Molecular tight-binding method. I. Many-electron method for hole bands of molecular crystals

A method for calculating ab initio electronic excitation energies of molecular crystals, based on a many-electron tight-binding approximation, is described. The method follows Frenkel's model for excitons and allows a many-electron treatment of the band-structure problem of molecular crystals. The case of hole bands is studied in detail and various versions of the method are considered. A computational scheme is proposed, in which approximate correlation corrections to the HFR matrix equations of the one-electron LCMO method are calculated. The main effects contributing to these corrections are the effect of relaxation of a molecular ion, the effect of intramolecular electronic-correlation change, and the effect of polarization of the remaining molecules in a crystal. The method developed in the present paper is applied to calculation of the hole bands of the HCP helium crystal.     

Intra‐ and intermolecular interactions in crystals of polar molecules. A study by the mixed quantum mechanical/molecular mechanical SCMP‐NDDO method

Stabilization energies of crystals of polar molecules were calculated with the recently developed NDDO‐SCMP method that determines the wave function of a subunit embedded in the symmetrical environment constituted by the copies of the subunit. The total stabilization energies were decomposed into four components. The deformation energy is the difference between the energy of the molecule in the geometries adopted in the crystal on the one hand, and in vacuo, on the other hand. Further energy components are derived from the molecular geometry found in the crystal phase. The electrostatic component is the interaction energy of the molecule with the crystal field, corresponding to the charge distribution obtained in vacuo. The polarization component is the energy lowering resulted in the self‐consistent optimization of the wave function in the crystal field. The rest of the stabilization energy is attributed to the dispersion–repulsion component, and is calculated from an empirical potential function. The major novelty of this decomposition scheme is the introduction of the deformation energy. It requires the optimization of the structural parameters, including the molecular geometry, the intermolecular coordinates, and the cell parameters of the crystal. The optimization is performed using the recently implemented forces in the SCMP‐NDDO method, and this new feature is discussed in detail. The calculation of the deformation energy is particularly important to obtain stabilization energies for crystals in which the molecular geometry differs considerably from that corresponding to the energy minimum of the isolated molecule. As an example, crystals of diastereoisomeric salts are investigated. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1679–1690, 2001     

Excess-Electron Attachment and Ionization of Aqueous Uridine Monophosphate Anion

We applied quantum mechanics/classical mechanics simulations to study excess-electron attachment and ionization of uridine monophosphate anion (dUMP\begin{document}$^-$\end{document}) in explicit aqueous solutions. We calculated vertical electron affinities (VEAs), adiabatic electron affinities (AEAs), vertical detachment energies (VDEs), vertical ionization energies (VIEs), and adiabatic ionization energies (AIEs) of the 40 structures obtained from molecular dynamic trajectory. The excess-electron and hole distributions were analyzed in electron attachment and ionization of aqueous dUMP\begin{document}$^-$\end{document}. The converged mean VEA (-0.31 eV) and AEA (2.13 eV) suggest that excess-electron can easily attach to dUMP\begin{document}$^-$\end{document}. The mean vertical (-0.50 e) and adiabatic (-0.62 e) excess-electron on uracil reveal that main excess-electrons are localized on nucleobases at the most snapshots. The distributions at several special snapshots demonstrate the excess-electron delocalization over nucleobases/ribose or ribose/phosphate group after the structural relaxations of dUMP\begin{document}$^{2-}$\end{document} dianion. The VDE value (2.78 eV) indicates that dUMP\begin{document}$^{2-}$\end{document} dianion could be very stable. Moreover, the mean VIE is 8.13 eV which is in agreement with the previous calculation using solvation model. The hole distributions on uracil suggest that the nucleobases are easily ionized after the irradiation of high-energy rays. In vertical ionizations, the holes would be delocalized over uracil and ribose at several snapshots. Observing the adiabatic hole distributions, it can be found that electrons on phosphate group and holes on nucleobases can be transferred to ribose at the special snapshots in the structural relaxation of neutral species.     

Nonempirical Description of the Atmospherically Important Anionic Species. I. Water Cluster Anions

Water cluster anions, comprising up to 20 molecules, are simulated at the second-order unrestricted Møller–Plesset perturbation theory level with 6-31++G** basis set augmented with a floating center of 8 s diffuse functions. Interface structures composed of two to four chainlike or cyclic subclusters found to be most stable among anions of the same molecular size are shown to serve as a reliable restricted model of the hydrated electron. The calculated values of the adiabatic electron affinity of neutral clusters and the vertical energies of electron detachment from anions fit in with n ^–1/3 dependences that provide the corresponding estimates of the bulk water or ice specimens. The radius of a circumsphere containing about 85% of the excess electron density is treated as an effective radius of the excess electron and found to approach 2.5 Å as the size of cluster increases to infinity.     

Dry excess electrons in room-temperature ionic liquids

In this article, we describe general trends to be expected at short times when an excess electron is generated or injected in different room-temperature ionic liquids (RTILs). Perhaps surprisingly, the excess electron does not localize systematically on the positively charged cations. Rather, the excess charge localization pattern is determined by the cation and anion HOMO/LUMO gaps and, more importantly, by their relative LUMO alignments. As revealed by experiments, the short-time (ps/ns) transient UV spectrum of excess electrons in RTILs is often characterized by two bands, a broad band at low energies (above 1000 nm) and another weaker band at higher energies (around 400 nm). Our calculations show that the dry or presolvated electron spectrum (fs) also has two similar features. The broad band at low energies is due to transitions between electronic states with similar character on ions of the same class but in different locations of the liquid. The lower-intensity band at higher energies is due to transitions in which the electron is promoted to electronic states of different character, in some cases on counterions. Depending on the chemical nature of the RTIL, and especially on the anions, excess electrons can localize on cations or anions. Our findings hint at possible design strategies for controlling electron localization, where electron transfer or transport across species can be facilitated or blocked depending on the alignment of the electronic levels of the individual species.     

A Continuum Reaction Field Theory of Polarizable, Nondipolar, Quadrupolar Solvents: Ab Initio Study of Equilibrium Solvation in Benzene

A continuum theory to describe solvation in nondipolar quadrupolar solvents is developed by accounting for electronic polarizability. A general Hamiltonian for a solute–solvent system in an arbitrary nonequilibrium configuration is obtained in terms of two field variables—densities of the solvent quadrupole and induced dipole moments. Equilibrium solvation is studied by optimizing this Hamiltonian with account of cavity boundaries. As an application, electronic structures and free energies of small molecules in benzene are examined with ab initio methods. Solvation stabilization due to solvent quadrupole moments is found to be substantial; for the solutes considered here, it is comparable to and often in excess of that arising from solvent-induced dipole moments.     

Time-resolved electron detachment imaging of the I- channel in I2Br- photodissociation

The evolution of the I(-) channel in I(2)Br(-) photodissociation is examined using time-resolved negative-ion photoelectron imaging spectroscopy. The 388 nm photodetachment images obtained at variable delays following 388 nm excitation reveal the transformation of the excess electron from that belonging to an excited trihalide anion to that occupying an atomic orbital localized on the I(-) fragment. With increasing pump-probe delay, the corresponding photoelectron band narrows on a approximately 300 fs time scale. This trend is attributed to the localization of the excess-electron wave function on the atomic-anion fragment and the establishment of the fragment's electronic identity. The corresponding band position drifts towards larger electron kinetic energies on a significantly longer, approximately 1 ps, time scale. The gradual spectral shift is attributed to exit-channel interactions affecting the photodetachment energetics, as well as the photoelectron anisotropy. The time-resolved angular distributions are analyzed and found consistent with the formation of the asymptotic I(-) fragment.     

Resonance energies of large conjugated hydrocarbons by a statistical method

We developed a theoretical method for studying the aromatic stability of large molecules, molecules having a dozen and more fused benzene rings. Such molecules have so far often been outside the domain of theoretical studies. Combining the statistical approach and a particular graph theoretical analysis, it is possible to derive the expressions for molecular resonance energy for molecules of any size. The basis of the method is enumeration of conjugated circuits in random Kekulé valence structures. The method has been applied to evaluation of the resonance energies of conjugated hydrocarbons having about a dozen fused benzene rings. The approach consists of (1) construction of random Kekulé valence structures, (2) enumeration of conjugated circuits within the generated random valence structures, and (3) application of standard statistical analysis to a sufficiently large sample of structures. The construction of random valence forms is nontrivial, and some problems in generating random structures are discussed. The random Kekulé valence structures allow one not only to obtain the expression for molecular resonance energies (RE ) and numerical estimates for RE , but also they provide the basis for discussion of local molecular features, such as ring characterization and Pauling bond orders.     

Soft Coulomb hole method applied to molecules

The soft Coulomb hole method introduces a perturbation operator, defined by ?e/r₁₂ to take into account electron correlation effects, where ω represents the width of the Coulomb hole. A new parametrization for the soft Coulomb hole operator is presented with the purpose of obtaining better molecular geometries than those resulting from Hartree–Fock calculations, as well as correlation energies. The 12 parameters included in ω were determined for a reference set of 12 molecules and applied to a large set of molecules (38 homo‐ and heteronuclear diatomic molecules, and 37 small and medium‐size molecules). For these systems, the optimized geometries were compared with experimental values; correlation energies were compared with results of the MP2, B3LYP, and Gaussian 3 approach. On average, molecular geometries are better than the Hartree–Fock values, and correlation energies yield results halfway between MP2 and B3LYP. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The one-particle Green's function method in the Dirac-Hartree-Fock framework. I. Second-order valence ionization energies of Ne through Xe

The one-particle Green's function theory in its various implementations is a well-established many-body approach for the calculation of electron ionization and attachment energies in atoms and molecules. In order to describe not only scalar-relativistic effects but also spin-orbit splitting on an equal footing an embedding of this theory in the four-component framework was carried out and fully relativistic ionization energies of the noble gas atoms Ne through Xe were calculated using the second-order algebraic diagrammatic construction [ADC2] approximation scheme. Comparison with nonrelativistic ADC2 results and experimental data was made.     

Computer simulation of the shape of absorption bands in electronic spectra ofJ-aggregates

The shape of absorption bands of aggregates formed by two, four, and nine molecules of a polymethine dye was calculated by the Monte-Carlo method. The energy of interaction of the molecules in the ground state was simulated using atom-atom potentials, and the energies of interaction between dipole moments of electronic transitions of the monomers were estimated by quantum-chemical methods. In the dimer aggregate the dipole moments of the electronic transitions in the monomers interact weakly; therefore, the electron absorption spectrum should be similar to that of the monomer. On going from the dimer to the aggregates consisting of four and nine monomers, the relative positions of monomers change and this, in turn, increases the energy of interaction between the dipole moments of their electronic transitions, resulting in a red shift characteristic ofJ-aggregates and narrowing of the absorption bands. Translated fromIzvestiya Akademii Nauk Seriya Khimicheskaya. No. 1, pp. 67–69, January, 1997.     

Ferromagnetic vs. nonmagnetic phases of 2‐D Wigner electron crystal

The ferromagnetic and nonmagnetic phases of 2‐D Wigner electron crystal are investigated using a localized representation for the electrons. The ground‐state energies of ferromagnetic and nonmagnetic phases of 2‐D Wigner electron crystal are computed in the range of r_s = 10–200. The low density favorable for Wigner crystallization is found to be 2.85 × 10¹³ e cm^?2 for ferromagnetic phase and 5.07 × 10¹³ e cm^?2 for the nonmagnetic phase of 2‐D Wigner electron crystal. For the given structure, the ground‐state energies of ferromagnetic and nonmagnetic phases are compared. It is found that the energy of the ferromagnetic phase is less than that of the nonmagnetic phase of the 2‐D Wigner electron crystal. Also, the results are compared with various experimental and theoretical works and it is found that our results are in good agreement with the experimental and other theoretical results for the 2‐D Wigner electron crystal. The structure‐dependent Wannier functions, which give proper localized representation for Wigner electrons, are employed in the calculation. The role of correlation energy is suitably taken into account. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Evolutionary chemical space exploration for functional materials: computational organic semiconductor discovery

Computational methods, including crystal structure and property prediction, have the potential to accelerate the materials discovery process by enabling structure prediction and screening of possible molecular building blocks prior to their synthesis. However, the discovery of new functional molecular materials is still limited by the need to identify promising molecules from a vast chemical space. We describe an evolutionary method which explores a user specified region of chemical space to identify promising molecules, which are subsequently evaluated using crystal structure prediction. We demonstrate the methods for the exploration of aza-substituted pentacenes with the aim of finding small molecule organic semiconductors with high charge carrier mobilities, where the space of possible substitution patterns is too large to exhaustively search using a high throughput approach. The method efficiently explores this large space, typically requiring calculations on only ∼1% of molecules during a search. The results reveal two promising structural motifs: aza-substituted naphtho[1,2-a]anthracenes with reorganisation energies as low as pentacene and a series of pyridazine-based molecules having both low reorganisation energies and high electron affinities.

Evolutionary optimisation and crystal structure prediction are used to explore chemical space for molecular organic semiconductors.     

Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part II. Accurate energy minimization

A method is described to perform ab initio energy minimization for crystals of flexible molecules. The intramolecular energies and forces are obtained directly from ab initio calculations, whereas the intermolecular contributions follow from a potential that had been parameterized earlier on highly accurate quantum‐chemical calculations. Glycol and glycerol were studied exhaustively as prototypes. Lists of hypothetical crystal structures were generated using an empirical force field, after which ab initio energy minimizations were performed for a few hundreds of these. The experimental crystal structures were found among the structures with lowest energy, provided that sufficiently large basis sets were used. Moreover, their crystal geometries were well reproduced. This approach enables a systematic comparison between the merits of force fields at various levels of sophistication. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 805–815, 2001     

Investigation of excess-electron transfer in DNA double-duplex systems allows estimation of absolute excess-electron transfer and CPD cleavage rates

To investigate the parameters and rates that determine excess-electron transfer processes in DNA duplexes, we developed a DNA double-duplex system containing a reduced and deprotonated flavin donor at the junction of two duplexes with either the same or different electron acceptors in the individual duplex substructures. This model system allows us to bring the two electron acceptors in the duplex substructures into direct competition for injected electrons and this enables us to decipher how the kind of acceptor influences the transfer data. Measurements with the electron acceptors 8-bromo-dA (BrdA), 8-bromo-dG (BrdG), 5-bromo-dU (BrdU), and a cyclobutane pyrimidine dimer, which is a UV-induced DNA lesion, allowed us to obtain directly the maximum overall reaction rates of these acceptors and especially of the T=T dimer with the injected electrons in the duplex. In line with previous observations, we detected that the overall dimer cleavage rate is about one order of magnitude slower than the debromination of BrdU. Furthermore, we present a more detailed explanation of why sequence dependence cannot be observed when a T=T dimer is used as the acceptor and we estimate the absolute excess-electron hopping rates.     

Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at R_int = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 Wiley Periodicals, Inc.     

A charge-conserving approximation method for ab initio calculations

A new method is presented for approximate ab initio calculations in quantum chemistry. It is called CCAM (charge conserving approximation method). The calculation method does not include the use of empirical parameters. We use Slater type orbitals as basis set, replacing STO's by STO-2G functions to evaluate three- and four-center integrals and making the STO-2G two-orbital charge distributions have the same total charge as STO. The results are presented for test calculations on five molecules. In view of these results, CCAM is better than ab initio calculations over STO-6G in the results on total energies, kinetic energies and occupied orbital energies. In atomic populations, dipole moments and unoccupied orbital energies, CCAM is also satisfactory. We estimate that CCAM would be as fast as ab initio calculations over STO-2G in evaluating molecular integrals.     

A theoretical investigation of electron correlation and relaxation in organometallic polymers

The importance of many-body interactions beyond the mean-field approximation of the Hartree–Fock (HF ) self-consistent-field crystal orbital formalism is analyzed in one-dimensional (lD) transition-metal (3d) polymers with extended organic π ligands. The correlation energies are expressed in a quasiparticle picture. They are divided into long-range contributions that are coordinated with the basis of spatially uncorrelated Bloch orbitals and into short-range correlations derived for local rearrangement processes that are described in terms of a one-electron basis which breaks the translational symmetry of the lD system. Both contributions (long-range and short-range correlations) are fragmented into elements of physical significance (hole and electron self-energies for the former interactions; relaxation, pair-relaxation and pairremoval terms for the local virtual excitations). The magnitude of these elements is analyzed as a function of the characters of the one-electron states in the HF bands, the occupation patterns at the 3d centers, the available particle and hole channels in the elementary fluctuations and the energies and shapes of the various bands. The broad spectrum of possible amplifications and compensations leading to the quasiparticle shifts in metallomacrocycles is discussed. The different mechanisms to change the dispersions and to modify the width of the ?(k) curves are studied. It is shown that electron correlation and relaxation in transition-metal polymers can lead even to a broadening of the energy bands. This behavior is in contrast to the influence of many-body effects in simpler homogeneous materials where electron correlation is in any case accompanied by a narrowing of the dispersions (i.e., detraction of the group velocities of particles and holes). Possible modifications in the shapes of the one-particle curves and the quasiparticle bands are also considered in the text [transition from a “normal ?(k) dispersion” to an energy band with a negative slope as a result of electron correlation]. Simplified formulas are derived that allow for a rough assessment of the various correction terms even in structurally complicated transition-metal stacks with extended organic ligands. The approximate relations are used to correct the HF band structures of complex onedimensional metallomacrocycles as well as simpler crystalline materials by means of the quasiparticle approximation.     

Size‐guided multi‐seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size‐guided multi‐seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest‐energy configurations of the cluster with n − 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.     

Polaron nature of critical size of ammonia cluster

A consistent polaron model is shown to result in a critical size of a cluster made of polar molecules. Over this size the existence of a bound state of an excess electron inside the cluster is possible. In the case of an ammonia cluster composed of n molecules the theory predicts an appearance of a stable polaron state of excess electron at n = 35. This threshold value and photodetachment energies are in a good agreement with existing experimental data. The theory predicts also metastable states of the ammonia cluster anions for 21 ≤ n < 35.