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.     

Update of the AIM2000-program for atoms in molecules

The second version of the program package AIM2000 is presented. AIM2000 makes use of the well established theory of atoms in molecules. AIM2000 analyzes the molecular structure and calculates properties of atoms in molecules as well as properties of interatomic surfaces. The program has an interactive, context-sensitive help component and extensive 2D and 3D visualization components.     

Atoms in molecules interpretation of the anomeric effect in the O--C--O unit

The conformational preferences of two model compounds for the O--CH2--O anomeric unit: methanediol and dimethoxymethane analyzed within the framework of the QTAIM theory provide a new interpretation of the anomeric effect. The characteristic stabilization of the gauche conformers of these compounds is accompanied by a progressive reduction of the electron population of the hydrogens of the central methylene as the number of their gauche interactions to lone pairs rises. The electron population removed from these atoms during the conformational change is gained in the gauche conformers by atoms of larger atomic number, which results in a more negative molecular energy. Also, the variations displayed by atomic populations and the QTAIM delocalization indexes are not keeping in line with the hyperconjugative model of the anomeric effect.     

Collisional quenching of electronically excited germanium atoms, Ge[4p(S0)], by small molecules investigated by time-resolved atomic resonance absorption spectroscopy

The collisional quenching of electronically excited germanium atoms, Ge[4p²(¹S₀)], 2.029 eV above the 4p²(³P₀) ground state, has been investigated by time-resolved atomic resonance absorption spectroscopy in the ultraviolet at λ = 274.04 nm [4d(¹P₁⁰) ← 4p²(¹S₀)]. In contrast to previous investigations using the ‘single-shot mode’ at high energy, Ge(¹S₀) has been generated by the repetitive pulsed irradiation of Ge(CH₃)₄ in the presence of excess helium gas and added gases in a slow flow system, kinetically equivalent to a static system. This technique was originally developed for the study of Ge[4p²(¹D₂)] which had eluded direct quantitative kinetic study until recently. Absolute second-order rate constants obtained using signal averaging techniques from data capture of total digitised atomic decay profiles are reported for the removal of Ge(¹S₀) with the following gases (k_R in cm³ molecule⁻¹ s⁻¹, 300 K): Xe, 7.1 ± 0.4 × 10⁻¹³; N₂, 4.7 ± 0.6 × 10⁻¹²; O₂, 3.6 ± 0.9 × 10⁻¹¹; NO, 1.5 ± 0.3 × 10⁻¹¹; CO, 3.4 ± 0.5 × 10⁻¹²; N₂O, 4.5 ± 0.5 × 10⁻¹²; CO₂, 1.1 ± 0.3 × 10⁻¹¹; CH₄, 1.7 ± 0.2 × 10⁻¹¹; CF₄, 4.8 ± 0.3 × 10⁻¹²; SF₆, 9.5 ± 1.0 × 10⁻¹³; C₂H₄, 3.3 ± 0.1 × 10⁻¹⁰; C₂H₂, 2.9 ± 0.2 × 10⁻¹⁰; Ge(CH₃)₄, 5.4 ± 0.2 × 10⁻¹¹. The results are compared with previous data for Ge(¹S₀) derived in the single-shot mode where there is general agreement though with some exceptions which are discussed. The present data are also compared with analogous quenching rate data for the collisional removal of the lower lying Ge[4p²(¹D₂)] state (0.883 eV), also characterized by signal averaging methods similar to that described here.     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

DFT and TDDFT investigations on the ground and excited states for polynuclear platinum(Ⅱ) complexes containing the rigid phenylacetylide ligand

We have studied the ground and excited states of the three dendritic polynuclear Pt(Ⅱ) complexes 1-[Cl(PH3)2PtC≡C]-3,5-[HC≡C]C6H3 (1), 1,3-[Cl(PH3)2PtC≡C]2-5-[HC≡C]C6H3 (2), and 1,3,5-[Cl(PH3)2- PtC≡C]3C6H3 (3), by using the B3LYP and UB3LYP methods, respectively. TDDFT approach with the PCM model was performed to predict the emission spectra properties of 1-3 in CH2Cl2 solution. We first predicted the excited-state geometries for the three complexes. With the change of the number of Pt(Ⅱ) atom, 1-3 show the different geometry structures in both the ground and excited states; furthermore, the increase of the metal density from 1 to 3 results in the red shift of the lowest-energy emissions along the series. The luminescent properties of 1 are somewhat different from those of 2 and 3. The emission properties of 2 and 3 are richer than 1. Our conclusion can give a good support for designing the high efficient luminescent materials.     

Structure of electronically excited complexes in styrene and α-methylstyrene anion polymerizations

The spatial and electronic structure of styrene and α-methylstyrene monomer molecules and their complexes with living polymers in the ground singlet state (S ₀) and excited singlet (S ₁) and triplet (T ₁) states has been studied by RHF, ROHF/6-31G*, and DH quantum-chemical methods. The mechanism of anionic polymerization is considered in the context of the concept of electronic excitation in an elementary process. The excited states of (S·T)₁ biradical type are characterized by low energies (6–15 kcal/mole), which have the sense of activation energies E _a of chain propagation. Calculation gave higher values of E _a for free C^? anions compared to those for C^?M⁺ ion pairs, which indicates that anions show lower chemical activity in the general polymerization process.     

Biphenyl: A stress tensor and vector‐based perspective explored within the quantum theory of atoms in molecules

We use quantum theory of atoms in molecules (QTAIM) and the stress tensor topological approaches to explain the effects of the torsion φ of the C‐C bond linking the two phenyl rings of the biphenyl molecule on a bond‐by‐bond basis using both a scalar and vector‐based analysis. Using the total local energy density H( r _b), we show the favorable conditions for the formation of the controversial H–H bonding interactions for a planar biphenyl geometry. This bond‐by‐bond QTAIM analysis is found to be agreement with an earlier alternative QTAIM atom‐by‐atom approach that indicated that the H–H bonding interaction provided a locally stabilizing effect that is overwhelmed by the destabilizing role of the C‐C bond. This leads to a global destabilization of the planar biphenyl conformation compared with the twisted global minimum. In addition, the H( r _b) analysis showed that only the central torsional C‐C bond indicated a minimum for a torsion φ value coinciding with that of the conventional global energy minimum. The H–H bonding interactions are found to be topologically unstable for any torsion of the central C‐C bond away from the planar biphenyl geometry. Conversely, we demonstrate that for 0.0° < φ < 39.95° there is a resultant increase in the topological stability of the C nuclei comprising the central torsional C‐C bond. Evidence is found of the effect of the H–H bonding interactions on the torsion φ of the central C‐C bond of the biphenyl molecule in the form of the QTAIM response β of the total electronic charge density ρ( r _b). Using a vector‐based treatment of QTAIM we confirm the presence of the sharing of chemical character between adjacent bonds. In addition, we present a QTAIM interpretation of hyperconjugation and conjugation effects, the former was quantified as larger in agreement with molecular orbital (MO) theory. The stress tensor and the QTAIM H atomic basin path set areas are independently found to be new tools relevant for the incommensurate gas to solid phase transition occurring in biphenyl for a value of the torsion reaction coordinate φ ≈ 5°. © 2015 Wiley Periodicals, Inc.     

Further investigations about the zwitterionic excited states of twisted conjugated molecules

For twisted zwitterionic excited states, the single-determinant closed-shell SCF approach favours one of the two possibly resonant structures A⁺B^– or A^–B⁺, but gives a very low energy by allowing reorganization and polarization under the field. This effect is very difficult to include in CI developments using neutral symmetry adapted MO's. The closed-shell SCF approach is always relevant for energy, and only fails for the wavefunction in the (near) degeneracy region between A^–B⁺ and A⁺ B^–, where the Born-Oppenheimer approximation, anyway, breaks down. The process is applied in nonempirical (minimal + diffuse AO basis set) calculations of butadiene. The role of geometry optimization and of further electron correlation is illustrated. The extent of polarization is shown in ethylene, suggesting a neutral two carbene limit picture of this excited state.     

Potential functions of inversion of R2CO (R=H, F, Cl) molecules in the lowest excited electronic states

The inversion potentials of R₂CO (R=H, F, Cl) molecules in the lowest excited electronic states were determined from experimental data using various model potential functions and approximations for the kinetic energy operator of inversion motion. The estimates of the heights of the barriers to inversion and the equilibrium values of the inversion coordinate for the H₂CO molecule in the S₁ and T₁ states are fairly stable. The results for the F₂CO and Cl₂CO molecules are strongly dependent on the approximation used; for these molecules, the most reliable parameters of the potential functions were chosen. The problem of qualitative characteristics of the shape of inversion potentials is discussed using the results ofab initio quantum-chemical calculations of the molecules under study. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 645–651, April, 1999.     

Ritz variational method for the high‐lying nonautoionizing doubly excited 1,3Fe states of two‐electron atoms

Energy eigenvalues of nonautoionizing doubly excited states originating from 2pnf ( ) configuration of two‐electron atoms have been calculated by expanding the basis set in explicitly correlated Hylleraas coordinates under the framework of Ritz variational method. A detailed discussion on the evaluation of correlated basis integrals is given. The energy eigenvalues of a number of these doubly excited states are being reported for the first time especially for the high lying states. The effective quantum numbers ( ) for the states mentioned above have been calculated by using the theory of quantum defect.     

An insight into the local aromaticities of polycyclic aromatic hydrocarbons and fullerenes

In this work we quantify the local aromaticity of six-membered rings in a series of planar and bowl-shaped polycyclic aromatic hydrocarbons (PAHs) and fullerenes. The evaluation of local aromaticity has been carried out through the use of structurally (HOMA) and magnetically (NICS) based measures, as well as by the use of a new electronically based indicator of aromaticity, the para delocalization index (PDI), which is defined as the average of all the Bader delocalization indices between para-related carbon atoms in six-membered rings. The series of PAHs selected includes C(10)H(8), C(12)H(8), C(14)H(8), C(20)H(10), C(26)H(12), and C(30)H(12), with benzene and C(60) taken as references. The change in the local aromaticity of the six-membered rings on going from benzene to C(60) is analyzed. Finally, we also compare the aromaticity of C(60) with that of C(70), open [5,6]- and closed [6,6]-C(60)NH systems, and C(60)F(18).     

Modeling absorption spectra of molecules in solution

The presence of solvent tunes many properties of a molecule, such as its ground and excited state geometry, dipole moment, excitation energy, and absorption spectrum. Because the energy of the system will vary depending on the solvent configuration, explicit solute–solvent interactions are key to understanding solution-phase reactivity and spectroscopy, simulating accurate inhomogeneous broadening, and predicting absorption spectra. In this tutorial review, we give an overview of factors to consider when modeling excited states of molecules interacting with explicit solvent. We provide practical guidelines for sampling solute–solvent configurations, choosing a solvent model, performing the excited state electronic structure calculations, and computing spectral lineshapes. We also present our recent results combining the vertical excitation energies computed from an ensemble of solute–solvent configurations with the vibronic spectra obtained from a small number of frozen solvent configurations, resulting in improved simulation of absorption spectra for molecules in solution.     

Prediction of spectroscopic constants for diatomic molecules in the ground and excited states using time-dependent density functional theory

Spectroscopic constants of the ground and next seven low-lying excited states of diatomic molecules CO, N2, P2, and ScF were computed using the density functional theory SAOP/ATZP model, in conjunction with time-dependent density functional theory (TD-DFT) and a recently developed Slater type basis set, ATZP. Spectroscopic constants, including the equilibrium distances r(e), harmonic vibrational frequency omega(e), vibrational anharmonicity omega(e)x(e), rotational constant B(e), centrifugal distortion constant D(e), the vibration-rotation interaction constant alpha(e), and the vibrational zero-point energy E(n)0 were generated in an effort to establish a reliable database for electron spectroscopy. By comparison with experimental values and a similar model with an established larger Slater-type basis set, et-QZ3P-xD, it was found that this model provides reliably accurate results at reduced computational costs, for both the ground and excited states of the molecules. The over all errors of all eight lowest lying electronic states of the molecules under study using the effective basis set are r(e)(+/-4%), omega(e)(+/-5% mostly without exceeding +/-20%), omega(e)x(e)(+/-5% mostly without exceeding 20%, much more accurate than a previous study on this constant of +/-30%), B(e)(+/-8%), D(e)(+/-10%), alpha(e)(+/-10%), and E(n)0(+/-10%). The accuracy obtained using the ATZP basis set is very competitive to the larger et-QZ3P-xD basis set in particular in the ground electronic states. The overall errors in r(e), omega(e)x(e), and alpha(e) in the ground states were given by +/-0.7, +/-10.1, and +/-8.4%, respectively, using the efficient ATZP basis set, which is competitive to the errors of +/-0.5, +/-9.2, and +/-9.1%, respectively for those constants using the larger et-QZ3P-xD basis set. The latter basis set, however, needs approximately four times of the CPU time on the National Supercomputing Facilities (Australia). Due to the efficiency of the model (TD-DFT, SAOP and ATZP), it will be readily applied to study larger molecular systems.     

Analysis of chemical bonding in electronic excited states using parity function

The parity function (Schmider, J Chem Phys 1996, 105, 11134) is a projection of the spin‐traced one‐particle density matrix, which is strongly influenced by chemical bonding and its type. In this article, we apply the Parity Function to analyze chemical bonding in the electronic excited states of some small molecules, computed with the time‐dependent density functional theory. The calculations were carried out within the standard linear combination of atomic orbitals framework. We found that the changes in the parity function upon the excitation can be interpreted in terms of chemically relevant concepts such as bond breaking. We hope that the parity function will become a useful tool for understanding electronic excited states. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

TDDFT modeling of the CO‐photolysis of Fe2(S2C3H6)(CO)6, a model of the [FeFe]‐hydrogenase catalytic site

Upon irradiation with ultraviolet wavelengths, Fe₂(S₂C₃H₆)(CO)₆, a simple model of the [FeFe]‐hydrogenase active site, undergoes CO dissociation to form the unsaturated Fe₂(S₂C₃H₆)(CO)₅ species and successively a solvent adduct at the vacant coordination site. In the present work, the CO‐photolysis of Fe₂(S₂C₃H₆)(CO)₆ was investigated by density functional theory (DFT) and time‐dependent DFT (TDDFT). Trans Fe₂(S₂C₃H₆)(CO)₅ form and the corresponding trans heptane or acetonitrile solvent adducts are the lowest energy ground state forms. CO dissociation barriers computed for the lowest triplet state are roughly halved with respect to those for the ground state suggesting that some low‐lying excited potential energy surface (PES) could be loosely bound with respect to Fe? C bond cleavage. The TDDFT excited state PESs and geometry optimizations for the excited states likely involved in the CO‐photolysis suggest that the Fe? S bond elongation and the partial isomerization toward the rotated form could take place simultaneously, favoring the trans CO photodissociation. © 2014 Wiley Periodicals, Inc.     

Molecular orbitals for excited states of atoms and molecules

A method is described for calculating SCF wavefunctions for excited electronic states of atoms and molecules. The orthogonality conditions with the ground state wavefunction and the underlying excited states wavefunctions are introduced in the SCF process in a simplified form.     

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

In a series of papers in the last 10 years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, new mathematical problems also emerged during these studies that were reviewed elsewhere [Sh. Shahbazian Int. J. Quantum Chem. 2011 , 111, 4497.]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi‐component quantum theory of atoms in molecules [M. Goli, Sh. Shahbazian Theor. Chem. Acc. 2013 , 132, 1365.]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation, the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules and its multi‐component version.