Time‐Dependent Density Functional Theory Molecular Dynamics Simulations of Liquid Water Radiolysis

The early stages of the Coulomb explosion of a doubly ionized water molecule immersed in liquid water are investigated with time‐dependent density functional theory molecular dynamics (TD–DFT MD) simulations. Our aim is to verify that the double ionization of one target water molecule leads to the formation of atomic oxygen as a direct consequence of the Coulomb explosion of the molecule. To that end, we used TD–DFT MD simulations in which effective molecular orbitals are propagated in time. These molecular orbitals are constructed as a unitary transformation of maximally localized Wannier orbitals, and the ionization process was obtained by removing two electrons from the molecular orbitals with symmetry 1B₁, 3A₁, 1B₂ and 2A₁ in turn. We show that the doubly charged H₂O²⁺ molecule explodes into its three atomic fragments in less than 4 fs, which leads to the formation of one isolated oxygen atom whatever the ionized molecular orbital. This process is followed by the ultrafast transfer of an electron to the ionized molecule in the first femtosecond. A faster dissociation pattern can be observed when the electrons are removed from the molecular orbitals of the innermost shell. A Bader analysis of the charges carried by the molecules during the dissociation trajectories is also reported.     

Localized charge distributions

A localized molecular orbital has been found to extend slightly and regularly into regions away from the chemical bond which contains most of its charge cloud. This was made the basis for a method of transferring localized orbitals among similar molecules. Each localized orbital induces a set of so-called molecule invariant fragments consisting of one bond fragment and collections of geminal fragments, vicinal fragments, and third and fourth neighbor fragments. Localized orbital expansion coefficients in a hybrid basis can be calculated for these molecule invariant fragments without solving any equations or performing any laborious computations. The present work is an application to acylic hydrocarbons. The results are based on the analysis of 33 INDO-SCF molecular orbital wavefunctions in the localized representation. Computational methods for obtaining close approximations to localized orbitals are also discussed. The application of a suggested pseudo-eigenvalue localization method and its accompanying self-consistent iteration process are found to not converge.     

Momentum–space electron densities—localized orbitals in hydrocarbons,boranes, and transition metal complexes

Position and momentum space plots are presented for localized molecular orbitals in hydrocarbons, boranes, a carborane, and two octahedral transition metal complexes. The p-space representation proves to be valuable for visualizing such orbitals since it highlights the differences in their character from one molecule to another. Factors influencing the form of the orbitals in p space, including the oscillatory behavior caused by contributions to an orbital from more than one center, are examined in detail. © 1996 John Wiley & Sons, Inc.     

Density functional study of platinum polyyne monomer,oligomer, and polymer: Ground state geometrical and electronic structures

Geometries of monomers and oligomers of a platinum polyyne and its free ligands were optimized using density functional theory with B3LYP hybrid functional. The LANL2DZ basis set was used for Pt and the 6‐31G* for other atoms in geometry optimizations. The electronic structures of these compounds were analyzed using Stuttgart/Dresden ECPs (SDD) basis set for metal atoms and 6‐311G* for others. The polymerization has very little effect on the bond lengths and by introducing the metal, the acetylide bond length increases slightly. The strong overlap between metal sp_x orbitals and σp_x orbitals of acetylides results in localized σ bonding. The hybridization between the ligand pπ orbitals and the platinum dπ orbital resulted in the π‐conjugation enhancement. This conjugation enhancement causes some effects such as the highest‐occupied molecular orbital–lowest‐unoccupied molecular orbital gap reduction and charge transfer characteristic of low‐energy vertical transitions. © 2013 Wiley Periodicals, Inc.     

A “double-zeta” type wavefunction for an organometallic: Bis-(π-allyl)nickel

A wavefunction which is of double-zeta quality at the level of the valence orbitals [based on a (11, 7, 5/8, 4/4) gaussian basis set contracted to (4, 3, 2/3, 2/2)] is reported for thebis-(π-allyl)nickel molecule. Independant SCF calculations for two ionized states substantiate the conclusion reached previously for a number of organometallics with a minimal basis set that Koopmans' theorem is not valid for these molecules, namely that the highest occupied orbital from the ground state calculation for the neutral molecule is mostly a ligand π orbital whereas the lowest ionization potential corresponds to the removal of an electron from a molecular orbital which is mostly a metal 3d orbital. The nature of the bonding inbis-(π-allyl)nickel is discussed on the basis of the possible interactions between the metal orbitals and the π orbitals of the allyl group. The interaction between the filled nonbonding π orbital of the allyl group and the empty 3d _xz orbital of the Ni atom appears responsible for most of the bonding, together with some backbonding through an interaction between the 3d x ²?y ²and 3d xyorbitals and the σ and π orbitals of the ligands. The computed value for the rotation barrier about the C-C allyl bond, 90 kcal/mole, rules out this rotation as one of the possible mechanisms which account for the equivalence of the terminal hydrogens in the proton magnetic resonance spectra of π-allyl complexes.     

Unrestricted CNDO-MO calculations. II. MnO 4 2− and CrO 4 3−

The electronic structures of the tetrahedral molecule ions MnO ₄ ^2– and CrO ₄ ^3– have been investigated within an unrestricted CNDO-MO approximation [Theoret. Chim. Acta (Berl.)20, 317 (1971)]. Calculations assuming the unpaired electron occupies the 3a ₁, 2e, and 4t2 molecular orbitals indicate that the 3a ₁ and2e orbitals have similar orbital energies and that the 4t ₂ orbital is at a higher energy. The experimentally indicated2e orbital for the unpaired electron is obtained with expanded O^1– type atomic orbitals for oxygen and valence metal orbitals of the expanded 3d and plus one ion 4p types. The metal 4s orbitals must be held to the neutral atom type. The optimum valence orbitals above with a slightly contracted 4s type metal orbitals yield the minimum total energy and places the unpaired electron in the 3a ₁ orbital. Since the contracted 4s metal orbital produces results that are not in agreement with experimental data, the method used apparently does not adequately take into account the increased electron-electron repulsions that contracted 4s orbitals produce.     

Radial moment analysis of isovalent hybridization in N2

A radial moment analysis has been performed for the Hartree–Fock molecular orbitals of the nitrogen molecule. The objective of the analysis was to determine the extent of isovalent hybridization in even and odd sigma molecular orbitals. The radial moment analysis for the LC -SCF -AO fragments of the 2σ_g, 2σ_u, and 3σ_g molecular orbitals substantiates Mulliken's earlier conjecture concerning promotion into 3s atomic orbitals for the 3σ_g molecular orbital. The concept of free isovalent hybridization is discussed in terms of the atomic orbital shape defined by the extracted moments.     

Parallel, linear-scaling building-block and embedding method based on localized orbitals and orbital-specific basis sets

We present a linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any localization method of choice and on the use of orbital-specific basis sets. The full set of localized orbitals of a large molecule is seen as an orbital mosaic where each tessera is made of only a few of them. The orbital tesserae are computed out of a set of embedded cluster pseudoeigenvalue coupled equations which are solved in a building-block self-consistent fashion. In each iteration, the embedded cluster equations are solved independently of each other and, as a result, the method is parallel at a high level of the calculation. In addition to full system calculations, the method enables to perform simpler, much less demanding embedded cluster calculations, where only a fraction of the localized molecular orbitals are variational while the rest is frozen, taking advantage of the transferability of the localized orbitals of a given localization method between similar molecules. Monitoring single point energy calculations of large poly(ethylene oxide) molecules and three dimensional carbon monoxide clusters using an extended Huckel Hamiltonian are presented.     

Localization measure and maximum delocalization in molecular systems

A mathematically well-defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core- and lone-pair orbitals, 2 for two-atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N-electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one-electron orbitals, characterizing in this way the localized or extended representation of the N-electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N-electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree–Fock orbitals, the Parr–Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.     

Ab initio through‐space/bond interaction analysis of the long C–C bonds in Bi(anthracene‐9,10‐dimethylene) photoisomers

The bi(anthracene‐9,10‐dimethylene) photoisomer has remarkably long C–C single bonds. To examine the lengthening of the C–C bond, we propose a novel procedure for quantitatively analyzing orbital interactions in a molecule at the level of the ab initio molecular orbital method. In this procedure, we can cut off the specific through‐space/bond interactions in a molecule by artificially increasing the absolute magnitude of the exponents in a Gaussian function. Then, the spatial orbital interactions were perfectly cut off, and, each term that makes up the total energy, that is, the nuclear–electron attractions, the electron–electron repulsions, and the nuclear–nuclear repulsions cancel each other. Several model molecules of the photoisomer were analyzed by this procedure. It was found that the orbital interaction between the p orbital on the benzene ring and the σ* orbital on the C–C bond in question, σ→σ* electron transfer through π orbital, weakens the C–C bond efficiently when these orbitals were located in the “periplanar” conformation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Bonding analysis using localized relativistic orbitals: water, the ultrarelativistic case and the heavy homologues H2X (X = Te, Po, eka-Po)

We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).     

Model study of the impact of orbital choice on the accuracy of coupled-cluster energies. II. Valence-universal coupled-cluster method

The impact of the choice of molecular orbital sets on the results of the valence-universal coupled cluster method involving up to three-body amplitudes (VU-CCSDT) was studied for the H4 model. This model offers a straightforward way of representing all possible symmetry-adapted orbitals. Moreover, the degree of quasi-degeneracy of its lowest ¹A₁ states can be varied over a wide range by changing its geometry. Calculations were performed both for 13 sets of standard quantum chemical orbitals and for a vast variety of nonstandard orbital sets defined by nodes of a two-dimensional orbital grid. The performance of various standard orbital sets in VU-CCSDT calculations is compared. It is also documented that for every quasi-degeneracy region there exist nonstandard orbital sets which allow one to obtain more accurate VU-CCSDT energies than the standard orbital sets. In an attempt to provide a general interpretation for some of the alternative orbital sets, we defined a set of orbitals which maximize the proximity of the model and target spaces—maximum proximity orbitals (MPO). It is demonstrated that outside the strong quasi-degeneracy region the energies obtained for the VU-CCSDT approach based on the MPOs are more accurate than for the standard orbital sets. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 221–237, 1998     

Orbital Interaction and the Mulliken-Walsh Diagram for AH2 Systems

We define θ- (or R-) bonding (or antibonding) character of the molecular orbitals according to the slopes of the orbital energy curves when the internuclear angle (or internuclear distance) is varied. So far the slope of the orbital curve has only been accounted for by the qualitative argument based on two factors: the orbital overlap and the s-p mixing. We employ the bond orbitals instead of the usual atomic orbitals as the basis set to analysis the character of the molecular orbitals. The Fock matrix in the bond orbital basis can then quantitatively account for the effects of both the overlap and s-p mixing factors. Our analysis also show that a third factor, the orbital interaction, is essential to account for both the “typical” and “abnormal” behavior of the slopes.     

Scanning‐Tunneling‐Spectroscopy‐Directed Design of Tailored Deep‐Blue Emitters

Frontier molecular orbitals can be visualized and selectively set to achieve blue phosphorescent metal complexes. For this purpose, the HOMOs and LUMOs of tridentate Pt^II complexes were measured using scanning tunneling microscopy and spectroscopy. The introduction of electron‐accepting or ‐donating moieties enables independent tuning of the frontier orbital energies, and the measured HOMO–LUMO gaps are reproduced by DFT calculations. The energy gaps correlate with the measured and the calculated energies of the emissive triplet states and the experimental luminescence wavelengths. This synergetic interplay between synthesis, microscopy, and spectroscopy enabled the design and realization of a deep‐blue triplet emitter. Finding and tuning the electronic “set screws” at molecular level constitutes a useful experimental method towards an in‐depth understanding and rational design of optoelectronic materials with tailored excited state energies and defined frontier‐orbital properties.     

Orbital phase in Suzuki–Miyaura cross-coupling reactions

We investigated the electronic structures of the transition states of the oxidative addition, transmetalation, and reductive elimination steps in the catalytic cycle of the title reaction. The frontier orbital theory was surprisingly found to be applicable whereas any d orbitals of transition metals can be a main component of frontier orbitals because of their close energies. Visualizing the actually calculated HOMO and LUMO of the two parts of the transition structure of each step clearly demonstrated their orbital phase matching in favor of overlapping. The HOMO for the transmetalation step suggests that electron-donating ability of the carbon–metal bond of organometallic compounds (RMX) could control the reactivities of related cross-coupling reactions. The energies of the molecular orbitals having large amplitudes of the C–M bonding orbitals of RMX explain why the Suzuki–Miyaura cross-coupling reaction needs a base while the Kumada–Tamao and Negishi reactions take place without any bases.     

Application of combined Hartree–Fock–Roothaan theory to molecules with arbitrary number of closed and open shells

In this study, the applicability of the combined Hartree–Fock–Roothaan (CHFR) theory of atomic-molecular and nuclear systems (Guseinov, J Math Chem 42:177, 2007) to the molecules is demonstrated using minimal basis set of Slater type orbitals (STO). As an example of application of CHFR theory, the calculations have been performed for the ground state of electronic configuration of methylene molecule CH ₂ which has two open shells. The results of computer calculations for the orbital, kinetic and total energies, linear combination coefficients of symmetrized molecular orbitals and virial ratios are presented.     

Use of Electron-Density Plots in Applied Quantum Chemistry

The uses in applied quantum chemistry of computer-produced three-dimensional diagrams of electron-density distributions are discussed. The two major catagories of such diagrams are contrasted; and advantages are described for plots showing as the third dimension the point-by-point electron density in a cross-sectional cut (corresponding to the other two dimensions) through a molecule. Examples are presented to show how these plots may be used (1) to assess the adequacies of a given mathematical representation employed in the calculation of a wavefunction, (2) to clarify the interrelationship between an individual molecular orbital and the atomic orbitals of the constituent atoms, as well as (3) to explain the canonical set of molecular orbitals of any selected molecule. Furthermore these plots serve(4) to demonstrate clearly a replication of key characteristics between certain molecular orbitals in different molecules. These examples are accompanied by others which indicate how the electron-density plots may be used(5) to understand and clarify accepted chemical dogma. Finally, the possibility is discussed of employing quantum calculations on a wider scale so as to be of value in the more practical aspects of chemistry.     

Large-scale RPA calculations of chiroptical properties of organic molecules: Program RPAC

The computational considerations involved in calculating ordinary and rotatory intensities and electronic excitation energies in the random phase approximation (RPA ) are examined. We employ a localized orbital formulation in order to analyze the results in terms of local and charge-transfer excitations. Occupied orbitals are localized by the Foster–Boys procedure. The virtual space is transformed into a localized “valence” set that maximizes dipole strengths with the occupied counterparts, and a delocalized remainder. The two-electron integral transformation is performed with an efficient algorithm, based on Diercksen's, that generates only the particle–hole-type integrals required in the RPA . The lowest solutions of the RPA equations are obtained iteratively using a modification of the Davidson-Liu simultaneous vector expansion method. This allows the inclusion of the entire set of particle–hole states supported by a basis set of up to 102 orbitals. Calculations at this level give better excitation energies and intensities than SDCI methods, at substantial savings in computational effort. Comparative timings, computed results and analysis in terms of localized orbitals are given for planar and distorted ethylene using extended atomic orbital bases including diffuse functions. The results for planar ethylene are in excellent agreement with experiment.