Diatomic interaction energies in the topological theory of atoms in molecules

Summary.  A partitioning of the ab initio total energy into one-center and two-center terms is proposed. The partitioning scheme is developed using the auxiliary function L˜(2, 1; 1, 2)=γ(2, 1)γ(1, 2) and the topological theory of atoms in molecules. It is shown that this scheme can be used at theoretical levels beyond Hartree–Fock. The numerical results indicate that the two-center terms follow the experimental trend of the dissociation energies for a series of related compounds. Received March 5, 1996/Final revision received August 19, 1996/Accepted August 29, 1996     

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|.     

Failures of the topological resonance energy method

The topological resonance energy (TRE) is nowadays considered as one of the most reliable indices of stability and aromaticity of conjugated molecules. Seven groups of examples are constructed showing that the TRE concept leads sometimes to obviously false chemical conclusions.Presented on the International Symposium on Aromaticity, Dubrovnik, Yugoslavia, September 1979.     

Analysis of the delocalization in the topological theory of chemical bond

The topological analysis of the gradient field of the electron localization function provides a convenient theoretical framework for the partition of the molecular space into basins of attractors having a clear chemical meaning. The basin populations are evaluated by integrating the one-electron density over the basins. The variance of the basin population provides a measure of the delocalization. The behavior of the core C(X) and protonated valence basins V(X, H) populations were investigated. The analysis of the population variance in terms of cross-contributions is presented for aromatic and antiaromatic systems, hypervalent molecules and hydrogen-bonded complexes. For hypervalent molecules this analysis emphasizes the importance of the ionic resonance structures.     

Electrostatic interaction energies of independent aspherical atoms in molecules

Matter may be looked upon as consisting of superimposed independent atoms, which are spatially confined around specific positions by the chemical forces and which are weakly deformed thereby. Independent atoms with degenerate ground states are not fixed to be spherically symmetric as often supposed; it is more convenient for the interpretation of molecular and crystal charge distribution to refer to nonspherical atomic ground-state densities, the orientation of which is also determined by the chemical forces. In accordance with the virial theorem, one half of the quasiclassical electrostatic interaction energy, EE, of superimposed independent atoms is an approximation to the total bond energy, BE. The BE≈EE/2 correlation also improves if oriented nonspherical instead of spherically averaged atoms are superimposed. This correlation does not mean that the bond energy has been explained electrostatically, because one must know the atomic positions (and orientations) in advance. Furthermore, density deformations due to the quantum-mechanical interactions contribute 2–3 eV to BE.     

Interatomic exchange-correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding—integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)—and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.     

Revisiting the foundations of the quantum theory of atoms in molecules: Toward a rigorous definition of topological atoms

An explicit classification of consistent variational constraints within the context of the “quantum theory of proper open subsystems” as well as the “quantum theory of atoms in molecules” (QTAIM) it presented. It is demonstrated that the general variational procedure is not sensitive enough to discriminate between different mathematically consistent variational conditions. The uniqueness of the regional kinetic energy is employed to derive the net zero‐flux condition and the regions satisfying this condition are named as quantum divided basins. A modified form of the local zero‐flux is proposed in order to define topological atoms within the context of the orthodox QTAIM. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

A quantified resonance theory and its relation with MO — excited state behaviour of conjugated hydrocarbons and heteroconjugate molecules

Summary Quantified resonance theory (QRT) involving the use of weight has been applied successfully to ionization potential, electron affinity, energy of the lowest * transition, charge density and bond order in excited state for alternant and nonalternant hydrocarbons and heteroconjugate molecules. A number of close relations between QRT and HMO or PMO are found. QRT naturally leads to the frontier orbital theory results, and the natural hypsochromic shift in electronic spectra of fulvenes is also explained satisfactorily.     

Density functional theory studies on the dissociation energies of metallic salts: relationship between lattice and dissociation energies

The formation and physicochemical properties of polymer electrolytes strongly depend on the lattice energy of metal salts. An indirect but efficient way to estimate the lattice energy through the relationship between the heterolytic bond dissociation and lattice energies is proposed in this work. The heterolytic bond dissociation energies for alkali metal compounds were calculated theoretically using the Density Functional Theory (DFT) of B3LYP level with 6‐311+G(d,p) and 6‐311+G(2df,p) basis sets. For transition metal compounds, the same method was employed except for using the effective core potential (ECP) of LANL2DZ and SDD on transition metals for 6‐311+G(d,p) and 6‐311+G(2df,p) calculations, respectively. The dissociation energies calculated by 6‐311+G(2df,p) basis set combined with SDD basis set were better correlated with the experimental values with average error of ca. ±1.0% than those by 6‐311+G* combined with the LANL2DZ basis set. The relationship between dissociation and lattice energies was found to be fairly linear (r>0.98). Thus, this method can be used to estimate the lattice energy of an unknown ionic compound with reasonably high accuracy. We also found that the dissociation energies of transition metal salts were relatively larger than those of alkaline metal salts for comparable ionic radii. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 827–834, 2001     

Proof of finiteness of Kohn–Sham theory electron interaction potential at the nucleus of atoms

We employ Kato's theorem to prove that the electron interaction potential of Kohn–Sham density functional theory is finite at the nucleus of spherically symmetric and sphericalized atoms and ions. Therefore, this finiteness is a direct consequence of the electron–nucleus cusp condition for the density. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 205–208, 2000     

Second-order atomic Fukui indices from the electron-pair density in the framework of the atoms in molecules theory

Atomic Fukui indices, which are obtained from the electron density, have been previously shown to be useful in predicting which atoms in a molecule are most likely to suffer nucleophilic, electrophilic, or radicalary attacks. Here, we present a second-order generalization of these indices based on the electron pair density. We show how second-order atomic Fukui indices can be used to analyze the effects of electron loss or gain in several molecules from an electron pair point of view. Further, these indices also highlight which atoms or pairs of atoms are more likely to suffer nucleophilic, electrophilic, or radical attacks. In conclusion, second-order indices can complement first-order ones by affording relevant information on molecular reactivity from an electron pair perspective.     

Two-electron integrations in the quantum theory of atoms in molecules with correlated wave functions

A recent method proposed to compute two-electron integrals over arbitrary regions of space [Martin Pendas, A. et al., J Chem Phys 2004, 120, 4581] is extended to deal with correlated wave functions. To that end, we use a monadic factorization of the second-order reduced density matrix originally proposed by E. R. Davidson [Chem Phys Lett 1995, 246, 209] that achieves a full separation of the interelectronic components into one-electron terms. The final computational effort is equivalent to that found in the integration of a one determinant wave function with as many orbitals as occupied functions in the correlated expansion. Similar strategies to extract the exchange and self-interaction contributions from the two-electron repulsion are also discussed, and several numerical results obtained in a few test systems are summarized.     

Structural properties and interaction energies affecting drug design. An approach combining molecular simulations,statistics, interaction energies and neural networks

In order to elucidate some basic principles for protein–ligand interactions, a subset of 87 structures of human proteins with their ligands was obtained from the PDB databank. After a short molecular dynamics simulation (to ensure structure stability), a variety of interaction energies and structural parameters were extracted. Linear regression was performed to determine which of these parameters have a potentially significant contribution to the protein–ligand interaction. The parameters exhibiting relatively high correlation coefficients were selected. Important factors seem to be the number of ligand atoms, the ratio of N, O and S atoms to total ligand atoms, the hydrophobic/polar aminoacid ratio and the ratio of cavity size to the sum of ligand plus water atoms in the cavity. An important factor also seems to be the immobile water molecules in the cavity. Nine of these parameters were used as known inputs to train a neural network in the prediction of seven other. Eight structures were left out of the training to test the quality of the predictions. After optimization of the neural network, the predictions were fairly accurate given the relatively small number of structures, especially in the prediction of the number of nitrogen and sulfur atoms of the ligand.     

Energy decomposition in the topological theory of atoms in molecules and in the linear combination of atomic orbitals formalism: a note

 It is shown that the molecular energy calculated at the self-consistent-field level can be strictly expressed as a sum of one- and two-atom energy components in the framework of Bader's topological theory of atoms in molecules (AIM). The expressions of our recent “chemical energy component analysis” can be obtained from the AIM ones as some linear combination of atomic orbitals mappings of the integrations over the atomic basins. Received: 15 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

Studies on the interaction of bacterial capsular polysaccharide- Klebsiella K16 with cationic and mixed surfactants

The spectral studies of cationic dyes, pinacyanol chloride (PCYN) and acridine orange (AO) with capsular polysaccharide Klebsiella K16 (PK16) biopolymer in micellar media reveal many interesting phenomena. Intensity of the metachromatic band (μ) at 490 nm decreases gradually on addition of cationic single surfactant to the biopolymer PK16–dye system of P/D = 30, whereas the intensity of α and β bands reach to the value of original pure dye. As a result, the cationic surfactant destroys the metachromatic compound and forms a new complex with biopolymer PK16 by freeing the dye molecule. Enhancement of fluorescence intensity of AO-PK16 system with cationic surfactant is another evidence for the binding between the biopolymer and the surfactant. Interaction between the biopolymer and mixed surfactant has also been studied. Finally, the binding ability of cationic surfactants with or without non ionic surfactant, the idea of the critical aggregation concentration (cac) of the surfactant, mole fraction and the charge density of mixed surfactant for binding with PK16 and also the site of interaction have been pointed out.     

A theoretical study of the intramolecular interaction between proximal atoms in planar conformations of biphenyl and related systems

The nature of the interaction between proximal hydrogens in planar biphenyl has been recently a matter of debate as arguments in favor of and against the existence of “H–H” bonding have been recently put forward. This issue is addressed here through the study of both the electron density ρ(r) and the electron localization function (ELF) η(r) obtained in quantum calculations on molecular systems with F atoms replacing hydrogens in the moiety that presents this interaction. The analysis of geometries and properties of ρ(r) and η(r) at both planar and twisted equilibrium conformations of those systems along with biphenyl, permits to get information on this intramolecular interaction that is compared with the use of the traditional chemical concepts (steric hindrance and π-resonance effects) involved. It is shown that although the ELF gives information compatible with these classical terms, this does not preclude the existence of bonds between proximal atoms with features rather similar to those of well-established intramolecular hydrogen bonds.     

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.     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.     

Multipole analysis of electron repulsion energies in many-electron atoms

The repulsion energy W between two electrons located at r ₁ and r ₂ can be expressed by the sum of the interaction energies W _k between an electron located at and linear electric multipoles located at the coordinate origin along the vector , where and are the vectors with smaller and larger moduli, respectively, of the two vectors r ₁ and r ₂. All the existing multipole contributions W _k to the Hartree–Fock electron repulsion energy W are examined for the 102 atoms He through Lr in their ground states. It is found that |W _k | decreases rapidly with increasing k, W ₀ > W, and W _k with k ≥ 1 work to reduce W ₀. The effect of electron correlation is also discussed for some helium-like atoms.     

The formulation of a self-consistent constricted variational density functional theory for the description of excited states

We outline here a self-consistent approach to the calculation of transition energies within density functional theory. The method is based on constricted variational theory (CV-DFT). It constitutes in the first place an improvement over a previous scheme [T. Ziegler, M. Seth, M. Krykunov, J. Autschbach, F. Wang, Chem. Phys. 130 (2009) 154102] in that it includes terms in the variational parameters to any desired order n including n = ∞. For n = 2, CV(n)-DFT is similar to TD-DFT. Adiabatic TD-DFT becomes identical to CV(2)-DFT after the Tamm-Dancoff approximation is applied to both theories. We have termed the new scheme CV(n)-DFT. In the second place, the scheme can be implemented self-consistently, SCF-CV(n)-DFT. The procedure outlined here could also be used to formulate a SCF-CV(n) Hartree-Fock theory. The approach is further kindred to the ΔSCF-DFT procedures predating TD-DFT and we describe how adiabatic TD-DFT and ΔSCF-DFT are related through different approximations to SCF-CV(n)-DFT.