On the use of spatial symmetry in atomic-integral calculations: An efficient permutational approach

The minimal number of independent nonzero atomic integrals that occur over arbitrarily oriented basis orbitals of the form ?(r) · Y_lm(Ω) is theoretically derived. The corresponding method can be easily applied to any point group, including the molecular continuous groups C_∞v and D_∞h. On the basis of this (theoretical) lower bound, the efficiency of the permutational approach in generating sets of independent integrals is discussed. It is proved that lobe orbitals are always more efficient than the familiar Cartesian Gaussians, in the sense that GLO s provide the shortest integral lists. Moreover, it appears that the new axial GLO s often lead to a number of integrals, which is the theoretical lower bound previously defined. With AGLO s, the numbers of two-electron integrals to be computed, stored, and processed are divided by factors 2.9 (NH₃), 4.2 (C₅H₅), and 3.6 (C₆H₆) with reference to the corresponding CGTO s calculations. Remembering that in the permutational approach, atomic integrals are directly computed without any four-indice transformation, it appears that its utilization in connection with AGLO s provides one of the most powerful tools for treating symmetrical species.     

Infrared intensities of methane and ethane. A starting set of electrooptical parameters for n-hydrocarbons

Sets of electrooptical parameters (eop's), suitable for longer n-paraffins and less constrained than those already used to fit the IR intensities of CH₄ and C₂H₆ and their deuterated derivatives, are presented and discussed. The technique adopted in the least-squares refinement of eop's from experimental data is discussed in detail.     

Multiconfiguration self-consistent wavefunctions for CH4, C2H4 and C2H6

The results of several MC SCF calculations on CH₄, C₂H₄ and C₂H₆ with minimun bases of Slater type AO's are reported. The computing method is a quadratically convergent process. Better final energies are obtained if localized MO's are used.     

A theory of molecules in molecules

SCF wave functions have been calculated using a minimal atomic basis set of Gaussian lobe functions for the para-, meta-, and ortho-forms of the molecules C₆H₄XY, where X, Y can be either of CN, OH, or F. It is found that in all cases the total energies increase in the sequence meta-, para-, ortho-compound. For the molecules containing the CN group the energy differences are extremely small (0.1–1 kcal/mole) for the other molecules they are one to two orders of magnitude larger. The reliability of these results is discussed. The theory of molecules in molecules is applied to these cases. The wave function of C₆H₄XY is constructed from the fragments C₆H₅X and HY by transferring some of the localized orbitals of the wave functions of the fragments and recalculating the orbitals in the region of interaction. For the molecules containing the CN group the energy differences are too small so that they are not correctly reproduced except by the most exact calculations, which involve no approximations other than the transfer of localized orbitals. For the other molecules satisfactory results are obtained.     

A new algorithm for inactive orbital optimization in valence bond theory

This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field (VBSCF) method with non-orthogonal orbitals. The frozen core approximation method is extended to the case of non-orthogonal orbitals. The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals, where inactive orbitals are orthogonal, while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals. It is shown that our new algorithm has a low scaling of (N _a + 1)m ⁴, where N _a and m are the numbers of the active orbitals and basis functions, respectively, and is more efficient than the existing VBSCF algorithms.     

The delocalisation energy of benzene and the non-empirical MO theory

Algebraic expressions for the vertical Delocalisation Energy (DE) of benzene are derived from non-empirical MO theory. For comparison with early work in the π-electron approximation, and ultimately with Hückel theory, the results are formulated in terms of a core resonance integral,β, and π-electronic repulsion integrals. All integral values are inferred from the results ofab initio SCF calculations. Two expressions are derived, which refer to two ways of forming the localised π MOs: one where three pairs of adjacent atomic orbitals are selected from a set of six orthogonalised orbitals; and another where a non-orthogonal set of atomic orbitals is used. The first expression is formally similar to an expression originally derived by Pople from a different point of view and with many approximations. This expression gives too large a magnitude for DE when used with anab initio value ofβ. The second expression gives a result much closer to an empirical value of DE and shows that the main reason for DE being about 50% of 2β rather than 2β is the stabilising effect of overlap in the localised structure, and that the less important factor is the inclusion of electronic repulsion.     

Ab initio calculations on large molecules using molecular fragments First order electronic properties for hydrocarbons

A number of first order electronic properties for the hydrocarbons C₂H₆, C₃H₈, C₂H₄, C₆H₆, and C₁₀H₈ are investigated. The wavefunctions employed here result from SCF calculations, using basis orbitals that have been optimized in molecular fragment studies. Comparisons are made with experimental values as well as with other calculated values, and the suitability of various molecular fragment bases is discussed.     

Localized molecular orbitals for polyatomic molecules

Molecular wavefunctions have been generated by the PRDDO (Partial Retention of Diatomic Differential Overlap) method for the monocyclic aromatic rings containing six π-electrons (C₄H ₄ ^?2 , C₅H ₅ ^? , C₆H₆, C₇H ₇ ⁺ , and C₈H ₈ ⁺² ) and ten π-electron species (C₈H ₈ ^?2 , C₉H ₉ ^? , C₁₀H₁₀). The eigenvalue spectra of the canonical molecular orbitals are presented. Localized molecular orbitals (LMO's) generated using the Boys criterion are reported for localizations involving all occupied molecular orbitals (complete localizations) and localizations of the π orbitals only. We find evidence for σ-π separation in the complete localizations for some of these molecules even though the Boys criterion is often biased against such results. We demonstrate for C₆H₆ and find for the other molecules that the π-orbital localizations are indeterminate (i.e. there are an infinite number of equally satisfactory LMO structures between two limiting extremes). This result may be viewed as a corollary of Hückel's (4n+2) rule for aromaticity.     

Transferability of intensity parameters

The transferability of different kinds of intensity parameters is discussed. In order to transfer dipole moment derivatives with respect to internal or symmetry coordinates (dmd's) among similar modes in different molecules they must be split up into a mode-specific part (the dmd with respect to rotation-free reference coordinates) and a molecule-specific part (the rotational contribution). The calculation of reference coordinates and rotational contributions is discussed. The dmd's with respect to reference coordinates can be expressed in terms of first-order intensity parameters (bcp's or aop's). Expressions are given for CH₃X, propyne, butyne-2 and acetylene. The transferability of bcp's (or eop's) is tested by searching for a common set of bcp's for the following molecules: C₂H₂, C₂D₂, CH₃CCH, CD₃CCH, CH₃CCCH₃, CD₃CCCD₃. The final results are discussed in relation to the basic assumptions and the adopted constraints.     

One electron orbitals intrinsic to the reduced hamiltonian

One electron orbitals are determined from the reduced hamiltonian by a simple one-step diagonalization. These reduced hamiltonian orbitals (RHO's) are uniquely determined and virtual orbitals obtained in this procedure are on a par with filled orbitals. These RHO's appear well suited for CI calculations. Minimum basis set calculations are presented for H₂O and compared with similar SCF studies.     

A new parallel algorithm of MP2 energy calculations

A new parallel algorithm has been developed for second‐order Møller–Plesset perturbation theory (MP2) energy calculations. Its main projected applications are for large molecules, for instance, for the calculation of dispersion interaction. Tests on a moderate number of processors (2–16) show that the program has high CPU and parallel efficiency. Timings are presented for two relatively large molecules, taxol (C₄₇H₅₁NO₁₄) and luciferin (C₁₁H₈N₂O₃S₂), the former with the 6‐31G* and 6‐311G** basis sets (1032 and 1484 basis functions, 164 correlated orbitals), and the latter with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets (530 and 1198 basis functions, 46 correlated orbitals). An MP2 energy calculation on C₁₃₀H₁₀ (1970 basis functions, 265 correlated orbitals) completed in less than 2 h on 128 processors. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 407–413, 2006     

Optisch aktive übergangsmetall-komplexe : XXXIX. Stereospezifische phenyl-addition an das C5H5(CO)2 Mo-Pyridin-Carbaldimin-Kation

The addition of C₆H₅^? to the NN' ligand (NN' = Schiff base of pyridine carbaldehyde-(2) and (S)-(—)-α-phenylethylamine) in [C₅H₅ Mo(CO)₂ NN'] PF₆ occurs stereospecific from the side opposite to the C₅H₅-ring.     

Three-dimensional aromaticity in deltahedral boranes and carboranes

Methods derived from topology and graph theory indicate that the deltahedral boranes B _n H _n ^2– and the corresponding carboranes C₂B_n–2H _n (6 n 12) may be regarded as three-dimensional delocalized aromatic systems in which surface bonding and core bonding correspond to -bonding and -bonding, respectively, in planar polygonal two-dimensional hydrocarbons CinnH _n ^(n–6)+ (n=5/7). The two extreme types of topologies which may be used to model core bonding in deltahedral boranes and carboranes are the deltahedral (D _n ) topology based on the skeleton of the underlying deltahedron and the complete (K _n ) topology based on the corresponding complete graph. Analyses of the Hoffmann-Lipscomb LCAO extended Hückel computations, the Armstrong—Perkins—Stewart self-consistent molecular orbital computations, and SCF MOab initio GAUSSIAN-82 computations on B₆H₆ ^2– indicate that the approximation of the atomic orbitals by the sum of the molecular orbitals, as is typical in modernab initio computations, leads to significantly weaker apparent core bonding approximated more closely by deltahedral (D _n ) topology than by complete (K _n ) topology.This work was presented at the Workshop The Modern Problems of Heteroorganic Chemistry sponsored by the A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences (May 8–13, 1993).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1353–1360, August, 1993.     

A predictive model for unimolecular reactions: Reactions of unsaturated carbonium ions

The major slow unimolecular reactions undergone by C₄H₇⁺, C₅H₉⁺ and C₆H⁺₁₁ are discussed in terms of a potential surface approach and the organic chemist's concept of mechanism. It is shown that the observed decompositions which do not involve σ-bond formation in the dissociation step are precisely those expected from the model. Further use of the model correctly predicts the slow reactions of C₇H⁺₁₃ which have not previously been reported. The approach also permits useful limits to be set on the transition state energies for reactions involving σ-bond formation in the dissociation step (H₂,CH₄ loss). It is concluded that stepwise addition of ethylene to the allyl cation is preferred to a concerted 4-electron process which is symmetry forbidden.     

A quantum-mechanical study of the lone-pairs in H2O and H2S

It is shown from SCF-MO studies using localised orbitals that the angles between the lone-pairs in H₂O and H₂S are 115° and 127°, in agreement with the qualitative predictions of the Sidgwick-Powell theory.     

Cluster calculations of the H2O/Pt(111) system

The electronic interaction between water and a Pt(111) surface as evaluated for different Pt_x(H₂O)_y clusters is discussed. Hartree–Fock–Slater (HFS ) one-electron ground state energies, ionization potentials, partial densities of states, and Mulliken occupation numbers are related to bonding shifts, as well as initial and final state screening for different orientations of the molecule. The formation of Pt? H₂O bonds are sensitive to the orientation since surface oriented H atoms bridge the spatial separation between O 2p and Pt 5d orbitals and thus increase the intermixing of metal and adsorbate orbitals. The dipole moment and the net charge of the H₂O molecule is also discussed. Finally, approximations of the metal–H₂O potential for use in statistical models of the liquid–metal interface are suggested.     

On the use of local basis sets for localized molecular orbitals

Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li₂, HF, H₂O, NH₃, CH₄ and C₂H₆.     

Additivity of atomic static polarizabilities and dispersion coefficients

A new empirical method is proposed to evaluate the average molecular polarizabilities assuming the additivity of atomic static polarizability. Atomic static polarizability for each atom in a particular valence state is obtained. Calculated molecular polarizabilities of 94 non-halogenated compounds and of the bases in nucleic acids show the excellent agreement with experimental data.To check the further validity of this method, dispersion coefficients for CH₄, C₂H₆, C₃H₈,n–C₄H₁₀,n–C₅H₁₂,n–C₆H₁₄,n–C₇H₁₆,n–C₈H₁₈, H₂, H₂O and NH₃ are obtained from a sum of atomic terms using a London-type formula, and are compared with the accurate values of dipole oscillator strength distribution (DOSD) method. The results show the excellent agreement between theory and experiment.     

Analytical applications of the reaction of thorium with benzenephosphonic acid

Benzenephosphonic acid quantitatively precipitates thorium as Th(C₆H₅PO₃)₂·3H₂O at pH values as low as 0.5. The compound may be dried at 140° to 180° C and weighed, as a gravimetric means of determining thorium. On ignition, Th (C₂H₅PO₃)₂ 3 H₂O undergoes decomposition at 240° to 300° C to form Th(C₆H₅PO₃)₂·2H₂O, at 450° to 650° C to form Th(HPO₄)₂·2H₂O and finally at 800° to 1000° C to form Th(HPO₄)₂. The latter compound is stable to 1200° C.Potentiometrically (pK₁' = 0.91, pK₂' = 6.41) and spectrophotometrically (pK₁' = 0.96, pK₂' = 6.51) determined pK' values are reported. Absorption spectra of C₆H₅PO₃H₂, C₆H₅PO₃H^- and C₆H₅PO₃^-2 are reported. The solubility of Th (C₆H₅PO₃)₂·3H₂O was studied as a function of pH and the average value of the solubility product (K_sp = 4s³) was found to be 3.24·10^-31.     

On the use of localized orbitals and restricted alternant orbitals in chemical systems

An analysis of the transformation of localized orbitals into restricted alternant orbitals is proposed. This approach has the advantage of expressing the wave-function in an orbital product while some electron correlation is introduced permitting the study of dissociation reactions. All applications of the orbital technique may be made as easily as with RHF, but with the additional possibility of studying chemical radicals. Some illustrations of this fact are shown for the molecules HF, H₂O, NH₃, CH₄, C₂H₆ and for the dissociation reactions of CH₄ and C₂H₆ generating CH₃ radicals.