Half-projected and projected Hartree-Fock calculations for singlet ground states. II. Lithium hydride

The half-projected Hartree–Fock function (HPHF ) for singlet states is defined as a linear combination of two Slater determinants which contains only spin eigenstates with even spin quantum numbers. The possible uses of such an approach for determining molecular properties are investigated computing the potential energy curve, binding energy, force constant, and dipole moment variation corresponding to the lithium hydride ground state. Full projected and restricted Hartree–Fock calculations (PHF and RHF ) are performed simultaneously for comparison purposes. It is found that the HPHF model yields very satisfactory results, very close to those of the PHF scheme. Both models predict properly the molecular behavior as a function of nuclear separation, whereas the RHF one fails. A discussion is given in terms of configuration equivalents. It is concluded that the HPHF scheme seems to be useful for determining molecular properties specially in the case of large systems in which the more sophisticated methods are unmanageable.     

Half-projected Hartree–Fock natural orbitals for defining CAS–SCF active spaces

We have extended the range of systems to which the half-projected Hartree–Fock (HPHF ) method has been applied, including the triplet state of the wave function. In our implementation, DIIS overcomes the convergence difficulties reported in earlier studies. HPHF allows generation of a symmetry-broken wave function in regions of the potential energy surface where the RHF wave function is triplet-stable. The fractionally occupied natural orbitals (FONOS ) of the HPHF wave function are good starting vectors for CAS –SCF calculations. A CAS –SCF in the space defined by the HPHF FONOS should be used instead of the unrestricted natural orbital CAS –SCF method in regions of triplet stability and for small active space problems. We draw extensive comparisons between the results of both the UNO –CAS and HPNO –CAS methods and those of full CAS –SCF calculations. © 1993 John Wiley & Sons, Inc.     

Analysis of the half-projected Hartree–Fock function: Density matrix,natural orbitals,and configuration interaction equivalence

The half-projected Hartree–Fock function for singlet states (HPHF ) is analysed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more that two atoms is criticized.     

The half projected Hartree-Fock function for determining singlet excited states. Application to cyclobutanone and 3-cyclopenten-1-one

The Half-Projected-Hartree-Fock procedure (HPHF) for determining singlet ground states is briefly described and extended to the direct determination of singlet excited states. The procedure is applied, using a [7s,3p/2s,1p] basis set, to determine the optimal geometry of two relatively large molecules, to which large CI calculations cannot be easily applied. These two molecules are cyclobutanone and 3-cyclopenten-1-one in their lowest singlet (n → π) excited state. Both molecules are found to exhibit in their excited state a pyramidal structure with the carbonyl oxygen atom pointing outward from the molecular plane. RHF calculations for the singlet ground state were also performed for comparison. The theoretical geometrical parameters compare well with the experimental data.     

Comparison of ground and excited state polarizabilities of thiophene,cyclopentadiene, and fulvene oligomers and their cyano substituted derivatives—Ab initio study

Ab Initio study of the ground and excited state polarizabilities of thiophene, fulvene, and cyclopentadiene based conducting oligomers and their cyano derivatives have been performed using the restricted Hartree–Fock (RHF) and the configuration interaction singles (CIS) approaches, respectively, with 3‐21G* basis set. For comparison purposes, for some small oligomers (monomers and dimers), higher basis sets (6‐31G*, 6‐31+G*, aug‐cc‐pVTZ) were also employed in the computations of polarizabilities. The trends in polarizability as a function of oligomer length were investigated. For all systems, the RHF polarizability increases as n^1.2–1.3 as n gets larger and the CIS polarizability increases as n^1.4–1.6 for n less than seven or eight rings and then increases approximately linearly with n for larger n. For the thiophene based systems the dependence of the polarizability on bond length alternation (BLA) along the backbone of the oligomers was also investigated using the RHF, density functional (DFT), and CIS theories (with 3‐21G* basis set). For thiophene dimer, we also performed RHF/aug‐cc‐pVTZ calculations of polarizabilities versus BLA. We found that the polarizability is largest when BLA is near zero (for both ground and excited states), which correlates with the lowest excitation energy. Comparison with experimental results has been made where possible. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1983–1995, 2007     

Ground-state and some excited states of Li2 by the half-projected Hartree–Fock method

The half-projected Hartree–Fock wave function (HPHF ) is one of simplest models for introducing some electronic correlation effects. In this model, the wave function is built up with only two Slater determinants. This simple form suggests its application for the direct determination of singlet excited states. On the other hand, because the HPHF model does not mix singlet and triplet states with M_s = 0, it can be used for determining independently singlet and triplet states without any mutual contamination. In the present work, we applied this model to determine nine electronic states of the lithium molecule; one of them exhibits even the same symmetry of the fundamental one. For this purpose, the 6-311G (d) basis was used. Potential energy curves were determined and some spectroscopic constants derived. The numerical results were compared with the available experimental data, as well as with other theoretical values. © 1995 John Wiley & Sons, Inc.     

Ground and first excited states electrostatic molecular potentials of ketene and diazomethane

INDO wavefunctions for ¹A₁, ¹A″ and ³A″ states of ketene and diazomethane, obtained with a RHF technique, after some geometry optimization for the excited states, are used to obtain electrostatic molecular potentials under ZDO assumptions. Ground-state results agree with the experimental behaviour and also with other theoretical calculations for both molecules.     

Exponential transformation of molecular orbitals. II. General formulation for UHF calculations and application to diatomics and molecular fragments

The exponential transformation of the molecular orbitals, that has been previously used to achieve a process with a convergence of quadratic quality in SCF closed-shell calculations [J. Chem. Phys. 72 , 1452 (1980)] has been extended to UHF determinantal wave functions built from different orbitals for different spins. Explicit formulas are given for the first and second derivatives of the energy to be varied. The method is illustrated by UHF calculations for systems described as standard singlets (Li₂ and F₂) or triplets (NH) at the RHF approximation level, as well as for CH, CH₂, CH₃ molecular fragments in their valence states.     

Theoretical characterization of the ground state of the alkaline-earth monocarbides: Ordering of the two lower-lying states of the BeC,MgC, and CaC molecules

The two lower-lying electronic states (³Σ⁻ and ⁵Σ⁻) of the BeC, MgC, and CaC molecules were investigated using restricted Hartree-Fock (RHF), generalized valence bond (GVB), and configuration interaction (CI) calculations to establish the relative ordering of those states as a function of the size of the alkaline-earth element. It is shown that as a result of the competition between bonding effects, which predominate for the ³Σ⁻ states, and exchange effects, which stabilize the ⁵Σ⁻ states, the ordering of these states can be reversed as we move from the Be to the Ca atom. For both the BeC and MgC molecules, the ground state was found to be a triplet X³Σ⁻ state, but for the CaC molecule, the high-spin X⁵Σ⁻ becomes more stable. © 1996 John Wiley & Sons, Inc.     

Hartree-Fock theory for negative ions

It is shown that HF computations which yield ?_i > 0 for an occupied MO do not minimize the HF energy. If ?_i > 0, which frequently occurs in the RHF treatment of negative ions, one can reduce ?_i to zero and simultaneously lower E_HF by an appropriate admixture of a continuum function to the corresponding MO ?. We propose a modification of the HF model that takes these facts into account. Applications to the systems O^2?, N^3?, C^4?, S^2?, O₂^2?, C₂^2? are reported and discussed.     

Intramolecular Pnicogen Interactions in PHF?(CH2)n?PHF (n=2–6) Systems

A computational study of the intramolecular pnicogen bond in PHF? (CH₂)_n? PHF (n=2–6) systems was carried out. For each compound, two different conformations, (R,R) and (R,S), were considered on the basis of the chirality of the phosphine groups. The characteristics of the closed conformers, in which the pnicogen interaction occurs, were compared with those of the extended conformer. In several cases, the closed conformations are more stable than the extended conformations. The calculated interaction energies of the pnicogen contact, by means of isodesmic reactions, provide values between ?3.4 and ?26.0 kJ mol^?1. Atoms in molecules and electron localization function analysis of the electron density showed that the systems in the closed conformations with short P ??? P distances have a partial covalent character in this interaction. The calculated absolute chemical shieldings of the P atoms showed an exponential relationship with the P ??? P distance. In addition, a search in the Cambridge crystallographic database was carried out to detect those compounds with a potential intramolecular pnicogen bond in the solid phase.     

Pathways of the reaction of nucleophilic addition of ammonia to formaldehyde in the gas phase and in the complex with formic acid:ab initio calculations

The gradient pathways of the reaction of nucleophilic addition of ammonia to formaldehyde were calculated for free molecules and in the NH₃...H₂CO...HC(O)OH complex by theab initio RHF/6-31G^**, MP2(fc)/6-31G^**, and MP2(full)/6-311++G^** methods. Both reactions proceed concertedly. In the first case, the reaction successively passes through two transitional states with an energy barrier exceeding 35 kcal mol⁻¹. In the case of the complex with formic acid, the reaction follows a conventional pathway, although its activation barrier calculated by the RHF/6-31G^** and MP2(fc)/6-31G^** methods decreases to 12.6 and 3.8 kcal mol⁻¹, respectively. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 13–20, January, 1998.     

Electron correlation and the compton profile of atomic neon

The radial momentum distribution I_o(p) and the Compton profile J_o(q) are determined for atomic neon from several restrictid Hartree-Fock (RHF) wavefunctions and two configuration interaction (CI) wavefunctions. The CI functions are the well correlated (full“second-order”) function of Viers, Schaeffer and Harris, and the Ahlrichs-Hinze multi-configuration Hartree-Fock (MCHF) function which includes only L-shell correlation. It is found for this completely closed shell system that the effects of electron correlation are quite small. This contrasts with the results for systems such as Be(²S) and B(²P) where the semi-internal and internal correlation effects were responsible for significant discrepancies between the RHF and CI results. These results indicate that a wavefunction which carefully includes the semi-internal, orbital polarization, and internal correlations beyond the RHF wavefunction (i.e., a “first-order” or “charge-density” function), should account for the principal correlation effects on the Compton profiles and momentum distributions.     

AB Initio and MNDO calculations of atomic interactions in the CH3OCOCl molecule

The CH₃OCOCl molecule is calculated by ab initio methods using the split-valence basis sets at RHF/3-21G//RHF/3-21G, RHF/6-31G^*//RHF/6-31G^*, and RHF/6-311G^*//RHF/6-31G^* levels of theory and in the MNDO approximation. The optimized geometry of the molecule is consistent with the experimental data. The populations of the p-AOs of this molecule and the MO compositions show that the electron distribution in this molecule should be interpreted without considering the conjugation between the lone electron pairs of the Cl or O atoms and the π-electron system of the carbonyl group. The asymmetry parameters of the electric field gradient on the³⁵Cl nucleus were calculated using the Cl p-AO populations and compared with the corresponding experimental value. Instite of Technical Chemistry, Ural Branch, Russian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 37, No. 4, pp. 646–651, July–August, 1996. Translated by I. Izvekova     

Ab initio study of molecular structure and internal rotation in methyldicyanophosphine and methyldiisocyanophosphine. The Raman spectrum of methyldicyanophosphine and its interpretation with the use of scaling ofab initio force fields

The equilibrium geometric parameters and structures of transition states of internal rotation for the molecules of methyldicyanophospine MeP(CN)₂ and its isocyano analog MeP(NC)₂ were calculated by the RHF and MP2 methods with the 6–31G^* and 6–31G^** basis sets. At the MP2 level, the total energy of cyanide is −35 kcal mol⁻¹ lower than that of isocyanide and the barriers to internal rotation of methyl group for MeP(CN)₂ and MeP(NC)₂ are 2.2 and 2.7 kcal mol⁻¹, respectively. For both molecules, the one-dimensionalab initio potential functions of internal rotation approximated by a truncated Fourier series were used to determine the frequencies of torsional transitions by solving direct vibrational problems for a non-rigid model. The Raman spectrum of crystalline MeP(CN)₂ was recorded in the range 3500–50 cm⁻¹. The vibrational spectra of this compound were interpreted by scalingab initio force fields calculated by the RHF and MP2 method. The vibrational spectrum of methyldiisocyanophosphine was predicted with the use of the obtained scale factors. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1703–1714, September, 1998.     

Hylleraas method for many‐electron atoms. I. The Hamiltonian

A general expression for the nonrelativistic Hamiltonian for n‐electron atoms with the fixed nucleus approximation is derived in a straightforward manner using the chain rule. The kinetic energy part is transformed into the mutually independent distance coordinates r_i, r_ij, and the polar angles θ_i, and φ_i. This form of the Hamiltonian is very appropriate for calculating integrals using Slater orbitals, not only of states of S symmetry, but also of states with higher angular momentum, as P states. As a first step in a study of the Hylleraas method for five‐electron systems, variational calculations on the ²P ground state of boron atom are performed without any interelectronic distance. The orbital exponents are optimized. The single‐term reference wave function leads to an energy of ?24.498369 atomic units (a.u.) with a virial factor of η = 2.0000000009, which coincides with the Hartree–Fock energy ?24.498369 a.u. A 150‐term wave function expansion leads to an energy of ?24.541246 a.u., with a factor of η = 1.9999999912, which represents 28% of the correlation energy. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Force in SCF theories. MC SCF and open-shell RHF theories

A theorem reported for Hartree-Fock SCF theory is shown to be valid for general MC SCF and open-shell RHF theories - a sufficient condition for these wavefunctions to satisfy the Hellmann-Feynman theorem is that the basis set includes the derivative AO ^?X_r/^?X_rfor any basis X_r. The new force approach is applicable to wider fields including electronic processes in chemical reactions. Test calculations are given for some simple systems.     

Intramolecular nucleophilicS N 2 substitution at the tetrahedral carbon atom: Anab initio study

Pentacoordination of carbon atom in bicyclic organic compounds of the pentalene type was studied by theab initio RHF/6-31G^** and MP2(full)/6-31G^** methods. It was shown that intramolecularS _N 2 reactions with energy barriers within the energy scale of NMR spectroscopy can occur in systems in which a linear orientation of the attacking and leaving groups is realized. The barrier to the intramolecular nucleophilic substitution reaction in 2,3-dihydro-3-formylmethylenefuran is 36.9 (RHF) and 27.7 kcal mol⁻¹ (MP2) and decreases to 16.4 and 19.4 kcal mol⁻¹, respectively, in the case of diprotonation at the O atoms in this system. For model pentalene type compounds containing electron-deficient B atoms in the ring, theab initio calculations predict a further decrease in the barrier height (down to less than 10 kcal mol⁻¹). Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 7, pp. 1246–1256, July, 1999.     

Magnetic properties of Cu(II) bischelate complexes with 3-imidazoline nitroxides. 1. Anab initio analysis of spin density delocalization channels

Spin density redistribution between the paramagnetic centers Cu²⁺, N-O, and N’-O’ of bischelate complexes CuL₂ of the copper ion with enaminoketone 3-imidazoline nitroxides (L) are investigated using an ab initio RHF (restricted Hartree-Fock) approach. The most important channels of unpaired electron delocalization over the systems of π- and Σ-bonds in such complexes are revealed. The conformation dependence of spin density localized on paramagnetic centers and delocalized due to a distortion of the structure of the environment of the Cu²⁺ ion from square planar to tetrahedral is analyzed and explained. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 5, pp. 840–849, September-October, 1997.