An improved Hellmann-type pseudopotential for atoms and molecules

The concept of pseudopotentials offers much attractiveness for the quantum mechanical evaluation of the physical properties of atoms and molecules. The ideas of Hellmann, in which the repulsive and fermion character of inner electrons can be mimicked by an experimentally fitted, exponentially damped potential term, are especially attractive. Unfortunately, it is found that such a simple expression can only be used in a very limited number of cases, such as for the alkali metals, and even then fails for the simple case of lithium. The present study shows that the Hellmann idea can readily be extended by including a second “shielded potential” term evaluated from tabulated previous Hartree-Fock calculations. The new expression for the model pseudopotential is both simple and effective. With it, the inner potential of any of the alkali metal atoms, including lithium, can be represented so that calculation of the molecular properties of the metal dimers can be accomplished. Calculations for Li₂, Na₂, and K₂ show the binding energies and equilibrium interatomic distances to be quite well given, in agreement with both chemical experience and spectroscopic evidence.     

A procedure for obtaining lower bounds for ground state energies of atoms and molecules

Using Löwdin's partition method we have re-derived the D. Weinstein lower bound, E > H ₁₁ - . By the same method, plus the assumption that the calculated first excited state energy is lower than a certain weighted average of approximate energies of all the excited states, we have derived a moderately better lower bound.     

苯甲酰硫脲类化合物生物活性的QSAR模型和结构修饰的理论研究

基于分子拓扑邻接矩阵,计算了18种苯甲酰硫脲衍生物的原子类型电性拓扑状态指数(En)。通过多元线性逐步回归方法,建立了令人满意的En与苯甲酰硫脲衍生物对金黄色葡萄球菌的抑制活性(D)的定量结构-活性相关模型(QSAR)。该模型的相关系数(R2)、标准偏差(S)分别为0.861及1.273,该模型的计算值与相应实验值基本吻合。经Rcv2、VIF、FIT、AIC等指标检验,所建模型具有良好的预测能力与稳健性。利用该模型探讨了苯甲酰硫脲衍生物对金黄色葡萄球菌的抑制机理。根据进入模型的2个电性拓扑状态指数E1、E7可知,影响苯甲酰硫脲衍生物对金黄色葡萄球菌的抑制活性的主要因素是分子的二维结构特征-CH3和在芳环中=CH-等结构碎片。由结构修饰提出5种化合物,其中3种的抑菌活性均超出18mm,有待以后生物实验予以证实。     

An analytical expression for interatomic surfaces in the theory of atoms in molecules

Summary According to the theory of Atoms in Molecules as developed by Bader and coworkers a molecule is partitioned into atoms separated by surfaces of zero flux in the gradient of the charge density. For the first time an accurate and explicit analytical expression is given for these interatomic surfaces. They are generated by a system of differential equations which can in principle be solved by using a series expansion. Unfortunately, this expansion has a small radius of convergence and can therefore not be applied in practice. However, by a combined Chebyshev-Fourier fit to a numerically obtained surface, the interatomic surface is globally described to any given accuracy. Finally, the algorithm is tested on a set of simple molecules and on the amide interatomic surfaces of the glycyl residue |HNCH₂CO|.     

Differential density matrix overlap: an index for assessment of electron correlation in atoms and molecules

Summary A new index, called the differential density matrix overlap (DDMO), is proposed for assessment of the electron correlation effects in atoms and molecules. DDMO can be easily calculated as the negative value of the correlation energy derivative with respect to the relative position of the occupied and virtual orbitals. DDMO is transparent to physical interpretation. It can serve as a tool for analyzing the accuracy of approximate electron correlation methods and the validity of the Hartree-Fock wavefunction as the zeroth-order approximation. The properties of DDMO are discussed using test calculations on 11 atoms and molecules as an example.     

Properties of atoms in molecules

Atomic charges calculated by the population analysis method for three types of semi-empirical wave functions have been compared with charges obtained by integrating the corresponding electronic density functions over individual atomic regions. It was found that the two sets of charges compare quite well for CNDO wave functions and for extended-Hückel functions which are in terms of orthogonalized basis orbitals. However only the CNDO charges are reasonably close to those obtained by integrating near-Hartree-Fock electronic density functions.     

Properties of atoms in molecules

The electronic charges and the positions of the centers of these charges have been calculated for the atoms of a number of second- and third-row heteronuclear diatomic molecules. For both the oxygen and the fluorine atoms, the charge associated with one of these atoms can be correlated, within a series of molecules containing that atom, with both the orbital energy of the atom's 1s electrons and also with the difference in electronegativities of the atoms that comprise the molecule. The centers of electronic charge are outside of the internuclear regions, except for the positive atoms in the more ionic molecules and in HF.     

QSAR modeling with the electrotopological state indices: Corticosteroids

A structure-activity analysis of a series of steroids binding to corticosteroid-binding globulin was made using the electrotopological state index for each atom in the molecule. Two indices were found to correlate well with the binding affinity. The indices encode structural characteristics in the A and the D rings of the steroids in the study. One of the indices was formulated as the difference between two indices in the A ring. The two were not intercorrelated, suggesting that the composite index signals the influence of structure changes in or near the A ring that can be monitored by the composite index. This is a new observation using this structure-activity method. It is suggested that this model makes some contributions towards detection of the pharmacophore.     

On a new semi‐empirical electrotopological index for QSRR models

A new semi‐empirical electrotopological index, I_SET, for quantitative structure–retention relationships (QSRR) models was developed based on the refinement of the previously published semi‐empirical topological index, I_ET. We demonstrate that the values of C_i fragments that were firstly attributed from the experimental chromatographic retention and theoretical deductions have an excellent relationship with the net atomic charge of the carbon atoms. Thus, the values attributed to the vertices in the hydrogen‐suppressed graph of carbon atoms (C_i) are calculated from the correlation of the net atomic charge in each carbon atom, which is obtained from quantum chemical semi‐empirical calculations, and the C_i fragments for primary, secondary, tertiary and quaternary carbon atoms (1.0, 0.9, 0.8 and 0.7, respectively) obtained from the experimental values. This shows that I_ET encoded this quantum physical reality and that it is possible to calculate a new I_SET (the semi‐empirical electrotopological index) through the net atomic charge values obtained from a Mulliken population analysis using the semi‐empirical AM1 method and their correlation with the values attributed to the different types of carbon atoms. This demonstrates that the I_SET encodes information on the charge distribution of the solute on which dispersive and electrostatic interactions between the solute (alkanes and alkenes) and the stationary phase strongly depend. Thus, this new method can be considered as an initial step towards forthcoming QSRR/QSAR studies. Copyright © 2008 John Wiley & Sons, Ltd.     

Electron delocalization and aromaticity in linear polyacenes: atoms in molecules multicenter delocalization index

Molecular aromaticity in the linear polyacenes is investigated using an atoms in molecules based six center index (SCI-AIM) which measures the electron delocalization. SCI-AIM values for the linear polyacenes indicate decreasing aromaticity going from outer to inner rings in the polyacene series. The SCI-AIM approach is compared to a Mulliken-like approach, and a critical comparison to the PDI index is made.     

Next-generation quantum theory of atoms in molecules for the ground and excited state of the ring-opening of cyclohexadiene

The factors underlying the experimentally observed branching ratio (70:30) of the (1,3-cyclohexadiene) CHD → HT (1,3,5-hexatriene) photochemical ring-opening reaction are investigated. The ring-opening reaction path is optimized by a high-level multi-reference DFT method and the density along the path is analyzed by the quantum theory of atoms in molecules (QTAIM) and stress tensor methods. The performed density analysis suggests that, in both S₁ and S₀ electronic states, there exists an attractive interaction between the ends of the fissile σ-bond of CHD that steers the ring-opening reaction predominantly in the direction of restoration of the ring. It is suggested that opening of the ring and formation of the reaction product (HT) can only be achieved when there is a sufficient persistent nuclear momentum in the direction of stretching of the fissile bond. As this orientation of the nuclear momentum vector can be expected relatively rare during the dynamics, this explains the observed low quantum yield of the ring-opening reaction.     

An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.