Intermolecular correlation in a new approximation scheme

It is demonstrated for a spin-free, nonrelativistic, complete molecular Hamiltonian that there is an optimal solution to the separation of electronic and nuclear motions. The adiabatic approximation is obtained as a special limiting case. A fruitful interpretation of intermolecular correlation results from the assumption that such correlation involves the degeneracy of a molecular-energy state of one molecule with that of another chemical species, e.g., cubane and cyclooctatetraene. As a consequence, rigorous relationships are established for the influence of nodal patterns of the electronic functions on intermolecular correlation. Also derived are stringent symmetry rules which both electronic and nuclear functions involved in the correlation must obey. Throughout the treatment is a many-electron one.     

Electron Correlations for Adiabatic Electrochemical Electron Transfer Reactions in a Model for an Electrode with an Infinitely Wide Conduction Band

Fresh general relationships for adiabatic free-energy surfaces (AFES) and corresponding diagrams of kinetic modes for adiabatic electrochemical electron transfer reactions are derived in the framework of an exactly solvable model for a metallic electrode with an infinitely wide conduction band. The model is a limiting case of the Anderson model applicable to the sp metals. In contrast to earlier studies of adiabatic reactions in a model for an electrode with an infinitely wide conduction band, this work accounts for the electron–electron correlation effects exactly. As an illustration, an AFES is calculated and a diagram of kinetic modes is constructed for a special case corresponding to the equilibrium electrode potential of a two-electron reaction. The exact AFES is compared with the AFES computed in the Hartree–Fock approximation and a spinless model. The correlation effects are shown to play a substantial role and lead to a considerable decrease in the activation free energy.     

Linear tension of two-dimensional drops on planar adsorbent faces

The size dependence of the linear tension of round two-dimensional equilibrium drops in the vapor phase on a homogeneous surface of an adsorbent is studied at the pressure of saturated two-dimensional vapor. The calculations are based on the lattice gas model in a quasi-chemical approximation with allowance for the correlation effects of the nearest interacting molecules. Methods for calculating linear tension using the equimolecular reference line are considered. Temperature dependences of the linear tension are studied for metastable and equilibrium drops. It is found that the differences between the thermodynamic properties of two types of drops are slight over a wide range of variation in drop radii.     

Viscoelastic behavior of an amorphous polymer under oscillations of large amplitude

The influence of periodic shear deformation and steady flow on a typical amorphous polymer is discussed. Forced sinusoidal vibrations were applied and the complex viscosity was determined. The action of a vibration of finite amplitude is equivalent to steady flow with a definite finite shear rate. Both processes cause truncation of the long-time part of the relaxation specturm. It may be accepted to a first approximation that the long-time boundary of the remaining part of the relaxation spectrum conforms to the long-time part of the initial spectrum, even if the plateau region of the spectrum is truncated. The concept of limiting truncation of the short-time part of the spectrum is introduced, this corresponding to the minimum absolute value of the complex viscosity versus reduced frequency and the lowest values of the dynamic and apparent viscosities. With an approximate representation of the relaxation spectrum, calculations were made of the maximum values of the viscosity and the coefficient relating the first difference of normal stresses to the square of the shear rate, and also of the apparent viscosity and normal stresses as functions of the shear rate. The calculated values are compared with experimental measurements, and it is shown that the correlation of the apparent viscosity and the absolute value of the complex viscosity is distributed at high frequencies, being superseded by a correlation between the apparent and dynamic viscosities.     

Correlation effects on hydrogen-bond potentials. SCF Cl calculations for the systems HF−2 and H3O−2

The effects of neglecting electron correlation in the Hartree-Fock approximation have been investigated for selected properties of two strongly hydrogen-bonded systems. Accounting for correlation will substantially lower and, in some cases, remove barriers for proton transfer which have been obtained using the Hartree-Fock approximation. As a consequence, the asymmetric hydrogen-bond stretching frequencies in HF^?₂ are found to increase when correlation is included in the calculations, contrary to the case for more regular stretching frequencies. The hydrogen-bond energies of the two systems are found to be rather insensitive to correlation effects.     

Theory of the excitation spectrum of nondiagonal disordered systems

The spectrum of a two-component solid solution with a nondiagonal disorder is studied in the framework of the average T matrix method. For a one-dimensional system in the nearest-neighbor approximation the criteria for the system parameters are given such that at an in-band resonance, one or two “impurity bands” may be realized, and the corresponding model calculation is performed. In the single-site approximation an expression of the self-energy part of a nondiagonal disordered system Green's function is found taking into account multiple occupancy corrections. The possibility of using it to describe a disordered system excitation spectrum and the calculation of state density moments are discussed.     

Effect of side-chain disorder on the electronic structure of proteins

The influence of side-chain disorder on the electronic structure of proteins has been investigated in the case of polypeptides containing two or three different amino acid residues. It has been found that due to the different potentials of different side-chain groups, the original valence and conduction bands of the homopolypeptides are split into narrow bands. The comparison of the densities of electronic states in simple homopolypeptides and in composite polymers shows that new forbidden regions in the energy spectrum of proteins may develop. The consequences of these effects for the semiconductive properties of proteins are discussed.     

Electron correlation effects in the adiabatic charge transfer reactions at the metal/polar liquid interface

New simple expressions for average number of electrons in the valence orbital of a reacting ion and the charge susceptibility are obtained that allow one to calculate adiabatic free energy surfaces (AFES) and corresponding kinetic regime diagrams (KRD) for adiabatic processes of electron transfer from the ion, located in a polar liquid, to a metal within the framework of the exactly solvable (in the limit T-->0) model of the metal with the infinitely wide conduction band. This model represents one of limiting cases of the Anderson model that may be applied to s-p metals. Unlike previous studies of the adiabatic reactions in the model of the metal with the infinitely wide conduction band, the present work takes into account the electron-electron correlation effects in an exact manner. General results are illustrated with KRD which determine the regions of the physical parameters of the system corresponding to various types of electron transfer processes. AFES are calculated for some typical parameters sets. The exact AFES are compared with those calculated within the Hartree-Fock approximation. It is shown that the correlation effects are of importance and results not only in a considerable decrease of the activation free energy but also to qualitatively different shapes of AFES in some regions of the system parameters.     

Electron-nuclear correlations for photo-induced dynamics in molecular dimers

Ultrafast photoinduced dynamics of electronic excitation in molecular dimers is drastically affected by the dynamic reorganization of inter- and intra- molecular nuclear configuration modeled by a quantized nuclear degree of freedom. The dynamics of the electronic population and nuclear coherence is analyzed by solving the chain of coupled differential equations for population inversion, electron-vibrational correlation, etc. Intriguing results are obtained in the approximation of a small change of the nuclear equilibrium upon photoexcitation. In the limiting case of resonance between the electronic energy gap and the frequency of the nuclear mode these results are justified by comparison to the exactly solvable Jaynes-Cummings model. It is found that the photoinduced processes in the model dimer are arranged according to their time scales: (i) Fast scale of nuclear motion, (ii) intermediate scale of dynamical redistribution of electronic population between excited states as well as growth and dynamics of electron-nuclear correlation, (iii) slow scale of electronic population approach to the quasi-equilibrium distribution, decay of electron-nuclear correlation, and decrease of the amplitude of mean coordinate oscillation. The latter processes are accompanied by a noticeable growth of the nuclear coordinate dispersion associated with the overall nuclear wave packet width. The demonstrated quantum relaxation features of the photoinduced vibronic dynamics in molecular dimers are obtained by a simple method, applicable to systems with many degrees of freedom.     

Comment on ab initio ground state potential energy surfaces for anions of polar molecules

Within the context of the Born-Oppenheimer approximation all molecules with dipole moments greater than 1.625 D have stable anions. The applicability of the Hartree-Fock approximation to describe the stability of such anions is discussed. It is concluded that correlation effects are relatively more important for molecules such as HF and HCN than the more polar alkali halides.     

Nomographische und numerische Korrekturen für trübungsbedingte Untergrundabsorption bei spektralphotometrischen Gehaltsbestimmungen

It is shown by the example of cyanomethaemoglobin in agreement with the literature, that light absorption of protein solutions due to turbidity is—because of the size of the particles—only in the limiting case dependent on the Rayleigh Law. The validity to correct with an exponential formula for absorption due to turbidity is confirmed. Relations are derived, permitting to correct for background absorption by measuring the sample at three wavelengths without plotting: one nomographic method without neglections, an iterative numerical method and a linear approximation sufficiently accurate. These methods are universally applicable.     

Nonadiabatic effects in the two-dimensional infrared spectra of peptides: application to alanine dipeptide

A method of simulating two-dimensional infrared spectra accounting for nonadiabatic effects is presented. The method is applied to the amide I modes of a dipeptide. The information necessary to construct the time-dependent Hamiltonian for the system is extracted from molecular dynamics simulations using a recently published ab initio-based model. It is shown that the linear absorption spectrum agrees with experiment only if the nonadiabatic effects are accounted for. The two-dimensional infrared spectrum is predicted for a range of mixing times. It is shown that population transfer between the amide I site vibrations affects the anisotropy at longer mixing times. It is also demonstrated that the population transfer can, to a good approximation, be extracted from the simulated spectra using a procedure that should also be applicable to experimental spectra.     

Relationship between phonon damping and pure dephasing of localized electronic excitations

Effects of quadratic electron—phonon interaction on the zero-phonon line shape of impurity-ion electronic transitions in crystals and on the spectrum of lattice phonons are investigated. Both subsystems (impurity ion and phonons) are treated on an equal fooling, employing the method of double-time thermal Green functions in the random-phase approximation. It is shown that in the case of weak dephasing due to destructive interference effects, a relationship can be established between the pure-dephasing rate of the electronic excitation and the temperature-dependent part of the electron—phonon-limited phonon damping. The phonon linewidth is shown to decrease to a lesser extent than the electronic linewidth when interference effects become enhanced, thus providing information on the dynamical broadening processes even if the electronic pure-dephasing width is too small to be observed.     

Electronic structure and hyperpolarizability of some conjugated molecules in excited states

For the examples of aromatic and antiaromatic five-membered heterocycles, the static electronic polarizabilities and hyperpolarizabilities are determined in the ground and first singlet- and triplet-excited electronic states. The theoretical calculations are carried out in the SOS formalism and the correlation effects are taken into account using all mono- and biexcited configuration in the PPP approximation. It is shown that the singlet excitation of the molecules for the antiaromatic case is connected to an significant decrease of both polarizabilities and hyperpolarizabilities. Their values are discussed in terms of the index of average bond-order alternation for the ground and excited states and the localization of the electronic transitions in the molecules. © 1993 John Wiley & Sons, Inc.     

星型高分子共混体系的相平衡、相分离和相界面的 统计力学理论

在平均场近似下求得了星型高分子共混体系的混合自由能及其相分离动力学方程。本文的理论结果表明,型高分子共混体系与线型高分子共混体系相比具有更快的相分离速度。而且,因其相界面张力较低,体系较易形成更多的相界面,浓度涨落的临界波矢也更大。除此之外,由于在相同分子量的条件下星型高分子的尺寸要小,因此其相界面更窄,当星型高分子的臂数为1或2时,所有结果均合理地还原到熟知的线型高分子共混体系的结果。因此,本文的结果具有更大的普遍性。     

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.     

Dynamical mean-field theory for molecules and nanostructures

Dynamical mean-field theory (DMFT) has established itself as a reliable and well-controlled approximation to study correlation effects in bulk solids and also two-dimensional systems. In combination with standard density-functional theory (DFT), it has been successfully applied to study materials in which localized electronic states play an important role. It was recently shown that this approach can also be successfully applied to study correlation effects in nanostructures. Here, we provide some details on our recently proposed DFT+DMFT approach to study the magnetic properties of nanosystems [V. Turkowski, A. Kabir, N. Nayyar, and T. S. Rahman, J. Phys.: Condens. Matter 22, 462202 (2010)] and apply it to examine the magnetic properties of small FePt clusters. We demonstrate that DMFT produces meaningful results even for such small systems. For benchmarking and better comparison with results obtained using DFT+U, we also include the case of small Fe clusters. As in the case of bulk systems, the latter approach tends to overestimate correlation effects in nanostructures. Finally, we discuss possible ways to further improve the nano-DFT+DMFT approximation and to extend its application to molecules and nanoparticles on substrates and to nonequilibrium phenomena.     

Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3

Accurate modeling of optical spectra requires careful treatment of the molecular structures and vibronic, environmental, and thermal contributions. The accuracy of the computational methods used to simulate absorption spectra is limited by their ability to account for all the factors that affect the spectral shapes and energetics. The ensemble-based approaches are widely used to model the absorption spectra of molecules in the condensed-phase, and their performance is system dependent. The Franck–Condon approach is suitable for simulating high resolution spectra of rigid systems, and its accuracy is limited mainly by the harmonic approximation. In this work, the absorption spectrum of the widely used cyanine Cy3 is simulated using the ensemble approach via classical and quantum sampling, as well as, the Franck–Condon approach. The factors limiting the ensemble approaches, including the sampling and force field effects, are tested, while the vertical and adiabatic harmonic approximations of the Franck–Condon approach are also systematically examined. Our results show that all the vertical methods, including the ensemble approach, are not suitable to model the absorption spectrum of Cy3, and recommend the adiabatic methods as suitable approaches for the modeling of spectra with strong vibronic contributions. We find that the thermal effects, the low frequency modes, and the simultaneous vibrational excitations have prominent contributions to the Cy3 spectrum. The inclusion of the solvent stabilizes the energetics significantly, while its negligible effect on the spectral shapes aligns well with the experimental observations.     

Role of the 3d orbitals of sulfur in the thiapyrylium cation

The electronic structure of the thiapyrylium cation with allowance for and neglect of the 3d orbitals of sulfur was investigated by the self-consistent field MO LCAO method within the CNDO/2 (complete neglect of differential overlap) approximation. Inclusion of the 3d AO of sulfur in the basis leads to slight redistribution of the electron density to favor equalization of the charges on the carbon atoms. A qualitative correlation of the calculated populations of the atoms with the chemical shifts of the PMR spectrum of the thiapyrylium cation was obtained.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1627–1629, December, 1976.