Fock Instabilities Research Articles

Albert Warner Overhauser

Albert Warner Overhauser

Theoretical study of the low lying states of Al 2As: Towards a reliable description

Recently the 2A′ ground state has been reported for Ga 2P and Ga 2As [7], however, there is no previous work on the C s structure state of Al 2As. This Letter reports the geometry optimisations and vibrational frequency calculations performed, using various approaches. In this study, the global minimum belongs to the 2A′ state, correlating with the 2B 2 state. The 2A 1 state is also reported for the first time. Difficulties in treating the 2B 2 state are discussed in terms of the Hartree–Fock instability. Based on our calculations, we discuss the Al 2As − photoelectron spectrum.

Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion

Equilibrium structure, vibrational frequencies, and ionization energies of the para-benzyne radical anion are characterized by coupled-cluster and equation-of-motion methods. Vibronic interactions with the low-lying excited state result in a flat potential energy surface along the coupling mode and even in a lower-symmetry C2v structures. Additional complications arise due to Hartree–Fock instabilities and near-instabilities. The magnitude of vibronic interactions was characterized by geometrical parameters, charge localization patterns and energy differences between the D2h and C2v structures. The observed trends suggest that the C2v minimum predicted by several theoretical methods is an artifact of incomplete correlation treatment. The comparison between the calculated and experimental spectrum confirmed D2h structure of the anion, as well as accuracy of the coupled-cluster and spin-flip structures, frequencies and normal modes of the anion and the diradical. Density functional calculations (B3LYP) yielded only a D2h minimum, however, the quality of the structure and vibrational frequencies is poor, as follows from the comparison to high-level wave function calculations and the calculated spectrum. The analysis of charge localization patterns and the performance of different functionals revealed that B3LYP underestimates the magnitude of vibronic interactions due to self-interaction error.

Imidazolopyrazinones as potential antioxidants

A series of imidazolopyrazinones 3, substituted at C-2, and C-2/C-6, has been prepared. The compounds behaved as quenchers of superoxide anion. The more active compounds are structurally related to coelenterazine, a natural substrate of marine bioluminescence. Theoretical parameters based on Hartree–Fock instabilities have been examined.

Hartree–Fock instabilities and electronic properties

Hartree–Fock instabilities and electronic properties

Ab initio study of organic mixed valency

A series of six radical cations of the type (DLD)+ was investigated at the ab initio unrestricted Hartree–Fock level. One localized and one delocalized conformation were systematically searched by full geometry optimization. At both nuclear arrangements, mostly found as being minima in the symmetry-restrained Hartree–Fock framework, excitation energies were calculated through the expansion of the wave function on single electronic excitations of the Hartree–Fock fundamental determinant and at the unrestricted Hartree–Fock or at the multiconfigurational self consistent field levels. Few calculations were also performed by taking into account some part of the electronic correlation. Except for N,N,N′,N′-tetramethyl p-phenylenediamine, all the studied compounds are localized stable cations, at the symmetry-restrained Hartree–Fock level. However, the reoptimization of their wave function changes this observation since only three of them seem to conserve a localized stable conformation. Most of the studied systems are characterized by one or two excited electronic states very close to the fundamental one and should thus present an unresolved broadened first absorption band in the near-infrared region. These features are in agreement with the available experimental data. Strong Hartree–Fock instabilities are found for the delocalized structure and put in relation with the existence of the large nonadiabatic coupling in this conformational region. The solvent influence is discussed in the Onsager dipolar reaction field framework. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 552–573, 2000

Isomerization of Cyclopropanecarbonitrile. Quantum Chemical and Model Calculations

Density functional theory (DFT) and two-configuration self-consistent-field (TCSCF) calculations including CI were carried out to investigate the pathways of the unimolecular isomerizations of cyclopropanecarbonitrile. Vibrational frequencies calculated at DFT and TCSCF levels of theory were used to estimate frequency factors by transition state theory. Transition states corresponding to both closed shell, concerted and biradical paths in the formation of the main products (cis- and trans-crotonitrile and vinylacetonitrile) were localized. However, owing to Hartree−Fock instabilities in the wave functions of the closed shell (concerted) transition states, it is not clear whether the concerted path is of any physical significance. RRKM calculations were carried out to transfer values of A∞ and E∞ of the isomerizations to A and Ea corresponding to the experimental conditions. Computer modeling, containing the biradical isomerization pathway and the interisomerizations between the products, was carried out, and the results are compared with the experiment. Methacrylonitrile, which is formed in trace quantities, proceeds via a concerted mechanism with a closed shell singlet transition state but with some contribution of a biradical character.

The biradical character of 1,2-dithiin and its valence isomers

1,2-Dithiin and its valence isomers were studied by ab initio methods at the UHF/6-31G * level and employing the guess=mix option. Solutions for these systems obtained without destroying the α–β spin-symmetry displayed Hartree–Fock instabilities. Optimized geometries of all structures are minima (even the cZc-isomer which according to previous work is a transition state). The biradical characters for all these structures were analyzed following the scheme of Yamaguchi. According to this scheme the 2-butenedithial isomers have significant singlet biradical character while 1,2-dithiin has only a small amount of biradical character. Proposals regarding the nature of the intermediates in the photolysis of 1,2-dithiin are made.

Comparison of ab Initio and Density Functional Theory for Alkali Peroxynitrite: A Highly Correlated System with Hartree−Fock Instability

Ab initio methods including density functional theory are used to study alkali peroxynitrite (ONOOM, M = Li, Na, and K). The energy, optimized geometries, and vibration frequencies are presented for different conformations of alkali peroxynitrite. The cis−cis (a pseudo-five-membered ring) and trans−cis conformers are minima from a search over the dihedral angles ONOO and NOOM, respectively. Other minima that appear on the potential surfaces depend on the level of theory and the alkali atom studied. All levels of theory predict the cis−cis structures to have the lowest energy, and the stability relative to the trans−cis structures decreases from Li to Na to K. The rotational barrier of cis−cis to trans−cis isomerization is about 20 kcal/mol in ONOOLi, 27 kcal/mol in ONOONa, and 22 kcal/mol in ONOOK. The barriers for the reverse process are 12, 17, and 13 kcal/mol, respectively. Singlet−triplet UHF Hartree−Fock wave function instabilities are found in some of the ONOOM molecules, which lead to poor values f...

About the relations between polarizability and Hartree—Fock instabilities. Part 1. The hydrogen molecule

Relations between ab initio Hartree-Fock non-singlet instabilities and electric dipole polarizabilities have been investigated by studying the H 2 dissociation using the minimal STO-3G and Sadlej polarized atomic basis sets. Particular attention is paid to the effects of including the electron correlation via unrestricted Hartree-Fock, Møller-Plesset, configuration interaction, and coupled cluster techniques.

A direct algorithm for self-consistent-field linear response theory and application to C60: Excitation energies, oscillator strengths, and frequency-dependent polarizabilities

We present a direct self-consistent-field (SCF)-type algorithm and its implementation for the computation of linear response properties: excitation energies, oscillator strengths, and frequency-dependent polarizabilities within the time-dependent SCF or random phase approximation. The treatment of singles configuration interaction for electronic excitations and Hartree–Fock instability criteria are covered as special cases. The algorithm is based on proven direct SCF methodology. This, together with full exploitation of molecular symmetry, opens the way to the treatment of large molecules. Applications to C60 strongly support the assignment of the lowest-lying dipole allowed transition to the strong band at 3.8 eV.

Magnetic susceptibilities of actinide 3d-metal intermetallic compounds

We have numerically calculated the magnetic susceptibilities which appear in the Hartree–Fock instability criterion for actinide 3d transition-metal intermetallic compounds. This calculation is based on a previous tight-binding description of these actinide-based compounds [A. Troper and A. A. Gomes, Phys. Rev. B 34, 6487 (1986)]. The parameters of the calculation, which starts from simple tight-binding d and f bands are (i) occupation numbers, (ii) ratio of d-f hybridization to d bandwidth, and (iii) electron-electron Coulomb-type interactions.

Hartree Fock instabilities in the S4N 4 2+ dication

The HF singlet stability of the S4N42+dication is investigated. At the experimental bond length, RSN=1.545 A, the D4h solution is stable but at 2.00 A a C2v broken symmetry solution is of lower energy. Population analysis shows that C2v solution has a nitrogen “π-hole” on one of the unique nitrogens. The sulphur π-hole (found for the anion S3N3−at this distance) is not a local minimum.

Hartree–Fock instabilities in the trisulphur–trinitride anion

Crystallographic evidence indicates that the structure of the trisulfur trinitride anion, S3N3−, is planar with equal SN bond lengths. Although the recent literature contains a number of molecular orbital calculations of D3h symmetry there are also calculations which indicate inequivalent nitrogens, suggesting broken symmetry. The results of an investigation of Hartree–Fock instabilities of the abinitio molecular orbital description of this system are reported. The D3h solution is indeed singlet stable but there are relatively close-lying C2v broken-symmetry solutions. In the broken-symmetry solutions the π electron network encompasses only five centres; the sixth centre, essentially free of π charge, may be either a sulphur or a nitrogen, thus yielding two distinct broken-symmetry solutions.

Instabilities of the Hartree–Fock solution and the vibrational mode in a molecule

The Hartree−Fock instability and the force constant formula for a normal coordinate of a molecule are discussed. (AIP)

A study of Hartree–Fock instabilities in Cr2(O2CH)4 and Mo2(O2CH)4

The Hartree–Fock instability of the SCF wave functions obtained for the quadruply bonded complexes Cr2(O2CH)4 and Mo2(O2CH)4 is studied at the ab initio level. Several cases of singlet, nonsinglet, and nonreal instabilities are found for each of these complexes at the experimental value of the metal–metal bond length. For Cr2(O2CH)4, these instabilities are still found at much shorter Cr–Cr distances. The ’’broken symmetry’’ wave functions corresponding to some of the singlet and nonsinglet instability roots of Cr2(O2CH)4 are computed and analyzed. Each of these broken-symmetry wave functions is characterized by an important decrease of the bonding character of the metal–metal interaction with respect to the symmetry-adapted wave function. Singlet instability can thus be considered as an attempt to reduce the strong bonding character imposed by the symmetry constraints to the whole class of D4h quadruply bonded complexes. The case of MoCr(O2CH)4 for which the symmetry of the system is broken from D4h to C4v, is analyzed. An examination of the singlet instability matrices As+Bs obtained for Cr2(O2CH)4 and Mo2(O2CH)4 suggests that the presence of a multiple metal–metal bond strongly favors instability. A single determinant Hartree–Fock wave function might lead in such a case to an erroneous description of metal–metal multiply bonded systems. For this class of molecules, singlet stability equations could provide a simple and accurate procedure to check the reliability of Hartree–Fock wave functions.