William J. Hunt

Self‐Consistent Procedures for Generalized Valence Bond Wavefunctions. Applications H3, BH, H2O, C2H6, and O2

Methods of efficiently optimizing the orbitals of generalized valence bond (GVB) wavefunctions are discussed and applied to LiH, BH, H_3, H_(2)O, C_(2)H_6, and O_2. The strong orthogonality and perfect pairing restrictions are tested for the X^(1)Σ^+ state of LiH, the X 1Σ+, a^(3)π, and A^(1)π states of BH, and the H_(2)+D⇄H+HD exchange reaction. The orbitals of H_(2)O and C_(2)H_6 naturally localize into OH, CH, and CC bonding pairs. The nonbonding orbitals of H_(2_O are approximately tetrahedral but this description is only 2 kcal lower than the optimum description in terms of σ and π lone‐pair functions. The calculated rotational barrier for C_(2)H_6 is 3.1 kcal, in good agreement with the experimental value (2.9 kcal). The description of the O2 molecule in the GVB approach is presented and the results of carrying out CI calculations using the GVB orbitals are discussed. The GVB orbitals are found to be a good basis set for configuration interaction calculations. The general features of GVB orbitals in other molecules are summarized.

The Rydberg Nature And Assignments Of Excited States Of The Water Molecule

Abstract We report ab initio theoretical calculation on 32 excited states of H2 O found to lie below 11.7 eV. Of the eight states observed experimentally, the average discrepancy between theoretical and experimental excitation energies is 0.1 eV. We find that the excited states can each be characterized as arising from an excitation to a Rydberg orbital. Our results indicate that the Ẽ and F states are both 3d-like excited states rather than one 3d state and one 4s state as previously assumed and similarly for the two Rydberg series joining onto Ẽ and F. The nsa1 Rydberg series is found to have a quantum defect of 1.38. joining onto the A(1B1 state. We have assigned the 9.81 eV transition observed by electron impact as the 1b1 – 3pb1 excitation to a 3A1 state.

The orthogonality constrained basis set expansion method for treating off-diagonal lagrange multipliers in calculations of electronic wave functions☆

Abstract We propose an alternative to the coupling operator approach for the solution of the self-consistent field equations containing off-diagonal Lagrange multipliers. This method involves a transformation of the basis set after formation of the Hamiltonian matrices and leads to considerable simplification in the equations to be solved, reducing th ehomogeneous equations to pseudo-eigenvalue form. Typical results are reported for the lowest 2 A 1 state of H 2 O + and the lowest 3 A 1 excited states of H 2 O.

The theoretical description of the (ππ*) excited states of ethylene

It is shown that the excited singlet (ππ*) state (V) of planar ethylene in both the Hartree-Fock and π-electron configuration interaction descriptions is quite diffuse. The extent of the π*-orbital in the π-direction as measured by 〈z2〉 is 42 a2o in the V state as compared to 2.7 a2o in the corresponding triplet state (T). In addition, we find that the Hartree-Fock vertical excitation energy for the V state is 7.42 eV as compared to the experimental value of 7.6 eV.

Generalized valence bond wavefunctions for the low lying states of methylene

Abstract Generalized valence bond (GVB) calculations are reported for the 3 B 1 , 1 A 1 , and 1 B 1 states of the CH 2 molecule. The GVB method is discussed and compared with other multi-configuration and separated pair methods. The lowest singlet state ( 1 A 1 ) is found to lie 0.50 eV about the lowest triplet state ( 3 B 1 ) and the 1 B 1 - 1 A 1 separation is found to be 1.40 eV.

Multiconfiguration wavefuntions for the lowest (ππ*) excited states of ethylene

Ab initio calculations have been carried out for the T(^(3)B_(1u)) and V(^(1)B_(1u)) states of ethylene in a planar nuclear configuration. A “double-zeta” gaussian basis, augmented by diffuse functions, was used. A wide variety of configuration interaction wavefunctions (including as many as 1605 configurations), optimized by the iterative natural orbital method, were computed. The calculations predict the ^(1)B_(1u) state to lie 3.8 – 4.1 eV above the 3B1u state. The spatial extent of the triplet state is that of a normal valence state with (x2) ≈ 12 bohr^2. The singlet state, on the other hand, is found to be quite diffuse or Rydberg-like, (x^2) ≈ 35 bohr^2; electron correlation was found to decrease (x^2) by 30% from the Hartree - Fock value (52 bohr^2). This result is not consistent with simple notions concerning π-electron theory.

The proper treatment of off-diagonal lagrange multipliers and coupling operators in self-consistent field equations☆

Abstract We show that past treatments of the off-diagonal Lagrange multipliers or coupling operators in the self-consistent field equations for open-shell systems and in the multi-configuration SCF equations are incomplete. In addition, we obtain the complete variational equations and show how these may be combined into one simple eigenvalue problem which is solved for all orbitals.

Generalized valence bond calculations on the ground state (X 1Σ+g) of nitrogen

Accurate generalized valence bond calculations (GVB) have been carried out on the ground state (X 1Σ+g) of the nitrogen molecule for internuclear distances from 0.80 to 5.00 A. For comparative purposes, corresponding Hartree–Fock (HF) and valence bond (VB) calculations are also reported. While accounting for only ∼25% of the correlation energy of N2 at R=Re, the GVB calculations account for ∼80% of the molecular extra correlation energy, and yield a dissociation energy of 8.58 eV (compared to 5.08 eV from the HF corresponding calculations). In addition to considerably improving on the HF and VB descriptions of N2, the GVB wavefunction retains a simple orbital form which is susceptible to analysis in terms of nonclassical, as well as classical, chemical concepts.

The incorporation of quadratic convergence into open-shell self-consistent field equations

Abstract The quadratically convergent approach to solving the correct SCF equations for general open-shell systems (with orthogonal orbitals, i.e., multiconfiguration-SCF or Hartree-Fock) is derived and used to discuss other less complicated approaches. Representative calculations on He 2 1 [(1s) (2s)] and H 2 O 2 1 A 1 [(1a 1 ) 2 (2a 1 ) 2 (1b 1 ) 2 (1b 2 ) 2 (3a 1 ) (4a 1 )] are reported.

Relation between electronic structure and the chemiluminescence arising from collisions between alkaline earth atoms and halogen molecules

The chemiluminescence ascribed by Jonah and Zare to radiative association of Ba and Cl2 is examined in the light of the electronic structure of the ground and excited states of alkaline earth dihalides. A simple discussion is first given in terms of the possible curve crossings and avoided crossings. In addition ab initio self-consistent-field calculations are reported for CaF2 using an extended basis set. The 1 B 2 excited state, from which the molecule may radiate to the ground state, is predicted to have an equilibrium bond angle of 54° and bond distance of 4·06 bohr. The bertical excitation energy to the 1 B 2 state is 7·3 eV and the vertical energy difference (1 A 1-1 B 2) at the 1 B 2 equilibrium geometry is 1·3 eV. These results appear consistent with the model proposed by Jonah and Zare. In addition, a variety of properties (dipole moments, field gradients, etc). of CaF2 are reported.