Extremely localized molecular orbitals (ELMO): a non-orthogonal Hartree-Fock method

A new optimization method for extremely localized molecular orbitals (ELMO) is derived in a non-orthogonal formalism. The method is based on a quasi Newton-Raphson algorithm in which an approximate diagonal-blocked Hessian matrix is calculated through the Fock matrix. The Hessian matrix inverse is updated at each iteration by a variable metric updating procedure to account for the intrinsically small coupling between the orbitals. The updated orbitals are obtained with approximately n ² operations. No n ³ processes such as matrix diagonalization, matrix multiplication or orbital orthogonalization are employed. The use of localized orbitals allows for the creation of high-quality initial “guess” orbitals from optimized molecular orbitals of small systems and thus reduces the number of iterations to converge. The delocalization effects are included by a Jacobi correction (JC) which allows the accurate calculation of the total energy with a limited number of operations. This extension, referred to as ELMO(JC), is a variational method that reproduces the Hartree-Fock (HF) energy with an error of less than 2 kcal/mol for a reduced total cost compared to standard HF methods. The small number of variables, even for a very large system, and the limited number of operations potentially makes ELMO a method of choice to study large systems. Received: 30 December 1996 / Accepted: 5 June 1997     

IMiCMO: a new integrated ab initio multicenter molecular orbitals method for molecular dynamics calculations in solvent cluster systems

A new computational scheme integrating ab initio multicenter molecular orbitals for determining forces of individual atoms in large cluster systems is presented. This method can be used to treat systems of many molecules, such as solvents by quantum mechanics. The geometry parameters obtained for three models of water clusters by the present method are compared with those obtained by the full ab initio MO method. The results agree very well. The scheme proposed in this article also intended for use in modeling cluster systems using parallel algorithms. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1107–1112, 2001     

Synthesis of (3,6-dihydro-2H-pyran-2-yl)phosphonate derivatives and investigation of catalyst effect on frontier molecular orbitals using DFT method

Hetero Diels-Alder (HDA) reactions between 2,3-dimethyl-1,3-butadiene and diethyl ester of aroyl phosphonates catalyzed by AlCl₃ to afford (3,6-dihydro-2H-pyran-2-yl) phosphonate derivatives were investigated. Aroyl phosphonates with electron-withdrawing groups generally resulted in better isolated chemical yields. A stoichiometric amount of AlCl₃ rather than a catalytic amount was necessary to activate the cycloaddition reaction. The amount of AlCl₃ catalyst and its effect on LUMO of ethyl ester benzoyl phosphonate were also investigated by performing density functional theory (DFT) (B97D/6-31+G(d,p)) computations in dichloromethane. An increased loading of AlCl₃ induced a considerable decrease in the LUMO energy of ethyl ester of benzoyl phosphonate. The computed Gibbs free activation energy is 17.03 kcal/mol in DCM at 0°C using the same computational level.     

Generalized hybrid orbital for the treatment of boundary atoms in combined quantum mechanical and molecular mechanical calculations using the semiempirical parameterized model 3 method

The application of combined quantum mechanical (QM) and molecular mechanical methods to large molecular systems requires an adequate treatment of the boundary between the two approaches. In this article, we extend the generalized hybrid orbital (GHO) method to the semiempirical parameterized model 3 (PM3) Hamiltonian combined with the CHARMM force field. The GHO method makes use of four hybrid orbitals, one of which is included in the QM region in self-consistent field optimization and three are treated as auxiliary orbitals that do not participate in the QM optimization, but they provide an effective electric field for interactions. An important feature of the GHO method is that the semiempirical parameters for the boundary atom are transferable, and these parameters have been developed for a carbon boundary atom consistent with the PM3 model. The combined GHO-PM3/CHARMM model has been tested on molecular geometry and proton affinity for a series of organic compounds.Acknowledgement We thank the National Institutes of Health for support of this research.Contribution to the Jacopo Tomasi Honorary Issue     

Isotope effect of hydrogen and lithium hydride molecules. Application of the dynamic extended molecular orbital method and energy component analysis

In order to explore the isotope effect including the nuclear–electronic coupling and nuclear quantum effects under the one-particle approximation, we apply the dynamic extended molecular orbital (DEMO) method and energy component analysis to the hydrogen and lithium hydride isotope molecules. Since the DEMO method determines both electronic and nuclear wave functions simultaneously by variationally optimizing all parameters embedded in the basis sets, the virial theorem is completely satisfied and guarantees the relation of the kinetic and potential energies. We confirm the isotope effect on internuclear distances, nuclear and electronic wave functions, dipole moment, the polarizability, and each energy component. In the case of isotopic species of the hydrogen molecule, the total energy decreases from the H₂ to the T₂ molecule due to the stabilization of the nuclear–electronic potential component, as well as the nuclear kinetic one. In the case of the lithium hydride molecule, the energy lowering by replacing ⁶Li with ⁷Li is calculated to be greater than that by replacing H with D. This is mainly caused by the small destabilization of electron–electron and nuclear–nuclear repulsion in ⁷LiH compared to ⁶LiH, while the change in the repulsive components from ⁶LiH to ⁶LiD increases. Received: 24 March 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

A Lie group method for molecular rovibrational spectra via the broken symmetry of U(r)(2)⊗U(υ)(4)

A special group chain that is appropriate for describing the rovibrational spectra of linear triatomic molecules with respect to both the vibration and the rotation of molecules as harmonic oscillators is given, and the corresponding Hamiltonian is constructed. The eigenvalue expression of the Hamiltonian is similar to the formula commonly used to calculate the rovibrational spectra of linear triatomic molecules. This method eliminates the physical uncertainty brought about by a variety of group chains. The relationships between parameters in the present expression and those in the commonly used expressions are given. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 53–59, 2001     

Epoxidation of α-pinene with molecular oxygen catalyzed by poly(vinylbenzyl)acetylacetonate complexes of some metal ions

Poly(vinylbenzyl)acetylacetonate complex of cobalt is a very effective catalyst for the epoxidation of α-pinene under an atmospheric pressure of molecular oxygen at 25°C. With isobutyraldehyde as a reductant, the yield of the epoxidation of α-pinene amounts to 94.3% within 6 hr. The catalyst can be recycled at least eight times without apparent loss of activity.     

A statistical method to detect chromosomal regions with DNA copy number alterations using SNP-array-based CGH data

Single nucleotide polymorphism (SNP) arrays were used to detect chromosomal regions with DNA copy number alterations. Current statistical methods for microarray-based comparative genomic hybridization (array-CGH) analysis generally assume certain relationships among adjacent markers on the same chromosome, and these assumptions may be questionable. For an SNP-array-based CGH study, multiple normal reference SNP arrays were collected. In order to utilize these normal reference SNP arrays, we derived an empirical distribution of signal ratios for each SNP marker. With an assumed threshold value for the overall error rate control and the defined signal ratio ranges for chromosomal amplification and deletion, we proposed a procedure to identify chromosomal alteration regions based on several bootstrapped one-sample t-tests and the false discovery rate control. When we have multiple arrays for different individuals with the same disease, our method can also be used to detect SNP markers for chromosomal alteration regions that are common among these individuals. We applied our method to a published SNP array data set for breast carcinoma cell lines. For an individual with breast cancer, numerous chromosomal alteration regions were identified. Compared to results of previous studies, our method identified more chromosomal alteration regions, with some being implicated in the literature to harbor genes associated with breast cancer. For multiple cancer arrays, our results suggested the existence of common chromosomal alteration regions. However, a high proportion of false positives also indicated that genetic variations among different individuals with breast cancer can be present.     

A rare occurrence of a β‐turn in an amyloid βA4 peptide

The fragment β(25–35) of the amyloid β‐peptide, like its parent βA4, has shown neurotrophic and late neurotoxic activities in cultured cells. The 3D structure of this important peptide was examined by ¹H and ¹³C 2D‐NMR and MD simulations in DMSO‐d₆ and water. The NMR parameters of chemical shift, ³J(N,Hα) coupling constants, temperature coefficients of NH chemical shifts and the pattern of intra and inter‐residue NOEs were used to deduce the structures. In DMSO‐d₆, the peptide was found to take up a type I β‐turn around the C‐terminal residues Ile⁸–Gly⁹–Leu¹⁰–Met¹¹, whereas in water at pH 5.5, it adopts a random coil conformation. This is only the second report of a β‐turn in the β‐amyloid class of peptides. The solution structures generated using restrained molecular dynamics were refined by MARDIGRAS to an R factor of 0.33 in the case of DMSO‐d₆ and to 0.56 for water. Copyright © 2002 John Wiley & Sons, Ltd.     

An Ab Initio Molecular Orbital Theory and Density Functional Theory (DFT) Study of Conformers and Rotamers of 4-Substituted (Methyl, Hydroxymethyl, Methanoyl, Ethanoyl, Cyano, Fluoro, Chloro, Bromo, Acetoxy) Tetrahydro-2H-thiopyran-1,1-dioxides

The structures and energies of axial and equatorial conformers and rotamers of 4-substituted tetrahydro-2H-thiopyran-1,1-dioxides (tetrahydrothiopyran-1,1-dioxides, thiacyclohexane-1,1-dioxides, thiane-1,1-dioxides, and 1,1-dioxothianes; CH₃, CH₂OH, CHO, COCH₃, CN, F, Cl, Br, and OCOCH₃) were calculated using the hybrid density functionals B3LYP, B3P86, and B3PW91, as well as MP2 and the 6-31G(d), 6-31G(2d), 6-31G(3d), 6-31G(d,p), and 6-31+G(d) basis sets. MP2/6-31+G(d)/ /HF/6-31+G(d) [–G° = 1.73 kcal/mol], B3P86/6-31G(d) [–G° = 1.75 kcal/mol], and B3PW91/6-31G(d) [–G° = 1.85 kcal/mol] gave conformational free energy (G°) values at 180 K for 4-methyltetrahydro-2H-thiopyran-1,1-dioxide which were similar to the reported experimental values for methylcyclohexane (–G° = 1.80 kcal/mol), 4-methyltetrahydro-2H-thiopyran (–G° = 1.80 kcal/mol), and other 4-methyl-substituted heterocycles. All levels of theory showed that the conformational preferences of the 4-methanoyl (4-formyl), 4-ethanoyl (4-acetyl), and 4-cyano substituents were small. The HF calculations gave conformational free energy (G°) values for 4-chlorotetrahydro-2H-thiopyran-1,1dioxide which were closer to the experimental value than the MP2 and density functional methods. The best agreement with available experimental data for 4-bromotetrahydro-2H-thiopyran-1,1-dioxide was obtained from the HF/6-31G(2d), HF/6-31G(3d), and B3LYP/6-31G(2d) calculations, and, for 4-acetoxytetrahydro-2H-thiopyran-1,1-dioxide, from the HF/6–31G(3d) calculations. The conformational free energies (G°) and relative energies (E) of the conformers and rotamers have been compared with the correspondingly substituted cyclohexanes and tetrahydro-2H-thiopyrans and are discussed in terms of dipole–dipole (electrostatic) interactions and repulsive nonbonded interactions (steric) in the most stable axial and equatorial conformers. The axial S=O bond lengths are shorter than the equatorial S=O bond lengths and the C2–C3 bond lengths in the substituents with carbon-bonded to the ring are shorter than the C3–C4 and C4–C-5 bond lengths. In contrast, the C2–C3 bond lengths in the 4-halogen and 4-acetoxy substituents are longer than the C3–C4 and C4–C-5 bond lengths.     

A new two‐dimensional anionic cadmium(II) polymer constructed through thiocyanate coordination bridges

A new cadmium–thiocyanate complex, poly[4‐(dimethylamino)pyridin‐1‐ium [di‐μ‐thiocyanato‐κ²N:S;κ²S:N‐thiocyanato‐κN‐cadmium(II)]], {(C₇H₁₁N₂)[Cd(NCS)₃]}_n, was synthesized by the reaction of cadmium thiocyanate and 4‐(dimethylamino)pyridine hydrochloride in aqueous solution. In the crystal structure, each Cd^II ion is square‐pyramidally coordinated by three N and two S atoms from five different thiocyanate ligands, four of which are bridging. The thiocyanate ligands play different roles in the build up of the structure; one role results in the formation of [Cd₂(NCS)₂] building blocks, while the other links the building blocks and cations via N—H...S hydrogen bonds. The N—H...S hydrogen bonds and weak π–π stacking interactions are involved in the formation of both a two‐dimensional network structure and the supramolecular network.     

Study of molecular structures for arylidene derivatives of 3R‐methylcyclohexanone by 1H NMR and molecular simulation

Conformational states of the cyclohexanone ring were established for 3R‐methyl‐6‐(4‐phenylbenzylidene)cyclohexanone and several 2,6‐bis(4‐X‐benzylidene)‐3R‐methylcyclohexanones (X = Br, OCOCH₃ and C₆H₅) by ¹H NMR spectroscopy combined with molecular simulation using the semi‐empirical methods AM1 and PM3. The first compound studied contains only one arylidene group, and exists predominantly in a chair conformation of the cyclohexanone ring with an equatorial orientation of the methyl substituent in C₆D₆ and CDCl₃ solutions at room temperature (22–23 °C). In contrast, the 2,6‐bis(arylidene) derivatives of 3R‐methylcyclohexanone preferentially adopt conformations with an axially oriented methyl group. The extent of twisting of enone fragments was also characterized for the compounds studied based on simulation results and comparison of chemical shifts for the arylidene protons of appropriate model compounds. Copyright © 2003 John Wiley & Sons, Ltd.     

Molecular structure and conformational analysis of chirai (−)-3-(4-bromobenzylidene)-1-isopropyl-2-methoxy-4-methylcyclohexene

(–)-3-(4-Bromobenzylidene)-1-isopropyl-2-methoxy-4-methylcyclohexene, capable of inducing spiral supramolecular ordering when introduced to nematic and some smectic mesophases, has been studied by an X-ray structural analysis. The crystals are orthorhombic; at 20 °Ca = 6.055(1),b = 13.282(3),c=20.734(4) Å,V=1668(1) ų,d _calc = 1.380 g cm^–3, space groupP2 ₁2₁2₁ Z=4. The cyclohexene ring has a conformation intermediate between a sofa and a half-chair. The methyl and methoxyl groups are in asyn orientation with respect to the mean plane of the cycle. The angle between the plane of the aryl substituent and the exocyclic double bond is 33°. The observed distortions of bond angles at unsaturated carbon atoms are typical of derivatives of benzylidenecyclohexene. Molecular mechanics calculations demonstrated that the conformation observed in the crystalline state is not the most favorable, and this conformation is stabilized through intermolecular interactions upon stacking in crystals. It was shown that the relative orientation of the methyl and methoxyl groups as well as the orientation of the aryl substituent substantially affect the conformation of the cyclohexene ring.Deceased.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2437–2442, December, 1995.