be orthogonal to and noninteracting with the wavefunctions for all lower states of the same symmetry. Test calculations were performed on the lowest excited ¹S state of Be. For a Hartree-Fock ground state wavefunction, singly excited configurations were insufficient to describe the lowest excited state, and triply excited configurations had to be added. For multiconfiguration ground state wavefunctions, however, singly excited configurations gave good results.     

Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces

The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

价键理论新进展

概要介绍了现代价键理论的几个主要方法,并讨论了它们各自的特点及其发展现状,并重点介绍了键表方法的基本理论、计算程序及一些应用。     

Electronic states and nature of bonding of the molecule NiSi by all electron ab initio HF-CI and CASSCF calculations

All electron ab initio Hartree-Fock (HF), configuration interaction (CI) and multiconfiguration self-consistent field (CASSCF) calculations have been applied to investigate the low-lying electronic states of the NiSi molecule. The ground state of the NiSi molecule is predicted to be¹Σ⁺. The chemical bond in the¹Σ⁺ ground state is a double bond composed of one σ and one π bond. The σ bond is due to a delocalized molecular orbital formed by combining the Ni 4s and the Si 3pσ orbitals. The π bond is a partly delocalized valence bond, originating from the coupling of the 3dπ hole on Ni with the 3pπ electron on Si. Withing the energy range 1 eV 18 electronic states have been identified. The lowest lying electronic states have been characterized as having a hole in either the 3dπ or the 3dδ orbital of Ni, and the respective final states are formed when either of these holes are coupled to the 3pπ valence electron of Si.     

A “double-zeta” type wavefunction for an organometallic: Bis-(π-allyl)nickel

A wavefunction which is of double-zeta quality at the level of the valence orbitals [based on a (11, 7, 5/8, 4/4) gaussian basis set contracted to (4, 3, 2/3, 2/2)] is reported for thebis-(π-allyl)nickel molecule. Independant SCF calculations for two ionized states substantiate the conclusion reached previously for a number of organometallics with a minimal basis set that Koopmans' theorem is not valid for these molecules, namely that the highest occupied orbital from the ground state calculation for the neutral molecule is mostly a ligand π orbital whereas the lowest ionization potential corresponds to the removal of an electron from a molecular orbital which is mostly a metal 3d orbital. The nature of the bonding inbis-(π-allyl)nickel is discussed on the basis of the possible interactions between the metal orbitals and the π orbitals of the allyl group. The interaction between the filled nonbonding π orbital of the allyl group and the empty 3d _xz orbital of the Ni atom appears responsible for most of the bonding, together with some backbonding through an interaction between the 3d x ²?y ²and 3d xyorbitals and the σ and π orbitals of the ligands. The computed value for the rotation barrier about the C-C allyl bond, 90 kcal/mole, rules out this rotation as one of the possible mechanisms which account for the equivalence of the terminal hydrogens in the proton magnetic resonance spectra of π-allyl complexes.     

The momentum distribution in some electronic states of the neutral and singly ionized nitrogen molecule

Momentum densities for the N₂ molecule are investigated. Differences between the ground state and low-lying excited states as well as the effects of ionization are discussed. The densities are calculated by taking Fournier transforms of natural spin orbitals of wavefunctions calculated in a minimal basis with configuration interaction.     

Computational developments in generalized valence bond calculations

In this article a procedure for generating starting orbitals for generalized valence bond (GVB) calculations is presented. This is achieved by selecting orbitals which correspond to specific bonds or electron pairs. These orbitals can be identified from the localized molecular orbitals, for both occupied and virtual orbitals, which are obtained through a unitary transformation of the Hartree-Fock canonical molecular orbitals using the Boys's localization method. A scheme has also been implemented which achieves optimum convergence of the pairwise orbital optimization. An object-oriented GVB program is developed which automatically generates reliable initial GVB orbitals, leading to proper and fast convergence. © 1996 by John Wiley & Sons, Inc.     

An investigation of the two electron chemical bond calculating energy expectation values from density matrix partitionings. II. The heteronuclear case HeH+

Bond energy contributions calculated from first and second order density matrix terms as partitioned by Ruedenberg's procedure have been obtained for HeH⁺ in the ground state and in the first excited 1Σ⁺. For the chemically bonded ground state the full partitioning is investigated for all internuclear distances R. The wavefunctions used for calculating the density matrices are obtained from an SCF calculation at near Hartree-Fock quality, using Slater orbitals with exponents which for each R are optimized simultaneously with the coefficients. For the excited state a limited CI has been performed. The results for promotional, charge transfer, and interference terms for kinetic and potential bond contributions are presented in the form of energy plots E(R). Starting from the promoted atoms and subsequently allowing for charge transfer the importance of the electron interaction is demonstrated by the unusually low quasiclassical electron repulsion curve due to electronic charge transfer, which makes an essential contribution to the decrease in energy during bond formation.     

Excited orbitals of sulphur in aliphatic and unsaturated sulphides

The energies of some electron configurations of sulphur in organic sulphides involving 3d and 4s orbitals have been derived by simulating the radial and angular perturbation of the molecular environment on sulphur valence orbitals, with electrostatic potentials. In order to discuss the relevance of the electron configurations in the molecular valence state and the role of the excited orbitals 4s and 3d to bonding, the energies were minimized in respect of size and orientation of sulphur valence orbitals. Interatomic exchange terms were included and the importance of interatomic exchange terms involving the electrons on carbons is discussed. The results are indicative for a negligible participation of 3d and 4s orbitals of sulphur to the ground state of aliphatic and unsaturated sulphides.     

具有辛群对称性的一类价激发n电子波函数的性质和应用

讨论了具有辛群对称性的一类价激发n电子波函数 ψ_(a,s_1,s_2)=N(multiply from t=s_1 to s_1+s_2-1)(a_1+(a_t))(multiply from k=s_1+s_2 to s_1+s_2+m-1)G+(ζ,k,V_(s+1))|0>的性质,它们对闭壳层和开壳层体系均适用.用此类函数计算了Li_2,LiH_2~-和CH_3~+,结果表明这类函数能较好地描述电子相关作用,并且变分得到的轨道都是自然轨道。