Some properties of the bivariational Hartree–Fock scheme for complex symmetric many-particle operators

The bivariational Hartree–Fock scheme for a general many-body operator T is discussed with particular reference to the complex symmetric case: T^? = T*. It shown that, even in the case when the complex symmetric operator T is real and hence also self-adjoint, the complex symmetric Hartree–Fock scheme does not reduce to the conventional real form, unless one introduces the constraint that the N-dimensional space spanned by the Hartree–Fock functions ? should be stable under complex conjugation, so that ?* = ?α. If one omits this constraint, one gets a complex symmetric formulation of the Hartree–Fock scheme for a real N-electron Hamiltonian having the properties H = H* = H^?, in which the effective Hamiltonian H_eff (1) may have complex eigenvalues ε_k. By using the method of complex scaling, it is indicated that these complex eigenvalues—at least for certain systems—may be related to the existence of so-called physical resonance states, and a simple example is given. Full details will be given elsewhere.     

Spin-projected EHF method. IV. Comparison of potential curves given by different one-electron methods

Some aspects of the computer realization of the spin-projected extended Hartree–Fock (EHF ) method at the ab initio level are briefly discussed for the algorithm of solution developed in the previous papers of this series. Calculations have been performed for the BH molecule by using a small basis of contracted Gaussian lobes with the purpose of comparing the potential curves given by the different one-electron methods RHF , UHF , UHF with subsequent spin projection, and EHF . It is concluded that the UHF and, in particular, the EHF methods give a qualitatively correct shape of the potential curve; the RHF method shows the known incorrect dissociation behavior while the potential curve obtained by subsequent spin projection of the UHF wave function exhibits spurious extrema at intermediate internuclear separations.     

Multiplicity,instability, and SCF convergence problems in Hartree–Fock solutions

We present a study of the instability and convergence of Hartree–Fock (HF) ab initio solutions for the diatomic systems H₂, LiH, CH, C₂, and N₂. In our study, we consider real molecular orbitals (MOs) and analyze the classes of single‐determinant functions associated to Hartree–Fock–Roothaan (HFR) and Hartree–Fock–Pople–Nesbet (HFPN) equations. To determine the multiple HF solutions, we used either an SCF iterative procedure with aufbau and non‐aufbau ordering rules or the algebraic method (AM). Stability conditions were determined using TICS and ASDW stability matrices, derived from the maximum and minimum method of functions (MMF). We examined the relationship between pure SCF convergence criterion with the aufbau ordering rule, and the classification of the HF solution as an extremum point in its respective class of functions. Our results show that (i) in a pure converged SCF calculation, with the aufbau ordering rule, the solutions are not necessarily classified as a minimum of the HF functional with respect to the TICS or ASDW classes of solutions, and (ii) for all studied systems, we obtained local minimum points associated only with the aufbau rule and the solutions of lower energies. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 600–610, 2000     

A note on density matrix extrapolation and multiple solutions of the unrestricted Hartree–Fock equations

Unrestricted Hartree–Fock (UHF) SCF–MO calculations on the doublet reaction surface for the addition of methylidyne (CH) to ethylene (C₂H₄) using the standard extrapolation techniques of the GAUSSIAN 70 program show erratic behavior. On the other hand, the potential energy surface calculated without extrapolation of the density matrix and by using the final density matrix of a neighboring point as the initial guess for the density matrix for the new point gave a smooth potential curve without any kinks or erratic pattern. Therefore, the density extrapolation technique should be used with particular caution in UHF calculations.     

6‐[(4‐Fluorophenyl)(1H‐imidazol‐1‐yl)methyl]‐1,3‐benzodioxol‐5‐ol and 6‐[(4‐methoxyphenyl)(1H‐imidazol‐1‐yl)methyl]‐1,3‐benzodioxol‐5‐ol

The title compounds, C₁₇H₁₃FN₂O₃ and C₁₈H₁₆N₂O₄, are new potent aromatase inhibitors combining the common features of second‐ and third‐generation nonsteroid anti‐aromatase compounds. The molecules have a propeller shape, with dihedral angles between adjacent planes in the range 49–86°. A quantum mechanical ab initio Roothaan–Hartree–Fock calculation for the isolated molecules shows values for these angles close to the ideal value of 90°. Docking studies of the molecules in the aromatase substrate show that their strong inhibitor potency can be attributed to molecular flexibility, hydrophobic interactions, heme Fe coordination and hydrogen bonding.     

Extended Hartree–Fock calculations for the helium ground state

The extended Hartree–Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97 , 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the ¹S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree–Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p₀), 2(d₀) and 1 (f₀) Slater orbitals has produced 90% of the correlation energy.     

Structure and electronic structure of polyacene

It is shown that infinite long polyacene chains may have three energetically close but structurally distinct isomers (a symmetrical, sym, form and two lower symmetry forms: one with double bonds in a trans and another isomer with double bonds in a cis pattern). The energetics is based on solid state MNDO theory. We discuss that the symmetrical form has a substantial energy gap E_g in the Hartree–Fock approach owing to exact exchange terms, which are nonlocal. Broken symmetry Hartree–Fock (HF ) solutions for polyacene are also described. An angularly distorted structure suggested earlier on Jahn–Teller grounds is found to be energetically not favorable.     

Applicability of MNDO techniques AM1 and PM3 to ring-structured polymers

Semiempirical Hartree‐Fock techniques are widely used to study properties of long ring‐structured chains, although these types of systems were not included in the original parametrization ensembles. These techniques are very useful for an ample class of studies, and their predictive power should be tested. We present here a study of the applicability of some techniques from the NDDO family (MNDO, AM1, and PM3) to the calculation of the ground state geometries of a specific set of molecules with the ring‐structure characteristic. For this we have chosen to compare results against ab initio Restricted Hartree‐Fock 6‐31G(d,p) calculations, extended to Møller‐Plesset 2 perturbation theory for special cases. The systems investigated comprise the orthobenzoquinone (O₂C₆H₄) molecule and dimers (O₂C₆H₄)₂, as well as trimers of polyaniline, which present characteristics that extend to several systems of interest in the field of conducting polymers, such as ring structure and heterosubstitution. We focus on the torsion between rings, because this angle is known to affect strongly the electronic and optical properties of conjugated polymers. We find that AM1 is always in qualitative agreement with the ab initio results, and is thus indicated for further studies of longer, more complicated chains. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1135–1142, 2002     

Fragmentation processes in phthalimide- and pyridine-2,3-dicarboimidoalkyl-α-diazoketones under resonant electron capture

Resonant electron capture (REC) mass spectra of phthalimide- and pyridine-2,3-dicarboimidoalkyl-α-diazoketones have been investigated. Based on calculations using the Hartree–Fock method and density functional theory with the B3LYP functional the structure of the negative ions (NIs) [M–N₂]^? and [M–N₂–C₃H₃RO]^? as well as the reactions leading to their formation have been proposed.     

Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene π-electron models

Methods accounting for correlation effects in quasi-one-dimensional π-electron systems and based on the restricted Hartree–Fock (RHF ) single determinantal reference state are briefly reviewed as well as their role in the bond length alternation (or dimerization) problem in polyactylene-like systems, as described by the semiempirical Hamiltonians of the Pariser–Parr–Pople (PPP ) type. Particular attention is given to the π-electron model of cyclic polyene homologous series C_NH_N, N = 2n = 4v + 2, v = 1,2,…, which can be regarded as an idealized model of one-dimensional metallic-like systems with imposed Born–von Kármán boundary conditions when N ∞. These models provide a useful bridge between the typical aromatic systems, represented by benzene (N = 6) π-electron model, and long linear polyenic chains, since the properties of these systems hardly change once a sufficiently large N (?26 or 30) is reached. It is shown that due to the quasidegenerate character of the RHF reference employed, and the related prominence of connected quadruply excited cluster components in the exact wave function, most of the standard technieques suffer a singular behavior break down entirely for large enough systems, particularly in the strongly correlated regime. The approximate coupled pair theory that accounts for quadruply excited clusters (ACPQ method) is shown to be free of these shortcomings and is extended to include also approximately the effects of connected triexcited cluster components. These results are compared with other recently examined approximate methods accounting for the tri- and quadruply excited clusters and the proposed ACPQ +T (ACPQ ) procedure is shown to provide the best results in the whole range of the coupling constant.     

2,2,4,4‐Tetra‐tert‐butyl‐1,3,5,2,4‐benzotrioxadisilepine‐7‐carbaldehyde

The mol­ecule of the title compound, C₂₃H₄₀O₄Si₂, features an approximate non‐crystallographic C₂ symmetry axis. The aldehyde group is disordered over two positions with similar occupancies. The geometry of the isolated mol­ecule was studied by ab initio quantum mechanical calculations employing a mol­ecular orbital Hartree–Fock method. The calculations reproduce well the equilibrium geometry but slightly overestimate the value of the Si—O bond lengths of the trioxadisilepine ring.     

3,17‐Dioxoandrost‐4‐en‐4‐yl acetate

The title compound, C₂₁H₂₈O₄, has a 4‐acetoxy substituent positioned on the steroid α face. The six‐membered ring A assumes a conformation intermediate between 1α,2β‐half chair and 1α‐sofa. A long Csp³—Csp³ bond is observed in ring B and reproduced in quantum‐mechanical ab initio calculations of the isolated molecule using a molecular‐orbital Hartree–Fock method. Cohesion of the crystal can be attributed to van der Waals interactions and weak C—H...O hydrogen bonds.     

Supramolecular study,Hirshfeld analysis and theoretical study of 6‐methoxyquinoline N‐oxide dihydrate

In the crystal structure of 6‐methoxyquinoline N‐oxide dihydrate, C₁₀H₉NO₂·2H₂O, (I), the presence of two‐dimensional water networks is analysed. The water molecules form unusual water channels, as well as two intersecting mutually perpendicular columns. In one of these channels, the O atom of the N‐oxide group acts as a bridge between the water molecules. The other channel is formed exclusively by water molecules. Confirmation of the molecular packing was performed through the analysis of Hirshfeld surfaces, and (I) is compared with other similar isoquinoline systems. Calculations of bond lengths and angles by the Hartree–Fock method or by density functional theory B3LYP, both with 6‐311++G(d,p) basis sets, are reported, together with the results of additional IR, UV–Vis and theoretical studies.     

2‐Bromo‐5‐hydroxy­benz­aldehyde

The mol­ecules of the title compound, C₇H₅BrO₂, form zigzag chains running along the b axis and are stacked in layers perpendicular to the a axis. Intermolecular bonding occurs through hydrogen bonds linking the hydroxyl and carbonyl groups, with an O?O distance of 2.804 (4) Å. The Br atom deviates significantly from the plane of the ring and the aldehyde group is twisted by 7.1 (5)° around the Csp²—C_aryl bond. The geometry of the mol­ecule in the crystal is compared to that given by ab initio quantum mechanical calculations for the isolated mol­ecule, using a molecular orbital Hartree–Fock method and density functional theory.     

Ab initio quantum chemical calculations of a cluster C8H12

Using unrestricted Hartree–Fock–Roothaan approximation and density functional theory on 6‐31G* basis, ab initio calculation cluster C₈H₁₂ has been carried out. It was shown as a result of calculations that a ground state for the conformation given is a septet state. This cluster can be used for investigation of the kinematic mechanism of magnetic exchange and magnetic ordering in polyradicals. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

1H‐Indazole and 2H‐indazole derivatives of androsta‐5,16‐dien‐3β‐ol

The title compounds, 17‐(1H‐indazol‐1‐yl)androsta‐5,16‐dien‐3β‐ol, (I), and 17‐(2H‐indazol‐2‐yl)androsta‐5,16‐dien‐3β‐ol, (II), both C₂₆H₃₂N₂O, have an indazole substituent at the C17 position. The six‐membered B ring of each compound assumes a half‐chair conformation. A twist of the steroid skeleton is observed and reproduced in quantum‐mechanical ab initio calculations of the isolated molecule using a molecular orbital Hartree–Fock method. In the 1H‐indazole derivative, (I), the molecules are joined in a head‐to‐head fashion via O—H...O hydrogen bonds, forming chains along the a axis. In the 2H‐indazole derivative, (II), the molecules are joined in a head‐to‐tail fashion with one of the N atoms of the indazole ring system acting as the acceptor. The hydrogen‐bond pattern consists of zigzag chains running along the b axis. Substituted steroids have proven to be effective in inhibiting androgen biosynthesis through coordination of the Fe atoms of some enzymes, and this study shows that indazole‐substituted steroids adopt twisted conformations that restrict their intermolecular interactions.     

Determination of ab initio polarizabilities of polymers: Application to polyethylene and polysilane

An ab initio method for calculating the longitudinal linear polarizability of polymeric chains is described. This method is equivalent to an uncoupled Hartree–Fock scheme. It is applied to polyethylene and polysilane in minimal STO-3G and extended 4-31G basis sets. The study describes important techniques for solving the difficulties met in actual calculations: band reordering of the band structures, calculation of analytical derivatives of the energy bands ?_n(k) and LCAO coefficients c_np(k), and errors caused by the improper lattice sum truncations of the Hartree–Fock matrix.     

Electronic and optical properties of functionalized carbon chains with the localized Hartree–Fock and conventional Kohn–Sham methods

The electronic and optical properties of extended functionalized carbyne chains, polyynes and cumulenes, are investigated with the localized Hartree–Fock method, with conventional Kohn–Sham methods, and with the Hartree–Fock method. It is found that even for very long polyynes the carbon–carbon bond lengths within a polyyne alternate while for long cumulenes no carbon–carbon bond length alternation occurs. Polyynes exhibit a finite HOMO–LUMO gap even if they become very long while cumulenes are found to become metallic in the limit of long chain lengths. The geometry and the electro-optical properties of polyynes cannot be influenced significantly by simple sp-σ-bonded end groups. The optically active ¹Σ_u⁺←X¹Σ_g⁺ electronic transition in polyynes is investigated by time-dependent density-functional theory (TDDFT). The known systematic underestimation of excitation energies in large chain-like systems by TDDFT methods is also found for the systems considered here. Deficiencies in the commonly used exchange-correlation kernels are identified as the main source of this shortcoming of TDDFT methods. Unphysical Coulomb self-interactions present in conventional Kohn–Sham potentials seem to not contribute significantly to the problem.     

Electronic structure and bonding of the pentasulfur hexanitride (S5N6) molecule

An ab initio version of the Hartree–Fock–Slater method is applied to obtain molecular orbitals and eigenvalues for S₅N₆. The electronic structure, bonding, stability, and electronic spectrum are discussed.