A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

氢原子在Be(0001)表面吸附的密度泛函理论研究

采用第一性原理的密度泛函理论研究单个氢原子和多个氢原子在Be(0001)表面吸附性质.给出了氢吸附Be(0001)薄膜表面的原子结构、吸附能、饱和度、功函数、偶极修正等特性参数.同时也讨论了相关吸附性质与氢原子覆盖度(0.06-1.33ML)的关系.计算结果表明:氢原子的吸附位置与覆盖度之间有强烈的依赖关系,覆盖度低于0.67ML时,氢原子能量上易于占据fcc或hcp的中空位置;覆盖度为0.78ML时,中空位与桥位为氢原子的最佳吸附位;覆盖度在0.89到1.00ML时,桥位是氢原子吸附能量最有利的位置;以上覆盖度中Be(0001)表面最外层铍原子的结构均没有发生明显变化.当覆盖度为1.11-1.33ML,高覆盖度下Be(0001)表面的最外层铍原子部分发生膨胀,近邻氢原子渗入到铍表面次层,氢原子易于占据在hcp和桥位.吸附结构中的氢原子比氢分子中的原子稳定.当覆盖度大1.33ML时,计算结果没有发现相对于氢分子更稳定的吸氢结构.同时从分析偶极修正和氢原子吸附垂直高度随覆盖度的变化关系判断氢覆盖度为1.33ML时,在Be(0001)表面吸附达到饱和.     

Density functional study of the conformers of Co4‐based single‐molecule magnet

We present a detailed density functional theory‐based investigation on the geometry and electronic structure of the [Co₄(hmp)₄(MeOH)₄Cl₄] molecule. It is experimentally found to behave as a molecular magnet. The all‐electron electronic structure calculations and geometry optimization of the 88‐atom molecule were carried out within the generalized gradient approximation to the exchange correlation energy. We also study the electronic structures and geometries of a few low‐lying conformers of this molecule. It is found that the magnetic anisotropy energy is highly sensitive to the geometric structure of the molecule. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 324–331, 2003     

Ab initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. III. Me2N?NO2 decomposition of dimethylnitramine in a large crystalline environment

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations, based on localized/local orbitals and an “effective” CI Hamiltonian, for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystalline or other solid environment. Our technique begins with an explicit quantum chemical SCF calculation for a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized, and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are then carried out for breaking a bond in the reference molecule. This method is completely general in that the space treated explicitly, as well as the surrounding space, may contain voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. Dimethylnitramine is the smallest prototype of the energetic R₂N—NO₂ nitramines, such as the 6-member ring RDX or the 8-member ring HMX. Decomposition of energetic compounds is initiated in the solid by a breaking of the target bond. Thus, it is crucial to know the difference in energy between breaking a bond in an isolated energetic molecule versus in the molecule in a solid. In the present study, we have carried out MRD-CI calculations for the Me₂N—NO₂ dissociation of dimethylnitramine in a dimethylnitramine crystal. The cases we investigated were one dimethylnitramine molecule (surrounded by 53 and 685 neighboring dimethylnitramine molecules represented by multipoles), three dimethylnitramine molecules, and three dimethylnitramine molecules (surrounded by 683 neighbors). All multipoles were cumulative atomic multipoles up through quadrupoles. The MRD-CI calculations on dimethylnitramine required large numbers of reference configurations from which were allowed all single and double excitations.     

Investigations of hydrogen-bonded systems: Local density approximation and gradient corrections

The applicability of the local density approximation (LDA ) and of corresponding gradient corrections (for the exchange and correlation energy) for the treatment of the hydrogen bond is investigated. As test systems, we consider the water dimer and the H₂O…?HX complexes (X = F, Cl, Br): Using an LCAO scheme, their equilibrium geometries and interaction energies are ?alculated and compared with experimental data and with other calculations. We obtain that the LDA gives the geometries in qualitative agreement with other data, whereas the energies are overestimated. The use of the gradient corrections (GC ) according to Becke and Perdew leads to a significant improvement of the geometry, and especially of the interaction energies. The calculations indicate further that LDA + GC should also be able to describe weaker intermolecular interactions than the usual hydrogen bond. Finally, a short discussion of the charge distribution and the dipole moments of the H₂O…?HX complexes is performed. © 1994 John Wiley & Sons, Inc.     

Ability of fullerenes to act as η6 ligands in transition metal complexes. A comparative PM3(tm)–density functional theory study

High‐quality DFT calculations are employed to estimate the arene exchange energies for reactions of general formula: For C₆₀ and C₇₀ complexes of Cr(CO)₃, full geometry optimizations at the DFT level using moderately large basis sets were performed, while for the other systems a hybrid approach was developed in which the geometries were obtained at the PM3(tm) level and the energetics were evaluated at the DFT level. C₇₀ is shown to be a slightly better arene ligand than C₆₀; however, no enhancements of arene‐like bonding capabilities are seen for C₇₈ and C₈₄ relative to C₇₀. Explicit calculation of a series of exchange energies at the DFT level using both DFT and PM3(tm) geometries demonstrates that PM3(tm) geometries are sufficiently accurate for the calculation of energetics at a higher theoretical level, but PM3(tm) calculations are inadequate for a quantitative assessment of exchange energies. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1881–1886, 2001     

Calculation of the electronic structure of formaldehyde using overlapping spheres in the SCF Xα scattered-wave method

It has recently been established that physical realism of the results can be improved within the framework of the self-consistent statistical exchange multiple scattering wave method if the atomic spheres are allowed to overlap. Here we report that by semi-empirically adjusting the overlap of the atomic spheres, the ionization potentials and total energy are in better agreement with experiment, and the order of levels A₁ and B₂ in formaldehyde is reversed with respect to some other calculations. The electronic energy level structure calculated here is in agreement with the experimental results. A systematic study of the overlapping scheme for formaldehyde is presented and the results are compared with experiments and other theoretical calculations.     

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)∞.     

Are metal-CO molecules linear? ScCO,TiCO, VCO,and CrCO cases studied in MRCI method compared with DFT method

The equilibrium geometries for the low-lying high-spin electronic states of ScCO, TiCO, VCO, and CrCO molecules were studied with the ab initio method. Restricted Hartree-Fock, multireference configuration interactions, and perturbation calculations were done employing flexible basis sets. We found the equilibrium geometries of the ScCO, TiCO, and VCO molecules to be linear, which is in agreement with a recent density functional calculation. In contrast, we found the CrCO molecule linear while the density functional calculation found it to be bent. As the CrCO molecule is very weakly bonded, we think that this molecule needs further studies with higher-level methods. © 1997 John Wiley & Sons, Inc.     

Valence bond studies of AH2 molecules

Minimal basis set (STO) molecular orbital and valence-bond calculations are reported for the³ B ₁ and¹ A ₁ states of CH₂. The open-shell molecular orbital calculations used the Roothaan formulation. The valence-bond calculations used the Prosser-Hagstrom biorthogonalisation technique to evaluate the cofactors required in using Löwdin's formulae. Optimisation of geometry and orbital exponents in the molecular orbital calculation on the³ B ₁ state gave a geometry of R_C-H=2.11 a.u. and H-C-H=123.2 °. The energy obtained was ?38.8355 a.u. The molecular orbital and valencebond calculations are compared. In the valence-bond calculations the variation with bond-length and bond-angle of the configuration energies was studied. Valence bond “build-up” studies are also reported. Valence-bond calculations using hybrid orbitals instead of natural atomic orbitals showed that the perfect-pairing approximation is not as good for CH₂ as BeH₂. The nature of the lone-pair and bonding orbitals is found to be significantly different between the³ B ₁ and¹ A ₁ states. In the³ B ₁ state the 2s and 2p orbitals are fairly equally mixed between both types of orbital. However in the¹ A ₁ state the bonding orbitals have mainly 2p character and the lone pair orbitals have mainly 2s character. As was found for H₂O, the bonding hybrid orbitals do not follow the hydrogen nuclei as the bond angle varies but continue to point approximately in their equilibrium directions.     

Ab-Initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. II.H3C—NO2 decomposition of nitromethane in a nitromethane crystal with voids

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H₃C? NO₂ bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H₃C? NO₂ bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H₃C? NO₂ bond dissociation energies.     

Assessment of Various Density Functional Theory Methods for Finding Accurate Structures of Actinide Complexes

Density functional theory (DFT) is a widely used computational method for predicting the physical and chemical properties of metals and organometals. As the number of electrons and orbitals in an atom increases, DFT calculations for actinide complexes become more demanding due to increased complexity. Moreover, reasonable levels of theory for calculating the structures of actinide complexes are not extensively studied. In this study, 38 calculations, based on various combinations, were performed on molecules containing two representative actinides to determine the optimal combination for predicting the geometries of actinide complexes. Among the 38 calculations, four optimal combinations were identified and compared with experimental data. The optimal combinations were applied to a more complicated and practical actinide compound, the uranyl complex (UO₂(2,2′-(1E,1′E)-(2,2-dimethylpropane-1,3-dyl)bis(azanylylidene)(CH₃OH)), for further confirmation. The corresponding optimal calculation combination provides a reasonable level of theory for accurately optimizing the structure of actinide complexes using DFT.     

Ab initio Hartree-Fock calculations of electronic wave functions for the c 3πu state of H2

Theoretical electronic wave functions, potential curves, and expectation values of some one-electron properties are given for the c³II_u state of the hydrogen molecule. The calculations are carried out by the matrix Hartree-Fock method and use a 2-center basis of Slater-type orbitals. A total energy of ?0.7292 a.u. is obtained in the best calculation. Our potential curve is reasonably consistent with that calculated by Browne, but we have examined the region of small internuclear distances (those at and below R_e for the ground state) more extensively than any previous calculation. At R ≦ 1.6 a.u. our calculated potential curve is in excellent agreement with experiment.     

An ab initio evaluation of the role of p,π interaction: I. Ethylene derivatives

The RHF/6-311G(d) and MP2/6-311G(d) calculations with full geometry optimization were performed for XCH=CH₂ molecules (X = F, Cl, Br, CH₃, CH₂CH₃, CH₂F, CHO). The p _y electron density distribution in these molecules and the bonding molecular orbitals formed by the p _y orbitals of atoms of the planar fragment of these molecule (atomic orbitals whose symmetry axes are perpendicular to this plane) are not determined by the p,π conjugation between the lone electron pair of the heteroatom in substituent X and π electrons of the C=C bond. Changes in the population of the p _y orbitals of the halogen and carbon atoms in going from X = F to X = Cl and Br are not associated with changes in the extent of this p,π interaction. Taking into account the electon correlation in the MP2 method does not noticeably alter the features of the electron density distribution in these molecules estimated by restricted Hartree-Fock calculations.     

An ab initio study of the p,π interaction: IV. Interaction of an ether oxygen atom with a carbonyl group

RHF/6-311G(d) calculations were performed for the H₃COCOH molecule with full geometry optimization and at varied angles of rotation of the methoxy group about the C-O bond, with all the other geometric parameters optimized. The molecule can exist in two stable conformations with the dihedral angle O¹C¹O²C² of 0.00° and 179.99°. The influence of the rotation angle on the population of the p _y orbital of the carbonyl oxygen atom in compounds with different types of the adjacent bond is essentially similar. The results obtained are inconsistent with the concept of the p,π conjugation involving the p _y orbitals of the planar molecular fragment (orbitals whose symmetry axes are perpendicular to this fragment).     

Nature of coordination bond in silatranes and its formation dynamics according to the ab initio calculations

Quantum-chemical calculations of 1-hydrosilatrane molecule with complete optimization of its geometry and at various fixed Si…N distances (2.0 to 3.7 Å) has been carried out at the MP2/6-31G(d) level. The silatranes coordination bond is formed of different atomic orbitals of Si and N atoms participating in a series of molecular orbitals. With the Si…N distance decreasing, contributions of the atomic orbitals in these molecular orbitals have been changed, number of the molecular orbitals has increased, and total energy of the molecule has decreased. At the coordination centers are getting closer, population of the nitrogen valence s and p _z orbitals have changed due to the corresponding bond angle change; the populations of Si and H orbitals are not significantly changed.     

Fully relativistic calculations of ThF4

Based on the results of first‐principles density functional theory calculations of the electronic structure of ThF₄ in solid state and molecular form, the study of the Th6p, 5f, 6d, 7s and F2s, 2p states was done. We used the fully relativistic cluster discrete variational method with the local exchange‐correlation potential. The hybridization of F2p and Th5f, 6d, 7s, 7p states in the valence molecular orbitals (VMOs) in the region 0–10 eV and of F2s and Th6p states in the inner valence molecular orbitals (IVMOs) in the region 10–50 eV was studied. The results of relativistic cluster calculations are compared with those obtained for ThF₄ molecule. The energies of ionization of VMOs and of IVMOs were evaluated on the basis of the ground‐state and Slater's transition‐state calculations. The MO energy levels provide a satisfactory interpretation of experimental photoelectron spectra. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010