An SCF-stabilization approach to excited states embedded in the continuum

By using SCF and stabilization‐like procedures, we have located a (π, π*) singlet resonance‐like state in ethylene at 10.21 eV. This state is embedded in the ionization continuum and carries an oscillator strength of 0.46 and is probably the analog to the spectroscopic V state in Hartree–Fock theory. Implications of these results for other systems are discussed

A Theoretical Investigation of Several Low-Lying States of trans, trans-1,3,5-hexatriene

Results from ab initio calculations concerning several low-lying electronic states of trans,trans-1,3,5-hexatriene are presented and compared with experimental and previous theoretical results. The lowest excited singlet state is predicted to be the ¹B_u state, having essentially valencelike π → π* character. The nominally doubly excited 2¹A_g state is found to lie approximately 0.6-0.9 eV above the 1¹B_u state. Results are also presented for several Rydberg states. The implications of the present results for current parametrizations of semiempirical π molecular orbital schemes are discussed

Quasidegenerate Variational Perturbation Theory and the Calculation of First‐Order Properties from Variational Perturbation Theory Wave Functions

In previous work on the treatment of correlation in molecular systems we have applied a multireference version of second‐order Hylleraas variational perturbation theory. The choice made for the partitioning of H treated the interactions between the correlating functions to infinite order and gave the corrections to the wave function to first order. The method was shown to be accurate in many cases, but became less so when near degeneracies occurred between the reference energy and other eigenvalues of H0. In this article we introduce an effective Hamiltonian method that is analogous to variational perturbation theory, but which is significantly more accurate when near degeneracies are important. This quasidegenerate variational perturbation theory (QDVPT) is an explicitly multireference procedure and treats the entire reference space as a quasidegenerate space. A novel method for solving the QDVPT equations is introduced that avoids explicit construction of the effective Hamiltonian. As a result, the work involved in application of QDVPT is on the roder of that required for variational perturbation theory. We also present an approximate method for calculating first‐order atomic and molecular properties based on Hylleraas variational perturbation theory, multireference linearized coupled cluster, and QDVPT wave functions. The properties are calculated as derivatives of the energy with respect to the field strength. Construction of a one‐electron density matrix based on the energy derivative expression allows rapid evaluation of one‐electron properties. Results are presented and compared to full and truncated CI results. Good agreement is found in the cases examined

A Theoretical Investigation of Some Low-lying Singlet States of 1,3-butadiene

Results are presented from extensive ab initio calculations on several low-lying singlet states of cis- and trans-1,3-butadiene. The results indicate a qualitative difference between the cis and trans isomers for the lowest π → π* transition. For the cis isomer, the first excited singlet state of the same symmetry as the ground state is found to lie above the lowest π → π* transition, and we estimate that this is also the case for the trans isomer

Ab Initio Investigation of Several Low-lying States of All-trans Octatetraene

The results of ab initio calculations that examine vertical and nonvertical transitions to several low-lying states of all-trans-octatetraene are presented. It is found that the lowest vertical excitation is to a valence π → π* ¹B_u state, and the nominally doubly excited 2¹A_g state occurs approximately 0.4 eV higher at the geometry of the ground state. Using estimated excited-state equilibrium geometries, we find that the 2¹A_g state is indeed the lowest singlet excited state, having a 0-0 tarnsition energy of 4.15 eV. The 0-0 transition energy for the 1¹B_u state is calculated to be 4.56 eV. The present results are compared with past theoretical and experimental results

Hylleraas Variational Perturbation Theory: Application to Correlation Problems in Molecular Systems

Hylleraas variational perturbation theory is applied through second order in energy to estimate the correlation energy in several molecular systems. The specific choices for H0 and V which are made lead to equations nearly identical to the multireference linearized coupled‐cluster method of Laidig and Bartlett. The results obtained are in virtually exact agreement where comparisons have been made. Results from test calculations are presented for BeH2, CH2, and C2H4. In addition, the utility of perturbation theory for selecting correlating configurations is examined. This procedure is found to be quite accurate while significantly reducing the size of the system of linear equations to be solved

An ab Initio Investigation of the Stabilization of Selected β-substituted Ethyl Cations and α-substituted Methyl Cations

In this study, we calculate the stabilization of β-substituted ethyl cations (R = H, Li, BeH, BH_2, CH_3, NH_2, OH, F, Na, MgH, AlH_2, SiH_3, PH_2, SH, Cl) and α-substituted methyl cations (R = H, Li, CH_3, NH_2, OH, F, Na, SiH_3, PH_2, SH, Cl) in order to obtain a relationship between the nature of the substituent and the degree of stabilization of the cation. Results show that the stabilization energy is related to the electronegativity of the β substituents, but not the α substituents. The rotational barrier of the β-substituted ethyl cation is linearly related to the Mulliken population of the 2p(C+) orbital. We found that the stabilization energy is linearly related to the ionization potential of the α- and PLA β-substituted radicals, and the HOMO energies of the PLA β-substituted radical are linearly related to the corresponding ionization potentials. Trends in the stabilization by second- and third-row substituents are discussed

A Theoretical Study of Models for X2Y2 Zintl Ions

Ab initio and extended Hückel calculations have been used to discuss the bonding scheme in X₂Y₂ neutral and ionic main group clusters. A qualitative analysis suggests that two different electron counts, 20 and 22, are possible for the butterfly structures of these systems. This results from two orbital crossings in the correlation diagram for the tetrahedral (T_d) -\u3e butterfly (C_2v) -\u3e square-planar (D_2h) transformation. Detailed ab initio computations substantiate this analysis and show that the 20-electron butterfly structure becomes increasingly favored over the tetrahedral one in X₂Y₂ clusters when the 2 atoms have increasing electronegativity difference. These results are in agreement with the known structures for the Pb₂Sb₂²­­­­­­̄ and Sb₂Bi₂²­­­­­­̄ clusters (tetrahedral-like) and the Tl₂Te₂²­­­­­­̄ one (butterfly-like)