Geometrically active atomic states and the formation of molecules in their normal shapes

We present a theory of molecular formation according to which the shape of polyhedral or coordination compounds is fixed to a very good approximation by the shape of a particular state (or states) of the central atom, which is activated by spin and spacial coupling of optimal strength between this state, called the geometrically active atomic state (GAAS) and the state of the ligands. For a molecule with a central atom, spacial coupling of optimal strength, means that the shape of the GAAS fixes the position of the ligands according to the maximum overlap principle of the Heitler–London, Slater, and Pauling theory of covalent bonding, whereby much of the energy lowering from the free atom limit is obtained by the maximization of the contribution of the exchange integrals. Hence, a direct causal relationship between the shape of the GAAS and the shape of the molecular state at equilibrium seems to exist. This relationship implies a picture of diabatic connection between the geometrically asymptotic region and the equilibrium region, which is driven by the coupled GAAS and provides the “why” of molecular shape. Since the latter is fixed by the shape of the GAAS (in cases of electronic complexity or of molecular instability it is possible that more than one GAAS contribute simultaneously), prediction of the shape of certain large systems can be made based on the a priori recognition of the corresponding GAAS. The concept of the shape of atomic states defined and computed quantum mechanically from the probability distribution ϱ(cos θ₁₂) of the angle θ₁₂ that the position vectors of two electrons form in the given atomic state. Specifically, it is deduced from the distribution's maxima which provide the most probable values of θ₁₂. As shown previously [Y. Komninos and C. A. Nicolaides, Phys. Rev. A 50 , 3782 (1994)], ϱ(cos θ₁₂) is obtainable directly from the state-specific expression for the Coulomb interaction, where the R^k integrals are replaced by Legendre polynomials P_k, multiplied by normalization constants and radial overlaps. The theory is demonstrated by explaining the shape of BeH₂, BH₂, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, SF₆, and TiH₄ in terms of the shapes of the following GAAS. Be: 2s2p ³P⁰, B: 2s2p^{2 4}P, C: 2s2p^{3 5}S⁰, Si: 3s3p^{3 5}S⁰, O: 2s2p^{5 3}P⁰, S: 3s²3p³3d ³P⁰, N: 2s2p^{4 4}P, P: 3s3p³3d ⁴P⁰, S: 3s3p³3d^{2 7}F⁰, and Ti: 3d²4s4p ⁵G⁰. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 321–328, 1998     

键能的分子轨道理论研究2: 键能与Mulliken布居对键强度的 判断的比较

用键能E~A~B和Mulliken布居对化学键强度的判别进行了分析比较。结果表明,键能判据比Mulliken布居判据所得结论更符合实际情况。作为衡量原子间化学键强度的尺度,不仅应考虑原子轨道间的布居因素,还应考虑分子轨道(或原子轨道)的能量因素。     

Shape and spin state in four-coordinate transition-metal complexes: the case of the d(6) configuration

Generalized polyhedral interconversion coordinates are defined within the framework of Avnir's continuous shape measures. The application of such interconversion coordinates to the study of the potential energy surfaces that define the stereochemical choice in four-coordinate transition metal complexes with different spin states is presented, and the correlation between potential energy curves and distribution of experimental structures along the tetrahedron to square interconversion path is shown for the case of the d(6) transition-metal complexes.     

Correlation effects in the valence x-ray photoionization spectra of ethylene,butadiene, and hexatriene

The x-ray photoemission spectra of the ethylene, butadiene, and hexatriene compounds were investigated using one-particle Green's function calculations which are exact up to third order in correlation. This study points to the importance of initial-state correlation and cross-section effects for a consistent reproduction of satellite bands recorded under x-ray photoionization. By extrapolating the results obtained to larger unsaturated hydrocarbons, it is clear that the signal recorded in the inner-valence region of polyacetylene must be exclusively assigned to many-body structures. This study also provides evidence for a partial contamination of the outer-valence band by shake-up lines. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 465–481, 1997     

Investigating the morphology and mechanical properties of blastomeres with atomic force microscopy

Atomic force microscopy (AFM) was used to directly investigate the morphology and mechanical properties of blastomeres during the embryo development. With AFM imaging, the surface topography of blastomeres from two‐cell, four‐cell, and eight‐cell stages was visualized, and the AFM images clearly revealed the blastomere's morphological changes during the different embryo developmental stages. The section measurements of the AFM topography images of the blastomeres showed that the axis of the embryos nearly kept constant during the two‐cell, four‐cell, and eight‐cell stages. With AFM indenting, the mechanical properties of living blastomeres from several embryos were measured quantitatively under physiological conditions. The results of mechanical properties measurements indicated that the Young's modulus of the two blastomeres from two‐cell embryo was different from each other, and the four blastomeres from the four‐cell embryo also had variable Young's modulus. Besides, the blastomeres from two‐cell embryos were significantly harder than blastomeres from four‐cell embryos. These results can improve our understanding of the embryo development from the view of cell mechanics. Copyright © 2013 John Wiley & Sons, Ltd.     

On the definition of the atomic charge. Relationship between 13C NMR chemical shifts,dipole moments,and charges in saturated hydrocarbons

The problem of defining a reliable quantum mechanical charge by comparison with one-electron properties is analyzed, and it is stressed that properties involving the virtual space are not suited to that end. Particular attention is devoted to the relationship between charges and chemical shifts for the case of saturated hydrocarbons. A simple explanation of the Grant and Paul α effect is suggested, which can also account for the modified population analysis proposed by Fliszár. Moreover the vexata quaestio of the direction of the C H bond dipole moment has been reexamined. The awkward theoretical prediction (C⁺ H⁻) can be reconciled with the one based on experimental data and electronegativities (C⁻ H⁺) if one considers that the former is determined by an hydridization contribution to the dipole moment, which tend to cancel in a summation over all the bonds formed by each atom. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 201–210, 1998     

The interplay between charge transfer,rehybridization, and atomic charges in the internal geometry of subunits in noncovalent interactions

When a noncovalent bond is formed, there is frequently some charge transfer from one subunit to the other. The interaction also causes changes in the atomic charges and hybridization patterns of bonding orbitals. The manner in which these various effects combine to cause elongations or contractions of bonds within the individual subunits is examined. In both the cases of CH···O H‐bonds and P···N pnicogen bonds, the bond length changes are consistent with the guiding principles generally known as Bent's rules. © 2014 Wiley Periodicals, Inc.     

Molecular shape and orientational order. Effects in the energy of cavity formation in liquids

A recently proposed method for calculating the energy of cavity formation in liquids is presented in which the cavity formation process is described as work against the surface forces of the solvent, at the microscopic scale. The energy involved in the cavity formation process is, on the other hand, viewed as a strictly interaction potential energy and the reference cavity, which has the size and the shape of the space occupied by each molecule in the liquid, is considered as having short-range orientational order characteristic of the pure liquid. The method is successfully applied to binary alkane mixtures at infinite dilution whose components have different chemical structure (linear, cyclic and branched alkanes). The importance of the changes in the molecular order of the solute and the solvent occuring in the mixing process is emphasized.     

Bond types of molecular orbitals and the photoelectron spectrum

The vibrational structures of the photoelectron spectra for diatomic molecules can be accounted for in terms of the slope of the orbital energy curve in the conventional correlation diagram with respect to internuclear distance. The vibrational structures of the photoelectron spectra for simple polyatomic molecules HCN, C₂H₂, and AH₂ type of hydrides can also be accounted for in terms of the slopes of the orbital energy curves in the correlation diagrams with respect to angles, as well as distances. Among all correlation diagrams, the slopes in the distance correlation diagram are related to the criterion for bond type—the positive for “bonding,” the negative for “antibonding,” while slopes with small magnitudes for “nonbonding.” The Fock matrix elements within the bond orbital basis provide heuristic and systematic rationalization of the slopes for the orbital energy curves. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 53–65, 2001     

BF分子X1Σ＋, A1P和B1Σ＋态的势能函数

使用SAC/SAC-CI和D95＋＋, 6-311＋＋g, 6-311＋＋g**及D95(d)基组, 分别对BF分子的基态X¹Σ^＋、第一简并激发态A¹Π和第二激发态B¹Σ^＋的平衡结构和谐振频率进行优化计算. 对所有计算结果进行比较, 得出6-311＋＋g**基组为最优基组. 运用6-311＋＋g**基组和SAC方法对基态X¹Σ^＋, SAC-CI方法对激发态A¹Π和B¹Σ^＋进行单点能扫描计算, 并用正规方程组拟合Murrell-Sorbie函数, 得到相应电子态的势能函数解析式, 由得到的势能函数计算了与X¹Σ^＋, A¹Π和B¹Σ^＋态相对应的光谱常数, 结果与实验数据较为一致.     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Understanding the Liquid States of Cyclic Hydrocarbons Containing N,O, and S Atoms via the 3D-RISM-KH Molecular Solvation Theory

The 3D-reference interaction site model (3D-RISM) molecular solvation theory in combination with the Kovalenko–Hirata (KH) closure is extended to seven heterocyclic liquids to understand their liquid states and to test the performance of the theory in solvation free energy (SFE) calculations of solutes in select solvents. The computed solvent site distribution profiles were compared with the all-atom molecular dynamics (MD) simulations, showing comparable performances. The computational results were compared against the structural parameters for liquids, whenever available, as well as against the experimental SFEs. The liquids are found to have local ordered structures held together via weak interactions in both the RISM and MD simulations. The 3D-RISM-KH computed SFEs are in good agreement with the benchmark values for the tetrahydrothiophene-S,S-dioxide, and showed comparatively larger deviations in the case of the SFEs in the tetrahydrofuran continuum.     

Molecular insight into the interaction mechanisms of amino‐2H‐imidazole derivatives with BACE1 protease: A QM/MM and QTAIM study

In this study, we described quantitatively the interactions between two new amino‐2H‐imidazole inhibitors ((R)‐1t and (S)‐1m) and BACE1 using a hybrid quantum mechanics‐molecular mechanical (QM/MM) method together with a quantum theory of atoms In Molecules (QTAIM) analysis. Our computational calculations revealed that the binding affinity of these compounds is mostly related to the amino‐2H‐imidazole core, which interact tightly with the aspartate dyad of the active site. The interactions were stronger when the inhibitors presented a bulky substituent with a hydrogen bond acceptor motif pointing toward Trp76, such as the 3,5‐dimethyl‐4‐methoxyphenyl group of compound (S)‐1m. Furthermore, the QTAIM analysis revealed that many hydrophobic interactions complement cooperatively the hydrogen bond which is not present when compound (R)‐1t is bound to the enzyme. The combined QM/MM‐QTAIM analysis allows identifying the interactions that account for the activity difference between compounds, even at a nanomolar range.     

Molecular parameters of tetraatomic carbonyls X2CO and XYCO (X,Y = H,F, Cl) in the ground and lowest excited electronic states,part 1: A test of ab initio methods

Geometrical parameters of tetraatomic carbonyl molecules X₂CO and XYCO (X, Y = H, F, Cl) in the ground (S₀) and lowest excited singlet (S₁) and triplet (T₁) electronic states as well as values of barriers to inversion in S₁ and T₁ states and S₁ ← S₀ and T₁ ← S₀ adiabatic transition energies were systematically investigated by means of various quantum‐chemical techniques. The following methods were tested: HF, MP2, CIS, CISD, CCSD, EOM‐CCSD, CCSD(T), CR‐EOM‐CCSD(T), CASSCF, MR‐MP2, CASPT2, CASPT3, NEVPT2, MR‐CISD, and MR‐AQCC within cc‐pVTZ and cc‐pVQZ basis sets. The accuracy of quantum‐chemical methods was estimated in comparison with experimental data and rather accurate structures of excited electronic states were obtained. MP2 and CASPT2 methods appeared to be the most efficient and CCSD(T), CR‐EOM‐CCSD(T), and MR‐AQCC the most accurate. It was found that at equilibrium all the molecules under study are nonplanar in S₁ and T₁ electronic states with CO out‐of‐plane angle ranging from 34° (H₂CO, S₁) to 52° (F₂CO, T₁), and height of barrier to inversion varying from 300 (H₂CO, S₁) to 11,000 (F₂CO, T₁) cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Carbon nanotube, graphene, nanowire, and molecule-based electron and spin transport phenomena using the nonequilibrium Green's function method at the level of first principles theory

Based on density functional theory, we have developed a program code to investigate the electron transport characteristics for a variety of nanometer scaled devices in the presence of an external bias voltage. We employed basis sets comprised of linear combinations of numerical type atomic orbitals, particularly focusing on k-point sampling for the realistic modeling of the bulk electrode. The scheme coupled with the matrix version of the nonequilibrium Green's function method enables calculation of the transmission coefficients at a given energy and voltage in a self-consistent manner as well as the corresponding current-voltage (I-V) characteristics. This scheme has advantages because it is applicable to large systems, easily transportable to different types of quantum chemistry packages, and extendable to time-dependent phenomena or inelastic scatterings. It has been applied to diverse types of practical electronic devices such as carbon nanotubes, graphene nanoribbons, metallic nanowires, and molecular electronic devices. The quantum conductance phenomena for systems involving quantum point contacts and I-V curves for a single molecule in contact with metal electrodes using the k-point sampling method are described.     

Density Functional Theory Investigations on Vibrational Spectra,Molecular Structure,and Properties of the L‐Serine,L‐Cysteine,and L‐Aspartic Acid Molecules

In this paper, we present a thorough investigation of the conformational space to characterize all possible gas‐phase structures of the neutral L‐serine, L‐cysteine, and L‐aspartic acid molecules. A total of 120 trial structures were generated for L‐aspartic acid and 96 trial structures for L‐serine and L‐cysteine by combining all internal single‐bond rotamers. Various combinations of the Hartree–Fock and density functional theory/B3LYP methods with different bases were used to optimize all possible trial structures. The theoretical studies on the structure, harmonic vibrational spectra, and molecular properties of these amino acids are presented. The assignments of the calculated wave numbers resulting from potential energy distributions were performed using the VEDA 4 program to allow a good interpretation of the theoretical vibrational spectra of the title compounds. The fundamental harmonic frequencies were found to be in good agreement with data in the literature. A natural bond orbital analysis was performed to investigate the charge delocalization throughout the molecules for the three test compounds. Moreover, an extensive discussion of the highest occupied molecular orbital–lowest unoccupied molecular orbital energy gap as well as other related molecular properties are reported.     

Isothermal frontal polymerization: Confirmation of the mechanism and determination of factors affecting the front velocity,front shape,and propagation distance with comparison to mathematical modeling

Isothermal frontal polymerization (IFP) is a directional polymerization that uses the Trommsdorff, or gel, effect to produce gradient materials for optical applications. When a solution of methyl methacrylate and a thermal initiator contacts a polymer seed (a small piece of polymer), a viscous region is formed in which the polymerization rate is faster because of the Trommsdorff effect. Using the optical techniques of laser line deflection (Weiner's method) and shadowgraphy along with controls, we obtained definitive experimental evidence of IFP. Moreover, we were able to measure accurately and precisely the front position and front concentration profile as a function of time by monitoring IFP systems and controls of various initiator concentrations and cure temperatures. The experimental data were compared with theoretical predictions from a model using mass‐diffusion and radical polymerization kinetics. The model reproduced the decrease of the propagation time and showed an increase in the propagation velocity for an increase in the initiator concentration and/or cure temperature. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5774–5786, 2005