Near Hartree-Fock limit study of the linear chain of hydrogen atoms

The linear, equidistant chain of hydrogen atoms has been studied with the aid of the crystal orbital method. Extended gaussin basis sets have been used, with the aim to obtain near Hartree—Fock limit ground state properties. The metallic type and the broken symmetry type solution yielded energies of ?0.5361 and ?0.5372 hartree, respectively, for the total energy per hydrogen atom. These values are estimated to be at most 0.5 millihartree above the Hartree-Fock limit. The corresponding values for the equilibrium distance r_e are 1.840 and 1.843 bohr, respectively.     

On the ground-state properties of the germanium dimer

A theoretical evaluation of the bond length, vibrational frequency and dissociation energy of the Ge₂ molecule is reported. The effective core-potential Hartree—Fock calculations followed by extensive Cl give the following values: R_e = 4.60 bohr, ω_e = 217 cm^?1, D_e = 2.54 eV. These values are discussed and compared with those or previous theoretical work and with the available experimental data.     

A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Self-consistent molecular hartree—fock—slater calculations. IV. On electron densities,spectroscopic constants and proton affinities of some small molecules

The use of the Xα exchange approximation in calculations on small molecules is studied. Electron densities are very similar to Hartree—Fock densities, as judged from density difference maps. The statistical total energy, E_Xα, is used in order to calculate R_eB_e, ω₃ and D_e of a series of diatomic molecules. The agreement with experiment is again similar to that in Hartree—Fock calculations. Proton affinities can also be calculated very well. The Hartree—Fock—Slater and Hartree—Fock models show on the whole very analogous behaviour. These results are obtained by using accurate, unapproximated, potentials and densities.     

Hartree—Fock—Slater functions as basis for one-electron perturbation calculations for molecules: I. Calculation of ground state electric dipole polarizabilities

The analysis of the decoupling of Hartree—Fock—Slater SCF perturbation equations for an external field is undertaken. The points of departure from the corresponding Hartree—Fock perturbation equations are stressed. Both formal and numerical results suggest that the fully uncoupled Hartree—Fock—Slater expression is a less drastic approximation than the same Hartree—Fock one. The uncoupled expression for the ground state electric dipole polarizability is calculated for CO, N₂, ethylene, acethylene and trans-butadiene in the dipole length—dipole length, dipole velocity—dipole length and dipole velocity—dipole velocity alternative formulations with an ab initio Hartree—Fock—Slater SCF basis set. The results compare well with other non-empirical results and the dipole velocity-dipole length results are in remarkably good agreement with experiments.     

Ab initio studies on clusters of polar molecules. stability of cyclic versus open-chain trimers of hydrogen fluoride

Large-scale ab initio calculations have been performed on cyclic and open-chain trimers of hydrogen fluoride including partial geometry optimization. The cyclic trimer turned out to be more stable by ≈ 2 kcal/mole. Equilibrium geometries and hydrogen bond energies are compared with corresponding quantities of (HF)₂ and of the infinite chain (HF)∞.     

Cooperativity and electron correlation effects on hydrogen bonding in infinite systems

Structural and electronic properties of hydrogen-bonded infinite chains of hydrogen cyanide and formamide molecules have been investigated by the ab initio crystal orbital method using several, partly highly polarized, atomic basis sets of increasing size at the Hartree–Fock (HF ) level and by including electron correlation effects in the second order of Møller–Plesset perturbation theory. The results obtained show that hydrogen bonding in molecular crystals of the type investigated is a highly cooperative phenomenon, both from the structural and energetic points of view. Comparison with clusters of up to four monomers demonstrate how various structural parameters converge toward their limiting values in the infinite system. The results obtained for infinite HCN chains show an excellent agreement with those observed for solid HCN, whereas the infinite formamide chain proves to be a reasonable model for the corresponding liquid phase. © 1994 John Wiley & Sons, Inc.     

The effect of electron correlation on one-electron distributions

Hartree—Fock wavefunctions and good approximations to the exact wavefunctions are used to demonstrate the effect of electron correlation on the radial density D(r₁) and the contours of the density distribution ?(r₁) in the He isoelectronic sequence. In general, correlation effects diminish as the charge-cloud becomes less diffuse.     

A theoretical study of the condensation reactions of methyl cation with ammonia,water, hydrogen fluoride and hydrogen sulphide

Ab initio molecular orbital calculations have been used to study the condensation reactions of CH₃^? with NH₃, H₂O, HF and H₂S. Geometry optimization has been carried out at the Hartree—Fock (HF) level with the split-valence plus d-polarization 6-31G* basis set and improved relative energies obtained from calculations which employ the split-valence plus dp-polarization 6-31G** basis set with electron correlation incorporated via Moller—Plesset perturbation theory terminated at third order (MP3). Zero-point vibrational energies have also been determined and taken into account in deriving relative energies. The structures of the intermediates CH₃XH^? (X = NH₂, OH, F and SH) have been obtained and dissociation of these intermediates into CH₂X⁺ + H₂ on the one hand, and CH₃^? + HX on the other, has been examined. It is found that for those species for which the methyl condensation reaction is observed to have an appreciable rate (X = NH₂ and SH), the transition structure for hydrogen elimination from CH₃XH^? lies significantly lower in energy than the reactants CH₃^? + HX (by 75 and 70 kJ mol^?1 respectively). On the other hand, for those species for which the methyl condensation reaction is not observed (X = OH and F), the transition structure for H₂ elimination lies higher in energy than CH₃^? + HX (by 6 and 87 kJ mol^?1 respectively).     

A microsolvation approach to the prediction of the relative enthalpies and free energies of hydration for ammonium ions

Hartree–Fock (HF) and second-order Møller–Plesset (MP2) calculations were used to investigate the structures and thermochemistry of methylammonium–water clusters (Me_4-m NH _m ⁺ (H₂O) _n , m=1–4, n=1–4). Water molecules were treated ab initio and with effective fragment potentials (EFP). In addition to a thorough phase-space search, the importance of basis set, electron correlation, and thermodynamic effects was systematically examined. Cluster structures resulted from hydrogen bond formation between the ammonium group and water molecules; upon saturation of the hydrogen bonding sites of the ammonium group, water molecules entered the second hydration shell. With only four water molecules, the experimental relative enthalpies of hydration were well reproduced at the HF level, while the MP2 relative free energies were in best agreement with experiment. Absolute energies of hydration were calculated using an empirical correction. These results strongly suggest that a HF-based microsolvation approach employing a small number of water molecules can be used to compute relative enthalpies of hydration.     

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.     

Conformation of cationic N,N‐di­methyl­glycine in di­methyl­glycinium tri­fluoro­acetate

In the title compound, C₄H₁₀NO₂⁺·C₂F₃O₂^?, the main N—C—COOH skeleton of the protonated amino acid is nearly planar. The C=O/C—N and C=O/O—H bonds are syn and the two methyl groups are gauche to the methyl­ene H atoms. The conformation of the cation in the crystal is compared to that given by ab initio calculations (Hartree–Fock, self‐consistent field molecular‐orbital theory). The tri­fluoro­acetate anion has the typical staggered conformation with usual bond distances and angles. The cation and anion form dimers through a strong O—H?O hydrogen bond which are further interconnected in infinite zigzag chains running parallel to the a axis by N—H?O bonds. Weaker C—H?O interactions involving the methyl groups and the carboxy O atoms of the cation occur between the chains.     

Molecular symmetry. IV. The coupled perturbed Hartree–Fock method

Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the coupled perturbed Hartree–Fock (CPHF) formalism, a key step in the analytical computation of energy first derivatives for configuration interaction (CI) wavefunctions, and energy second derivatives for Hartree–Fock (HF) wavefunctions. One possible computational strategy is to construct Fock-like matrices for each nuclear coordinate in which the one- and two-electron integrals of the usual Fock matrix are replaced by the integral first derivatives. “Skeleton” matrices are constructed from the unique blocks of electron-repulsion integral derivatives. The correct matrices are generated by applying a symmetrization operator. The analysis is valid for many wavefunctions, including closed- or open-shell spin-restricted and spin-unrestricted HF wavefunctions. To illustrate the method, we compare the computer time required for setting up the coupled perturbed HF equations for eclipsed ethane using D_3h symmetry point group and various subgroups of D_3h. Computational times are roughly inversely proportional to the order of the point group.     

Kramers' restricted hartree—fock method for polyatomic molecules using ab initio relativistic effective core potentials with spin—orbit operators

A two-component Kramers' restricted Hartree–Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin–orbit operators at the Hartree–Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin–orbit interactions at the HF level. KRHF calculations have been performed for the HX, X₂, XY(X, Y = I, Br), and CH₃I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin–orbit interactions.     

Study of the electronic structure of molecules. XV. Comments on the molecular orbital valency state and on the molecular orbital energies

The valency state (vs) concept is analyzed in the Hartree–Fock approximation. A valency state “standard” is defined for atoms at infinite separation. A molecular orbital valency state (Movs) is defined from a partitioning technique (bond energy analysis) previously introduced for the Hartree–Fock molecular wave functions. The Movs for a given atom in a molecule is much higher in energy than the vs and its energy varies from molecule to molecule depending on the exact field of the surrounding atoms. The examples selected in the discussion are the CH₄ CH₃F, CH₂F₂, CHF₃ and CF₄ molecules. An analysis of the orbital energies is then given in terms of the bond energy. The importance of the rearrangement effects following ionization of inner shell electrons (simulation of ESCA type experiments) is illustrated with computations of the positive ion for methane and its fluoroderivatives. It is concluded that rearrangement following ionization from inner shells is as important as rearrangements following ionization from valency electrons. A direct consequence is that the orbital energies should not be equated to the inner shell ionization potentials. The computation of such ionization potentials agrees to about 99.5% with ESCA data, when the energy of both the neutral and ionic species are computed; the use of the orbital energies limits this agreement to about 95%.     

Theoretical study of metiamide,a histamine H2 antagonist

The requirements for H₂-antagonist activity so far identified for most of the known antagonists of histamine are the presence of a heterocyclic ring containing a basic center linked via a methylene chain to a substituted guanidine or thiourea polar side chain. Metiamide is a potent H₂ antagonist (pA2=6.06). We have used the ab initio Hartree–Fock (HF) method in order to study the conformational properties of the N₃(SINGLE BOND)H tautomers of metiamide molecule and histamine monocation. Three basis set (the 3-21G*, 6-31G**, and 6-31+G**) were used, the results compared, and the geometric parameters fully optimized. Our results indicate the preference of metiamide for a folded conformation with an intramolecular hydrogen bonding between the imidazole ring and one of the NH groups. The optimized geometrical parameters and charge distributions of both molecules, using the Mulliken, and natural bond order (NBO) analysis, are given and discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 117–128, 1998     

Complexes self‐associate by hydrogen bonding and metallophilic attraction: Theoretical study

Hydrogen bonding and metallophilic attractions are studied in the model systems: [(AuNH₃Cl)₂], [(AuNH(CH₃)₂Cl)₂], [{Au₂(μ‐SH)(PH₂O)(PH₂OH)}₂], [(CuNH₃Cl)₂], and [{Cu(NH₃)Cl}₄] at the Hartree–Fock (HF) and second‐order Møller–Plesset (MP2) levels. The two interactions are found to be comparable and prevailing in the final structure. It is determined that the aurophilic contact has a same magnitude that the hydrogen bonding, and is stronger than the cuprophilic interaction. The presence of hydrogen bond directs the growth of the crystal. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

6β‐Hydroxy‐5β‐methyl‐20‐oxo‐19‐norpregn‐9(10)‐en‐3β‐yl acetate

In the title compound, C₂₃H₃₄O₄, which is an intermediate in the synthesis of pregnane derivatives with a modified skeleton that show potent abortion‐inducing activity, the conformation of ring B is close to half‐chair due to the presence of both the C=C double bond and the axial 5β‐methyl group. Rings A and C have conformations close to chair, while ring D has a twisted conformation around the bridgehead C—C bond. Molecules are hydrogen bonded via the hydroxyl and acetoxy groups into infinite chains. Quantum‐mechanical ab initio Roothan Hartree–Fock calculations show that crystal packing might be responsible for the low values of the angles between rings A and B, and between ring A and rings C and D, as well as for a different steric position of the methyl ketone side chain compared to the geometry of the free molecule.     

Theoretical determination of molecular structure and conformation: Part X. Geometry and puckering potential of azetidine, (CH2)3NH,combination of electron diffraction and ab initio studies

Restricted Hartree—Fock calculations on 21 planar and puckered conformers of azetidine have been done employing a split valence basis augmented by d functions. Complete geometry optimizations have been performed for eight conformers. In this way the puckering potential of azetidine is explored over the range ?40° < ø (puckering angle) < 40°, for both sp³ and sp² hybridization of the nitrogen atom. In its equatorial form, azetidine is slightly more puckered than cyclobutane. This is because of a decrease of van der Waals' repulsion between H atoms. Charge effects lead to destabilization of the axial forms. There is only moderate coupling between puckering and methylene group rocking. Previously published electron diffraction (ED) data are reinvestigated using vibrational corrections and information from the ab initio calculations. On the basis of this MO constrained ED (MOCED) analysis a puckering angle φ = 35.1(1.8)° is found. Observed r_g and r_e bond distances are compared with ab initio values.     

Ab initio studies on infinite linear hydrogen fluoride chains

Ab initio crystal orbital calculations on linear infinite chains of hydrogen fluoride and MO calculations on HF and the linear dimer have been performed. Equilibrium geometries, force constants, band structures, densities of states and longitudinal phonon dispersions are presented, and compared with the available data. In agreement with experiment the most common features of hydrogen bonding, elongation of HX bond length (ΔR_HX and decrease in HF stretching force constants, are much more pronounced in the solid state than in the isolated dimer.