Showing papers in "Journal of Chemical Physics in 1984"
TL;DR: In this paper, a method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling, which can be easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints.
Abstract: In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints The influence of coupling time constants on dynamical variables is evaluated A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath
25,256 citations
TL;DR: In this article, the authors compared the canonical distribution in both momentum and coordinate space with three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 77, 63 (1983); and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983).
Abstract: Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem. Phys. 77, 63 (1983)]; and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983)] are examined analytically via calculating the equilibrium distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N−1/2 from the canonical distribution (N the number of particles). The results for the constant temperature–constant pressure ensemble are similar to the canonical ensemble case.
13,921 citations
TL;DR: In this paper, a modified basis set of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions were defined for use with the 6.31G and 6.311G basis sets.
Abstract: Standard sets of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions (f functions) are defined for use with the 6‐31G and 6‐311G basis sets. Preliminary applications of the modified basis sets to the calculation of the bond energy and hydrogenation energy of N2 illustrate that these functions can be very important in the accurate computation of reaction energies.
7,230 citations
TL;DR: In this paper, the excited electronic states of semiconductor crystallites sufficiently small (∼50 A diam) that the electronic properties differ from those of bulk materials were modeled, and an approximate formula was given for the lowest excited electronic state energy.
Abstract: We model, in an elementary way, the excited electronic states of semiconductor crystallites sufficiently small (∼50 A diam) that the electronic properties differ from those of bulk materials. In this limit the excited states and ionization processes assume a molecular‐like character. However, diffraction of bonding electrons by the periodic lattice potential remains of paramount importance in the crystallite electronic structure. Schrodinger’s equation is solved at the same level of approximation as used in the analysis of bulk crystalline electron‐hole states (Wannier excitons). Kinetic energy is treated by the effective mass approximation, and the potential energy is due to high frequency dielectric solvation by atomic core electrons. An approximate formula is given for the lowest excited electronic state energy. This expression is dependent upon bulk electronic properties, and contains no adjustable parameters. The optical f number for absorption and emission is also considered. The same model is applied to the problem of two conduction band electrons in a small crystallite, in order to understand how the redox potential of excess electrons depends upon crystallite size.
4,322 citations
TL;DR: In this article, the angular-dependent components of these potentials are represented by compact one-and two-term Gaussian expansions obtained directly from the appropriate eigenvalue equation, and energy optimized Gaussian basis set expansions of the atomic pseudo-orbitals, which have a common set of exponents for the s and p orbitals, are also presented.
Abstract: Compact effective potentials, which replace the atomic core electrons in molecular calculations, are presented for atoms in the first and second rows of the periodic table. The angular‐dependent components of these potentials are represented by compact one‐ and two‐term Gaussian expansions obtained directly from the appropriate eigenvalue equation. Energy‐optimized Gaussian basis set expansions of the atomic pseudo‐orbitals, which have a common set of exponents (shared exponents) for the s and p orbitals, are also presented. The potentials and basis sets have been used to calculate the equilibrium structures and spectroscopic properties of several molecules. The results compare extremely favorably with corresponding all‐electron calculations.
1,952 citations
TL;DR: In this article, a nonionic Nisopropylacrylamide gel was found to undergo a discontinuous phase transition by changing a solvent composition or temperature, which is an evidence for the universality of the phase transition of polymer gels.
Abstract: Nonionic N‐isopropylacrylamide gel was found to undergo a discontinuous phase transition by changing a solvent composition or temperature. The observation that polymer gel with and without charge can undergo a first order volume phase transition is an evidence for the universality of the phase transition of polymer gels.
1,490 citations
TL;DR: In this paper, a simple expression for the radial dependent damping functions for the individual dispersion coefficients C2n for arbitrary even orders 2n was derived for the well region of the atom van der Waals potential with only five essential parameters A, b, C6, C8, and C10.
Abstract: Starting from our earlier model [J. Chem. Phys. 66, 1496 (1977)] a simple expression is derived for the radial dependent damping functions for the individual dispersion coefficients C2n for arbitrary even orders 2n. The damping functions are only a function of the Born–Mayer range parameter b and thus can be applied to all systems for which this is known or can be estimated. For H(1S)–H(1S) the results are in almost perfect agreement with the very accurate recent ab initio damping functions of Koide, Meath, and Allnatt. Comparisons with less accurate previous calculations for other systems also show a satisfactory agreement. By adding a Born–Mayer repulsive term [A exp(−bR)] to the damped dispersion potential, a simple universal expression is obtained for the well region of the atom–atom van der Waals potential with only five essential parameters A, b, C6, C8, and C10. The model has been tested for the following representative systems: H2 3Σ, He2, and Ar2 as well as NaK 3Σ and LiHg, which include four che...
1,381 citations
TL;DR: In this paper, a new propagation scheme for the time dependent Schrodinger equation is based on a Chebychev polynomial expansion of the evolution operator U =exp(−iHt) combined with the Fourier method for calculating the Hamiltonian operation.
Abstract: A new propagation scheme for the time dependent Schrodinger equation is based on a Chebychev polynomial expansion of the evolution operator U=exp(−iHt). Combined with the Fourier method for calculating the Hamiltonian operation the scheme is not only extremely accurate but is up to six times more efficient than the presently used second order differencing propagation scheme.
1,329 citations
TL;DR: In this paper, the authors derived the sign of the Laplacian of the charge density ρ to the relative magnitudes of the local contributions of the potential and kinetic energy densities to their virial theorem averages.
Abstract: The theory of molecular structure determined by the gradient vector field of the charge density ρ identifies the set of atomic interactions present in a molecule. The interactions so defined are characterized in terms of the properties of the Laplacian of the charge density ∇2ρ(r). A scalar field is concentrated in those regions of space where its Laplacian is negative and depleted in those where it is positive. An expression derived from the quantum mechanical stress tensor relates the sign of the Laplacian of ρ to the relative magnitudes of the local contributions of the potential and kinetic energy densities to their virial theorem averages. By obtaining a map of those regions where ∇2ρ(r) 0. The mechanics are characterized by the relatively large value of the kinetic energy, particularly the component parallel to the interaction line. In the closed‐shell interactions, the regions of dominant potential energy contributions are separately localized within the boundaries of each of the interacting atoms or molecules. In the shared interactions, a region of low potential energy is contiguous over the basins of both of the interacting atoms. The problem of further classifying a given interaction as belonging to a bound or unbound state of a system is also considered, first from the electrostatic point of view wherein the regions of charge concentration as determined by the Laplacian of ρ are related to the forces acting on the nuclei. This is followed by and linked to a discussion of the energetics of interactions in terms of the regions of dominant potential and kinetic energy contributions to the virial as again determined by the Laplacian of ρ. The properties of the Laplacian of the electronic charge thus yield a unified view of atomic interactions, one which incorporates the understandings afforded by both the Hellmann–Feynman and virial theorems.
1,235 citations
TL;DR: In this article, the authors presented a method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure.
Abstract: We present a new method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation. The method is based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure. As an application of the method we have recomputed the free energy of the fcc hard‐sphere solid at melting. Our results agree well with the single occupancy cell results of Hoover and Ree. The major source of error is the nature of the extrapolation procedure to the thermodynamic limit. We have also computed the free energy difference between hcp and fcc hard‐sphere solids at densities close to melting. We find that this free energy difference is not significantly different from zero: −0.001<ΔF<0.002.
1,025 citations
TL;DR: In this paper, a generalized process of solvation is defined, and it is argued that the thermodynamics of this solvation process is more informative as compared with other processes suggested before, and numerical examples are presented and compared with some recently published related data.
Abstract: A generalized process of solvation is defined. It is argued that the thermodynamics of this solvation process is more informative as compared with other processes suggested before. Numerical examples are presented and compared with some recently published related data.
TL;DR: In this paper, a detailed analysis of the structural properties of the liquid farther from the surface can be understood as effects imposed by this surface structure, and the results show that the hydration structure of large hydrophobic surfaces can be very different from that of small hydrophilic molecules.
Abstract: Molecular dynamics simulations have been carried out for liquid water between flat hydrophobic surfaces. The surfaces produce density oscillations that extend at least 10 A into the liquid, and significant molecular orientational preferences that extend at least 7 A into the liquid. The liquid structure nearest the surface is characterized by ‘‘dangling’’ hydrogen bonds; i.e., a typical water molecule at the surface has one potentially hydrogen‐bonding group oriented toward the hydrophobic surface. This surface arrangement represents a balance between the tendencies of the liquid to maximize the number of hydrogen bonds on the one hand, and to maximize the packing density of the molecules on the other. A detailed analysis shows that the structural properties of the liquid farther from the surface can be understood as effects imposed by this surface structure. These results show that the hydration structure of large hydrophobic surfaces can be very different from that of small hydrophobic molecules.
TL;DR: In this paper, the authors discuss the behavior of a liquid partially wetting a solid surface, when the contact angle at equilibrium θ 0 is small, but finite, and show that there may exist two stable positions for the line, obtained by a simple graphic construction.
Abstract: We discuss the behavior of a liquid partially wetting a solid surface, when the contact angle at equilibrium θ0 is small, but finite. The solid is assumed to be either flat, but chemically heterogeneous (this in turn modulating the interfacial tensions), or rough. For weak heterogeneities, we expect no hysteresis, but the contact line becomes wiggly. For stronger heterogeneities, we first discuss the behavior of the contact line in the presence of a single, localized defect, and show that there may exist two stable positions for the line, obtained by a simple graphic construction. Hysteresis shows up when the strength of the defect is above a certain threshold. Extending this to a dilute system of defects, we obtain formulas for the ‘‘advancing’’ and ‘‘receding’’ contact angles θa, θr, in terms of the distribution of defect strength and defect sharpness. These formulas might be tested by controlled contamination of a solid surface.
TL;DR: The relationship between the actual charge and the renormalized charge by solving the Boltzmann-Poisson equation numerically in a spherical Wigner-Seitz cell was analyzed in this article.
Abstract: The interactions between charged colloidal particles with sufficient strength to cause crystallization are shown to be describable in terms of the usual Debye–Huckel approximation, but with a renormalized charge. The effective charge in general is smaller than the actual charge. We calculate the relationship between the actual charge and the renormalized charge by solving the Boltzmann–Poisson equation numerically in a spherical Wigner–Seitz cell. We then relate the numerical solutions and the effective charge to the osmotic pressure and the bulk modulus of the crystal. Our calculations also reveal that the renormalization of the added electrolyte concentration is negligible, so that the effective charge computations are useful even in the presence of salts.
TL;DR: In this article, it was shown that to obtain the (2n)th and ( 2n+1)th energy gradients, it is only necessary to solve equations of the difficulty of the nth order coupled perturbed equations for the orbital and configuration interaction (CI) parameters.
Abstract: It is shown that to obtain the (2n)th and (2n+1)th energy gradients, it is only necessary to solve equations of the difficulty of the nth order coupled perturbed equations for the orbital and configuration interaction (CI) parameters. For example, to find analytic second and third energy derivatives for CI wave functions, it is only necessary to solve the first order coupled perturbed equations and some related equations, for the effects of orbital rotations. Similar results apply for gradients of energies derived using perturbation theory.
TL;DR: In this paper, a supersonic beam of carbon clusters is generated using graphite as the substrate, and carbon clusters Cn for n=1−190 have been produced having a distinctly bimodal cluster size distribution: (i) both even and odd clusters for Cn, 1≤n≤30; and (ii) only even clusters C2n, 20−n−90.
Abstract: Laser vaporization of a substrate within the throat of a pulsed nozzle is used to generate a supersonic beam of carbon clusters. The neutral cluster beam is probed downstream by UV laser photoionization with time‐of‐flight mass analysis of the resulting photoions. Using graphite as the substrate, carbon clusters Cn for n=1–190 have been produced having a distinctly bimodal cluster size distribution: (i) Both even and odd clusters for Cn, 1≤n≤30; and (ii) only even clusters C2n, 20≤n≤90. The nature of the bimodal distribution, and the intensity alterations in the observed C+n signals are interpreted on the basis of cluster formation and stability arguments. Ionizing laser power dependences taken at several different photon energies are used to roughly bracket the carbon cluster ionization potentials, and, at high laser intensity, to observe the onset of multiphoton fragmentation. By treating the graphite rod with KOH, a greatly altered carbon cluster distribution with mixed carbon/potassium clusters of for...
TL;DR: In this paper, the lowest charge transfer excited state (CT1) of electron donor-acceptor crystals or polymers is demonstrated to be a plausible precursor of free charge carriers when such materials are photoexcited.
Abstract: The lowest charge‐transfer excited state (CT1) of electron donor–acceptor crystals or polymers is demonstrated to be a plausible precursor of free charge carriers when such materials are photoexcited Rate constants for the dissociation of charge–transfer states are formulated for two approximate descriptions of CT1: classical ion pair and Wannier exciton The electric field dependence of the dissociation rate constant is postulated to be given by Onsager’s 1934 theory (O‐34) of ion pair dissociation This formulation of CT1 dissociation obviates the need to invoke electron–hole ‘‘thermalization’’ lengths of 2 to 3 nm in order to explain free charge carrier formation in donor–acceptor materials
TL;DR: In this paper, the authors used Monte Carlo simulations to find large deviations from the standard Poisson-Boltzmann treatment of the double layer force for divalent counterions at high surface charge densities and at short separations.
Abstract: Using a novel method the force between two charged surfaces with an intervening electrolyte solution has been determined from Monte Carlo simulations. We find large deviations from the standard Poisson–Boltzmann treatment of the so called double layer force for divalent counterions at high surface charge densities and at short separations. The deviations have two causes: (i) Due to the inclusion of the effect of ion–ion correlations the counterions concentrate more towards the charged wall reducing the overlap between the double layers; and (ii) correlated fluctuations in the ion clouds of the two surfaces lead to an attractive interaction of a van der Waals type. For some realistic values of the parameters the attraction overcomes the repulsive part and there is a net attractive force between similarly charged surfaces. This finding leads to a modification of our conceptual understanding of the interaction between charged particles and it shows that the DLVO theory is qualitatively deficient under some, realistic, conditions.
TL;DR: In this article, the development of bulk optical properties as a function of crystallite size for the inorganic direct gap semiconductor CdS was studied in situ at extreme dilution.
Abstract: This paper reports experimental studies of the development of bulk optical properties as a function of crystallite size for the inorganic direct gap semiconductor CdS. Small crystallites are synthesized via colloidal chemical techniques, and their optical properties are studied in situ at extreme dilution. The crystallites are characterized via high resolution transmission electron microscopy. Direct images show (111) lattice planes, and establish the crystallite structures as close to those of excised fragments of bulk CdS (zinc‐blende cubic). Large crystallites (> 100 A average diameter) show an optical absorption, in colloidal solution, close to that of bulk crystalline material. However, small crystallites of 30 A average diameter show a large blue shift (∼0.8 eV) in absorption edge (effective band gap), and an intensification of edge absorption relative to absorption at higher energy regions. These observations can be understood as quantum size effects resulting from confinement of an electron and hole in a small volume. 40 A average size crystallites show a smaller shift (∼0.25 eV), and corresponding changes in their fluorescence, and resonance Raman excitation, spectra.
TL;DR: In this article, a discretized version of Feynman's path integral is used for the numerical investigation of the properties of an electron solvated in molten KC1. But the local structure around the solute electron appears to be different from that of an F center in the solid.
Abstract: It is shown that a discretized version of Feynman’s path integral provides a convenient tool for the numerical investigation of the properties of an electron solvated in molten KC1. The binding energy and the pair correlation functions are calculated. The local structure around the solute electron appears to be different from that of an F center in the solid.
TL;DR: In this paper, a phenomenological core polarization potential (CPP) was proposed to account for intershell correlation effects in all-electron SCF and valence CI calculations, and a detailed analysis of core polarization effects on ionization energies, electron affinities, oscillator strengths, polarizabilities, van der Waals coefficients, the valence electron density, and spin densities.
Abstract: In the present approach the high reliability of ab initio techniques is combined with the easily amenable phenomenological core polarization concept for an efficient treatment of intershell correlation effects in all‐electron SCF and valence CI calculations. By use of only a single adjustable atomic parameter, which is related to the radius of the core and determines the cutoff at short range, our effective core polarization potential (CPP) accounts quantitatively for dynamical intershell correlation as well as exclusion effects on the correlation energy of the core. The applications refer to alkali and alkaline earth atoms (Li to K and Be to Ca) and a detailed analysis is performed for core polarization effects on ionization energies, electron affinities, oscillator strengths, polarizabilities, van der Waals coefficients, the valence electron density, and spin densities. Very accurate results are obtained for well‐known energetic properties and spin densities at the nucleus. With respect to the other app...
TL;DR: In this paper, the translational and rotational diffusion coefficients of a rod-like macromolecule were compared with the Tirado-Garcia de la Torre theory for a particle of given dimensions.
Abstract: Two theories relating the translational and rotational diffusion coefficients Dt and Dr of a rod‐like macromolecule to its length and diameter, proposed by Broersma [J. Chem. Phys. 74, 6989 (1981)], and Tirado and Garcia de la Torre [J. Chem. Phys. 71, 2581 (1979); 73, 1986 (1980)] are shown to predict different values of the coefficients for a particle of given dimensions. Next, we use the two theories to analyze existing experimental data of sedimentation coefficients s and translational and rotational diffusion coefficients of short DNA fragments, and obtain values of the hydrated diameter of DNA d which is treated as an adjustable parameter. The results are compared with the expected value, d≂26A. This comparison favors clearly the Tirado–Garcia de la Torre theory in the case of Dt and s. For Dr, and using a rise per base pair r=3.4 A, this theory gives best agreement for all the data examined, while when r=3.3 A, the agreement depends on the source of data.
TL;DR: In this paper, a constrained space orbital variation (CSOV) with the electrons of the metal member of the complex in the field of frozen ligand is performed, and the electrons are then frozen in the relaxed distribution given by the CSOV SCF wave function and the ligand electrons are allowed to relax.
Abstract: The nature of the bonding of CO and NH3 ligands to Al is analyzed, and the intra-unit charge polarization and inter-unit donation for the interaction of ligands with metals are studied. The consequences of metal-to-ligand and ligand-to-metal charge transfer are separately considered by performing a constrained space orbital variation (CSOV) with the electrons of the metal member of the complex in the field of frozen ligand. The electrons of the metal atoms are then frozen in the relaxed distribution given by the CSOV SCF wave function and the ligand electrons are allowed to relax. Quantitative measures of the importance of inter-unit charge transfers and intra-unit polarization are obtained using results of SCF studies of Al4CO and Al4NH3 clusters chosen to simulate the adsorption of the ligands at an on-top side of the Al(111) surface. The electrostatic attraction of the effective dipole moments of the metal and ligand units makes an important contribution to the bond.
TL;DR: In this article, it was shown that finite basis calculations using kinetic balance are safe from catastrophic variational collapse, but that the bounds provided by these calculations can be in error by an amount of order 1/c4.
Abstract: Recent publications have suggested that the satisfaction of a principle we call kinetic balance can provide variational safety in Dirac calculations. The theoretical foundation for this proposal is examined, first in simple one‐electron problems, and then (less rigorously) in SCF calculations. The conclusion is that finite basis calculations using kinetic balance are safe from catastrophic variational collapse, but that the ‘‘bounds’’ provided by these calculations can be in error by an amount of order 1/c4. The bounds are applicable to total SCF energies, but not to SCF orbital energies. The theory is illustrated by a series of one‐electron calculations.
TL;DR: In this article, the second-harmonic efficiency of a new organic molecular crystal N(4−nitrophenyl)−(L)−prolinol (NPP) was reported.
Abstract: The higher second‐harmonic efficiency, in powder, of a new organic molecular crystal N‐(4‐nitrophenyl)‐(L)‐prolinol (NPP) is reported. Electronic polarizability of NPP molecules relates to that of other para‐nitroaniline‐like structures such as that of previously reported N‐(2,4‐dinitrophenyl) methyl alaninate (MAP), and the increase in crystalline nonlinear efficiency by one order of magnitude above the latter is ascribed to an ‘‘optimized’’ crystalline structure rather than to minor changes of the molecular hyperpolarizability. The simultaneous chiral and hydrogen‐bonding character of the prolinol electron‐donating group leads to a quasioptimal angle, with respect to quadratic phase‐matched nonlinear interactions, between the molecular transition dipole moments and the twofold axis of the monoclinic P21 crystal structure. Based on a simple oriented gas description of the quasiplanar structure of the crystal, two possible mutually exclusive second‐harmonic phase‐matched configurations are evidenced and s...
TL;DR: In this article, the authors extended the theory of Ostwald ripening to include the dependence on the volume fraction of the minority phase and derived the size distribution function for droplets of the majority phase and the power laws of the time dependences.
Abstract: The theory of Ostwald ripening is extended to include the dependence on the volume fraction of the minority phase. The size distribution function for droplets of the minority phase and the power laws of the time dependences are derived for the late stages of phase separation. The asymptotic distribution function is found to be independent of initial conditions but does depend on the equilibrium volume fraction associated with a given quench. We show that the average radius grows as t1/3 and the density of droplets decays as t−1. The growth law and the amplitudes for these temporal power laws derivate from their value in the limit of zero volume fraction as the square root of the volume fraction. The effect of competition among droplets causes the distribution to broaden and to increase the coarsening rate.
TL;DR: In this paper, the authors report molecular dynamics studies of small liquid drops (41-2004 molecules) in which the atoms interact with a Lennard-Jones intermolecular potential cutoff at 2.5σ and shifted by the potential at cutoff.
Abstract: We report molecular dynamics studies of small liquid drops (41–2004 molecules) in which the atoms interact with a Lennard‐Jones intermolecular potential cutoff at 2.5σ and shifted by the potential at cutoff. We calculate the density profiles ρ(r) and the normal and tangential components of the pressure tensor pN(r) and pT(r), using both the Irving–Kirkwood and Harasima definitions of p. From these functions we calculate the surface thickness, the equimolar radius Re and surface of tension Rs, the surface tension γs referred to Rs, the length δ that appears in Tolman’s equation for γs, the pressure change across the drop, and the densities and pressures of the liquid at the drop center and of the gas. The variation of these properties with both surface curvature and temperature is studied, and the results are used to discuss the validity of Laplace’s equation for the pressure change, Tolman’s equation for the effect of curvature on surface tension, and Kelvin’s equation for the vapor pressure. We also make a qualitative comparison with previous theoretical calculations for drops using density gradient and integral equation theory.
TL;DR: In this article, the coupled-cluster model for electron correlation is generalized to include the effects of connected triple excitation contributions, and a simplified version implemented that retains the dominant terms is presented.
Abstract: The coupled‐cluster model for electron correlation is generalized to include the effects of connected triple excitation contributions. The detailed equations for triple excitation amplitudes are presented, and a simplified version implemented that retains the dominant terms. The model presented, CCSDT‐1, provides the energy correct through fourth order and the wave function through second order. The CCSDT‐1 model is illustrated by comparing with full CI results for HF, BH, and H2O, the latter at several geometries.
TL;DR: In this paper, the ground-state electron density was shown to be a functional of the highest occupied orbital in Kohn-Sham theory, and the ground state electron density is connected to three Fukui functions defined by Parr and Yang (J Am Chem Soc Soc, 106(14):4049, 1984,
Abstract: In this note we shall show that the ground-state electron density \(\rho ({\mathbf r})\) is a functional of the highest occupied orbital in Kohn–Sham (Phys Rev 140:A1133, 1965, [1]) theory, \(\psi _{\mathrm {max}}\). The functionals \(\rho [\psi _{\mathrm {max}}]\) for an \((M+\delta )\)-electron system are resolved into three cases and connected to three Fukui functions defined by Parr and Yang (J Am Chem Soc, 106(14):4049, 1984, [2]).
TL;DR: In this paper, a comprehensive formalism is developed to describe the decay of the fluorescence emission anisotropy r(t) in macroscopically isotropic systems where both excited state and orientational dynamics contribute to the depolarization.
Abstract: A comprehensive formalism is developed to describe the decay of the fluorescence emission anisotropy r(t) in macroscopically isotropic systems where both excited state and orientational dynamics contribute to the depolarization. It is shown how energy transfer, heterogeneity, and interconversion of excited states with different emission characteristics as well as both overall and internal reorientation can be treated in a unified way. Limits when the state and orientation dynamics are uncoupled and when the interconversion of the states is either much slower or much faster than the irreversible decay rates, are considered. A systematic treatment of the influence of internal motions is presented. First, the geometry of the transition dipoles is explicitly ‘‘factored out’’ and general expressions for r(t) are obtained for several cases including when the motion occurs about a fixed axis and an axis which in turn can ‘‘wobble’’ about a director. The initial and long‐time behavior of r(t) is examined and then, a variety of dynamical models (e.g., discrete jumps, free and restricted Langevin motion about an axis, diffusive motion of an axis in an orienting potential) are used to obtain the time dependence of the relevant correlation functions which appear in the above general expressions. In this way, one can obtain r(t) for a large class of models. Of particular interest is an approximate analytic expression for r(t), valid for any orientation of the transition dipoles and restricting potential, of a cylindrical probe in a membrane. The influence of collective (hydrodynamic) fluctuations of the membrane director are also considered.