Variationally determined electronic states for the theoretical analysis of intramolecular interaction: I. Resonance energy and rotational barrier of the C–N bond in formamide and its analogs

We present a new method that produces a variationally determined zeroth-order wave function for the analysis of intramolecular interactions between the fragments of a molecule. In our method, called the space-restricted wave function (SRW) method, this wave function is defined with nonorthogonal orbitals, which are obtained using the appropriately restricted variational spaces. The wave function thus obtained represents the electronic state with the target interactions deactivated, and it is constructed without unnecessarily breaking bonds, in contrast to some of the existing methods. Furthermore, we can perform energy decomposition analysis of intramolecular interactions using the zeroth-order functions that the SRW method yields. The validity of the SRW method is demonstrated in the analysis of the resonance energy and the rotational barrier of the C–N bond in formamide and its analogs. This method gives energy components that are different from those given by existing methods. With these components, we elucidate the origin of the rotational barrier from another point of view. Our SRW method gives meaningful results for the investigation of electron behavior and the nature of the molecular system.     

2‐Iodo‐N‐(3‐nitrobenzyl)aniline and 3‐iodo‐N‐(3‐nitrobenzyl)aniline exhibit entirely different patterns of supramolecular aggregation

In 2‐iodo‐N‐(3‐nitro­benzyl)­aniline, C₁₃H₁₁IN₂O₂, the mol­ecules are linked into a three‐dimensional structure by a combination of C—H?O hydrogen bonds, iodo–nitro interactions and aromatic π–π‐stacking interactions, but N—H?O and C—H?π(arene) hydrogen bonds are absent. In the isomeric 3‐iodo‐N‐(3‐nitro­benzyl)­aniline, a two‐dimensional array is generated by a combination of N—H?O, C—H?O and C—H?π(arene) hydrogen bonds, but iodo–nitro interactions and aromatic π–π‐stacking interactions are both absent.     

价键结构函数与键数Ⅰ.理论处理及甲烷的应用实例

采用键函数形式对键表进行逐级展开,其中荚函数的强正交积作为零级函数,进而构造了各级校正函数以描述多对键之间的相关作用,同时采用Heitler-london 函数作为键函数,对甲烷进行离键表计算,结果表明CH~4中一.二.三级校正能近似有4:2:-1的关系,即校正函数的收敛性能较好.     

Wave‐like structure in 3‐(4,6‐diamino‐1,3,5‐triazin‐2‐yl)‐2‐naphthonitrile

In the title compound, C₁₄H₁₀N₆, which crystallizes with Z′ = 2 in the C2/c space group, the molecules are linked by N—H...N hydrogen bonds into chains, which are arranged in a wave‐like form stabilized by aromatic π–π stacking interactions. This work demonstrates the usefulness of aromatic triazine derivatives in crystal engineering.     

Incommensurate Phase in Λ-cobalt (III) Sepulchrate Trinitrate Governed by Highly Competitive N−H⋅⋅⋅O and C−H⋅⋅⋅O Hydrogen Bond Networks**

Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C₁₂H₃₀N₈)]³⁺ ⋅ 3 NO₃⁻ is reported to undergo a disorder-order phase transition at T_c1 ≈133 K upon cooling. Temperature-dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below T_c1. The modulation wave vector varies as function of temperature and locks in at T_c3≈98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in T_c1<T<T_c3. Distinctive levels of competitions: trade-off between longer N−H⋅⋅⋅O and shorter C−H⋅⋅⋅O hydrogen bonds; steric constraints to dense C−H⋅⋅⋅O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock-in phase.     

On the Nature of Blueshifting Hydrogen Bonds

The block‐localized wave function (BLW) method can derive the energetic, geometrical, and spectral changes with the deactivation of electron delocalization, and thus provide a unique way to elucidate the origin of improper, blueshifting hydrogen bonds versus proper, redshifting hydrogen bonds. A detailed analysis of the interactions of F₃CH with NH₃ and OH₂ shows that blueshifting is a long‐range phenomenon. Since among the various energy components contributing to hydrogen bonds, only the electrostatic interaction has long‐range characteristics, we conclude that the contraction and blueshifting of a hydrogen bond is largely caused by electrostatic interactions. On the other hand, lengthening and redshifting is primarily due to the short‐range n(Y)→σ*(X?H) hyperconjugation. The competition between these two opposing factors determines the final frequency change direction, for example, redshifting in F₃CH ??? NH₃ and blueshifting in F₃CH ??? OH₂. This mechanism works well in the series F_nCl_3?nCH ??? Y (n=0–3, Y=NH₃, OH₂, SH₂) and other systems. One exception is the complex of water and benzene. We observe the lengthening and redshifting of the O?H bond of water even with the electron transfer between benzene and water completely quenched. A distance‐dependent analysis for this system reveals that the long‐range electrostatic interaction is again responsible for the initial lengthening and redshifting.     

Investigation of cation-pi interactions in biological systems

Noncovalent interactions, such as van der Waals interactions, hydrogen bonds, salt bridge and cation-Pi interactions play extremely important roles in biological systems and, in contrast to covalent bonds, many such noncovalent interactions are not well understood. In the present work a new protocol has been developed to measure the enhancement of binding energies due to cation-Pi interactions between aromatic amino acids and organic or metal ions. Investigation of the cation-Pi interactions will provide further insight into the structure and function of biological molecules.     

Patterns in Hydrogen Bonding: Functionality and Graph Set Analysis in Crystals

Whereas much of organic chemistry has classically dealt with the preparation and study of the properties of individual molecules, an increasingly significant portion of the activity in chemical research involves understanding and utilizing the nature of the interactions between molecules. Two representative areas of this evolution are supramolecular chemistry and molecular recognition. The interactions between molecules are governed by intermolecular forces whose energetic and geometric properties are much less well understood than those of classical chemical bonds between atoms. Among the strongest of these interactions, however, are hydrogen bonds, whose directional properties are better understood on the local level (that is, for a single hydrogen bond) than many other types of non-bonded interactions. Nevertheless, the means by which to characterize, understand, and predict the consequences of many hydrogen bonds among molecules, and the resulting formation of molecular aggregates (on the microscopic scale) or crystals (on the macroscopic scale) has remained largely enigmatic. One of the most promising systematic approaches to resolving this enigma was initially developed by the late M. C. Etter, who applied graph theory to recognize, and then utilize, patterns of hydrogen bonding for the understanding and design of molecular crystals. In working with Etter's original ideas the power and potential utility of this approach on one hand, and on the other, the need to develop and extend the initial Etter formalism was generally recognized. It with that latter purpose that we originally undertook the present review.     

Silver-Catalysed Enantioselective Addition of O?H and N?H Bonds to Allenes: A New Model for Stereoselectivity Based on Noncovalent Interactions

The ability of silver complexes to catalyse the enantioselective addition of O H and N H bonds to allenes is demonstrated for the first time by using optically active anionic ligands that were derived from oxophosphorus(V) acids as the sources of chirality. The intramolecular addition of acids, alcohols, and amines to allenes can be achieved with up to 73 % ee. The exploitation of a C H anomeric effect allowed the absolute configuration of a sample of 2-substituted tetrahydrofuran of low ee to be unambiguously assigned by comparison of the chiroptical ORD and VCD measurements with calculated spectra. In the second part of the work, the origin of the stereoselectivity was probed by DFT free-energy calculations of the transition states. A new model of enantiomeric differentiation was developed that was based on noncovalent interactions. This model allowed us to identify the source of stereoselectivity as weak attractive interactions; such dispersive forces are often overlooked in asymmetric catalysis. A new computational approach was developed that represents these interactions as colour-coded isosurfaces that are characterised by the reduced density-gradient profile.     

Fifth-order constant denominator perturbation theory within a localized bond model: Contributions from triple and quadruple excitations

The contributions of the triple and quadruple excitations to the fifth-order perturbation energy for the perturbation configuration interaction using localized orbitals (PCILO ) method are derived. This completes the development of a fifth-order constant denominator perturbation theory initiated in a previous paper [5] with the single and double excitations. This theory is tested on molecules containing strained ring geometries, stretched bonds, strongly polarized bonds, and delocalized pi systems: cases where the starting zero order reference wave function poorly describes the system. Although the perturbation expansions turn out to be slowly convergent, the Padé approximant taken from an energy series which itself is constructed from Padé approximants provides results accurate to within a few kilocalories/mole of benchmark calculations. Computational times as in the original PCILO procedure remain proportional to N³, where N is the number of bonds.     

Probing internal electric fields of π- and σ-hole bonds

π- and σ-holes are nonnuclear molecular regions of positive electric potential, which make non-covalent interactions with negative sites, for example, lone pairs of molecules containing nitrogen or oxygen, the so called π- and σ-hole bonds. We investigate these bonds locally using a probe programmed as a virtual molecule. Unlike the hydrogen bond, electric fields are detected having strengths that are different from the sum of the separated parts, meaning that molecular electrostatic potential surfaces analysis of the different parts are not enough to analyze the bonds. Based on an application of the Hellmann-Feynman theorem, which states that intermolecular bonds are fully described by Coulombian interactions (electrostatic plus polarization), we connect the electric field strength with the bond strength measured in experiments, so that it can be considered as a quantifier for the bonds.     

Characterization of the Surface Electrode Reaction in the Presence of Uniform Interaction: The Case of Mo(VI) Reduction in the Presence of Phenanthroline and an Excess of Fulvic Acids

Surface electrode reactions involving lateral uniform interactions between adsorbed species is studied by means of square‐wave voltammetry (SWV). Interactions are represented by the interaction product aΘ, were a is the Frumkin interaction parameter (a is positive for attraction and negative for repulsion forces) and Θ is the surface coverage. The properties of the SW voltammetric response enable detection of interactions and recognition of the type of interaction forces by a simple procedure. The influence of the interactions on the apparent electrochemical reversibility of the surface electrode reaction is studied in detail. Utilizing “quasireversible maximum” the simple methodology for estimation of the standard redox rate constant without knowing the exact value of the interaction product aΘ is developed. Theoretical predictions are illustrated and confirmed by experiments with Mo(VI) in the presence of phenantroline and an excess of fulvic acids.     

Third-order interaction approximation for linear polymer chains

Third-order interactions imposed by a pair of atoms separated by five bonds are taken into account in computations of the mean-square end-to-end distance and the mean-square radius of gyration for linear polymer chains. The statistical weight matrices are established on the basis of the rotational isomeric state model. The conformational energy of n-hexane is calculated as a function of the C? C bond rotation angles. The third-order interaction energy is obtained by comparison with that of n-pentane. The characteristic ratio of polymethylene is 6.6 in the third-order interaction approximation, which is in agreement with experimental data.     

Projected BCS Tamm-Dancoff method for molecular electronic structures

A new Tamm–Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number-projected BCS (PBCS ) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one-pair excitation terms in the Tamm-Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin-symmetry adapted first- and second-order Tamm–Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H₄ system with D_2h and D_4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second-order Tamm–Dancoff correction improves the result as much as the double excitation CI . The Tamm–Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.     

Density functional theory and topological analysis on the hydrogen bonding interactions in cysteine‐thymine complexes

Hydrogen bonding interactions between amino acids and nucleic acid bases constitute the most important interactions responsible for the specificity of protein binding. In this study, complexes formed by hydrogen bonding interactions between cysteine and thymine have been studied by density functional theory. The relevant geometries, energies, and IR characteristics of hydrogen bonds (H‐bonds) have been systematically investigated. The quantum theory of atoms in molecule and natural bond orbital analysis have also been applied to understand the nature of the hydrogen bonding interactions in complexes. More than 10 kinds of H‐bonds including intra‐ and intermolecular H‐bonds have been found in complexes. Most of intermolecular H‐bonds involve O (or N) atom as H‐acceptor, whereas the H‐bonds involving C or S atom usually are weaker than other ones. Both the strength of H‐bonds and the structural deformation are responsible for the stability of complexes. Because of the serious deformation, the complex involving the strongest H‐bond is not the most stable structures. Relationships between H‐bond length (ΔR_X‐H), frequency shifts (Δv), and the electron density (ρ_b) and its Laplace (?²ρ_b) at bond critical points have also been investigated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Electronic structure and optical spectra of transition metal complexes by the effective Hamiltonian method

Summary A semiempirical effective Hamiltonian treatment is proposed for transition metal complexes, taking into accountd-electron correlations, weak covalency of the metal-ligand bonds and the electronic structure of the ligand sphere. The technique uses the variation wave function which differs from the usual Hartree-Fock antisymmetrized product of molecular orbitals extended over the whole complex. The scheme is implemented and parameters describing the metal-ligand interactions are adjusted to reproduced-d-excitation spectra of a number of octahedral MF ₆ ^4– (M=Mn, Fe, Co, Ni) anions, Mn(FH) ₆ ²⁺ cation, CoCl ₆ ^4– anion, and a tetrahedral CoCl ₄ ^2– anion. The values of the parameters are reasonable, thus confirming the validity of the proposed scheme.     

Molecular structures and intramolecular interactions in dimethyl cyclohexane isomers

The geometries of ten isomers of dimethyl cyclohexane were determined by ab initio gradient geometry refinement with the 4-21G basis set. It is found that many intramolecular interactions are clearly manifested by correlated structural trends, and that they are consistent with strain energies calculated by employing previously defined ab initio group equivalents. Specifically, non-bonded interactions are found between two adjacent methyl groups in some of the forms, and between axial methyl groups and adjacent axial C? H bonds in others. Unperturbed axial C? H and C? C bonds are consistently longer than equatorial bonds. In general, C? H bonds which are involved in non-bonded repulsive interactions are shortened, i.e., strengthened, and the corresponding H? C? C angles are large, compared to non-interacting parameters.     

Molecular interaction potential: A new tool for the theoretical study of molecular reactivity

A new methodology to compute molecular interaction potentials (MIPs) is developed and tested. The calculation of the MIP is based upon the generalization of the rigorous quantum mechanical molecular electrostatic potential (MEP) and further addition of a classical repulsion-dispersion term. As a result, the MIP is able to represent not only with high accuracy electrostatic interactions but also represent in a suitable way steric effects. The analysis of the results obtained for different molecules demonstrates the superiority of the MIP with regard to the standard MEP to describe nonbonded interactions, in particular hydrogen bonds. The comparison of results calculated at the ab initio I 6-31G* and semiempirical AM1 levels points out the suitability of semiempirical calculations to qualitatively reproduce the most relevant reactive features of the molecules. Finally, possible applications of the MIP in different fields are discussed. © 1993 John Wiley & Sons, Inc.     

Interactions of Molecules with cis and trans Double Bonds: A Theoretical Study of cis‐ and trans‐2‐Butene

Noncovalent interactions of cis‐ and trans‐2‐butene, as the smallest model systems of molecules with cis and trans double bonds, were studied to find potential differences in interactions of these molecules. The study was performed using quantum chemical methods including very accurate CCSD(T)/CBS method. We studied parallel and displaced parallel interactions in 2‐butene dimers, in butane dimers, and between 2‐butene and saturated butane. The results show the trend that interactions of 2‐butene with butane are the strongest, followed by interactions in butane dimers, whereas the interaction in 2‐butene dimers are the weakest. The strongest calculated interaction energy is between trans‐2‐butene and butane, with a CCSD(T)/CBS energy of ?2.80 kcal mol^?1. Interactions in cis‐2‐butene dimers are stronger than interactions in trans‐2‐butene dimers. Interestingly, some of the interactions involving 2‐butene are as strong as interactions in a benzene dimer. These insights into interactions of cis‐ and trans‐2‐butene can improve understanding of the properties and processes that involve molecules with cis and trans double bonds, such as fatty acids and polymers.