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

Long-range interactions and the sign of natural amplitudes in two-electron systems

In singlet two-electron systems the natural occupation numbers of the one-particle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the two-electron wave function in a natural orbital basis. In this work we relate the sign of the natural amplitudes to the nature of the two-body interaction. We show that long-range Coulomb-type interactions are responsible for the appearance of positive amplitudes and give both analytical and numerical examples that illustrate how the long-distance structure of the wave function affects these amplitudes. We further demonstrate that the amplitudes show an avoided crossing behavior as function of a parameter in the Hamiltonian and use this feature to show that these amplitudes never become zero, except for special interactions in which infinitely many of them can become zero simultaneously when changing the interaction strength. This mechanism of avoided crossings provides an alternative argument for the non-vanishing of the natural occupation numbers in Coulomb systems.Comment: 10 pages, 4 figure

Inactivation of cloned Na channels expressed in Xenopus oocytes

This study investigates the inactivation properties of Na channels expressed in Xenopus oocytes from two rat IIA Na channel cDNA clones differing by a single amino acid residue. Although the two cDNAs encode Na channels with substantially different activation properties (Auld, V. J., A. L. Goldin, D. S. Krafte, J. Marshall, J. M. Dunn, W. A. Catterall, H. A. Lester, N. Davidson, and R. J. Dunn. 1988. Neuron. 1:449-461), their inactivation properties resemble each other strongly but differ markedly from channels induced by poly(A+) rat brain RNA. Rat IIA currents inactivate more slowly, recover from inactivation more slowly, and display a steady-state voltage dependence that is shifted to more positive potentials. The macroscopic inactivation process for poly(A+) Na channels is defined by a single exponential time course; that for rat IIA channels displays two exponential components. At the single-channel level these differences in inactivation occur because rat IIA channels reopen several times during a depolarizing pulse; poly(A+) channels do not. Repetitive stimulation (greater than 1 Hz) produces a marked decrement in the rat IIA peak current and changes the waveform of the currents. When low molecular weight RNA is coinjected with rat IIA RNA, these inactivation properties are restored to those that characterize poly(A+) channels. Slow inactivation is similar for rat IIA and poly(A+) channels, however. The data suggest that activation and inactivation involve at least partially distinct regions of the channel protein

Negative spatial regulation of the lineage specific CyIIIa actin gene in the sea urchin embryo

The CyIIIa·CAT fusion gene was injected into Strongylocentrotus purpuratus eggs, together with excess ligated competitor sequences representing subregions of the CyIIIa regulatory domain. In this construct, the chloramphenicol acetyltransferase (CAT) reporter gene is placed under the control of the 2300 nucleotide upstream regulatory domain of the lineage-specific CyIIIa cytoskeletal actin gene. CAT mRNA was detected by in situ hybridization in serial sections of pluteus stage embryos derived from the injected eggs. When carrier DNA lacking competitor CyIIIa fragments was coinjected with CyIIIa.CAT, CAT mRNA was observed exclusively in aboral ectoderm cells, i.e. the territory in which the CyIIIa gene itself is normally expressed (as also reported by us previously). The same result was obtained when five of seven different competitor subfragments bearing sites of DNA-protein interaction were coinjected. However, coinjection of excess quantities of either of two widely separated, nonhomologous fragments of the CyIIIa regulatory domain produced a dramatic ectopic expression of CAT mRNA in the recipient embryos. CAT mRNA was observed in gut, mesenchyme cells and oral ectoderm in these embryos. We conclude that these fragments contain regulatory sites that negatively control spatial expression of the CyIIIa gene

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