Open-shell reduced density matrix functional theory

Open-shell reduced density matrix functional theory is established by investigating the domain of the exact functional. For spin states that are the ground state, a particularly simple set is found to be the domain. It cannot be generalized to other spin states. A number of conditions satisfied by the exact density matrix functional is formulated and tested for approximate functionals. The exact functional does not suffer from fractional spin error, which is the source of the static correlation error in dissociated molecules. We prove that a simple approximation (called the Buijse-Baerends functional, Mu?ller or square root functional) has a non-positive fractional spin error. In the case of the H atom the error is zero. Numerical results for a few atoms are given for approximate density and density matrix functionals as well as a recently developed range-separated combination of both.     

Time-dependent density functional theory based Ehrenfest dynamics

Time-dependent density functional theory based Ehrenfest dynamics with atom-centered basis functions is developed in present work. The equation of motion for electrons is formulated in terms of first-order reduced density matrix and an additional term arises due to the time-dependence of basis functions through their dependence on nuclear coordinates. This time-dependence of basis functions together with the imaginary part of density matrix leads to an additional term for nuclear force. The effects of the two additional terms are examined by studying the dynamics of H(2) and C(2)H(4), and it is concluded that the inclusion of these two terms is essential for correct electronic and nuclear dynamics.     

Further test of third order + second-order perturbation DFT approach: hard core repulsive Yukawa fluid subjected to diverse external fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.     

A first-principles investigation on interactions between various surface-terminated diamond films

To elucidate the influence of different terminations on diamond surface interaction, the geometry and electronic structures of the diamond films modified by different terminations (H, F, O, NH₂, and OH) are studied by using the first principles method. Strong bonding is formed between the clean diamond surfaces, which suggest an obvious interface interaction. Both H and F terminals have significant effects on the reduction of the interface interactions. Due to the larger difference in electronegativity between C and F, the F termination layer has a higher electron density coverage to give a larger repulsive force. Therefore, the interaction between the F-terminated diamond interfaces is stronger than that between the H-terminated diamond interfaces. The O-terminated diamond surfaces are unstable. The NH₂- and OH-terminals have weak interaction due to the presence of large functional group atoms that leads to an electronic offset.     

高电位胶体颗粒强相互作用的近似表达式

When surface potential of the particles, ,is high,sinh y can be approximated by ≈ey/2 in the nonlinear Poisson Boltzmann equation.Thus,we present a simple method of calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential.These formulae could be applicable to the case of repulsive case,in which the derivative of y must vanish at an interior point,and a minimum ymin=u always exists.A turning point at ～kh≈2(1)e－y1/2 for the repulsion or attraction between dissimilar planar surfaces.These formulae are divergent at 阧∞,and zero point at kh≈2 .This means that they can only be used at 阧 < 2 and accurate location is at kh ≤ 4. 　　Agreement of the approximation for force,Eq.（13）,is good with the exact numerical values of the interaction of dissimilar plates given by Devereux [6] for high surface potentials.For y1 ≥5 kh ≤ 3.0 the relative errors of Eq.(13) are less than 5％,and for kh ≤ 3.5 relative errors are less than 10％.For the interaction energy,Eq.(15),the applicable range extends to kh =4.0.Beyond this range the error increases rapidly.The higher surface potential is the better the precision of Eq.（13）and Eq.( 15).The condition of the strong interaction has been satisfied.     

Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

The influence of discrete surface charges on the force between charged surfaces

The force between two parallel charged flat surfaces, with discrete surface charges, has been calculated with Monte Carlo simulations for different values of the electrostatic coupling. For low electrostatic coupling (small counterion valence, small surface charge, high dielectric constant, and high temperature) the total force is dominated by the entropic contribution and can be described by mean field theory, independent of the character of the surface charges. For moderate electrostatic coupling, counterion correlation effects lead to a smaller repulsion than predicted by mean field theory. This correlation effect is strengthened by discrete surface charges and the repulsive force is further reduced. For large electrostatic coupling the total force for smeared out surface charges is known to be attractive due to counterion correlations. If discrete surface charges are considered the attractive force is weakened and can even be turned into a repulsive force. This is due to the counterions being strongly correlated to the discrete surface charges forming effective, oppositely directed, dipoles on the two walls.     

Reaction of hydrogen with Ag(111): binding states, minimum energy paths, and kinetics

The interaction of atomic and molecular hydrogen with the Ag(111) surface is studied using periodic density functional total-energy calculations. This paper focuses on the site preference for adsorption, ordered structures, and energy barriers for H diffusion and H recombination. Chemisorbed H atoms are unstable with respect to the H(2) molecule in all adsorption sites below monolayer coverage. The three-hollow sites are energetically the most favorable for H chemisorption. The binding energy of H to the surface decreases slightly up to one monolayer, suggesting a small repulsive H-H interaction on nonadjacent sites. Subsurface and vacancy sites are energetically less favorable for H adsorption than on-top sites. Recombination of chemisorbed H atoms leads to the formation of gas-phase H(2) with no molecular chemisorbed state. Recombination is an exothermic process and occurs on the bridge site with a pronounced energy barrier. This energy barrier is significantly higher than that inferred from experimental temperature-programmed desorption (TPD) studies. However, there is significant permeability of H atoms through the recombination energy barrier at low temperatures, thus increasing the rate constant for H(2) desorption due to quantum tunneling effects, and improving the agreement between experiment and theory.     

Long-range excitations in time-dependent density functional theory

Adiabatic time-dependent density functional theory fails for excitations of a heteroatomic molecule composed of two open-shell fragments at large separation. Strong frequency dependence of the exchange-correlation kernel is necessary for both local and charge-transfer excitations. The root of this is the static correlation created by the step in the exact Kohn-Sham ground-state potential between the two fragments. An approximate nonempirical kernel is derived for excited molecular dissociation curves at large separation. Our result is also relevant when the usual local and semilocal approximations are used for the ground-state potential, as static correlation there arises from the coalescence of the highest occupied and lowest unoccupied orbital energies as the molecule dissociates.     

Hybrid density functional theory for pi-stacking interactions: application to benzenes, pyridines, and DNA bases

The suitability of a hybrid density functional to qualitatively reproduce geometric and energetic details of parallel pi-stacked aromatic complexes is presented. The hybrid functional includes an ad hoc mixture of half the exact (HF) exchange with half of the uniform electron gas exchange, plus Lee, Yang, and Parr's expression for correlation energy. This functional, in combination with polarized, diffuse basis sets, gives a binding energy for the parallel-displaced benzene dimer in good agreement with the best available high-level calculations reported in the literature, and qualitatively reproduces the local MP2 potential energy surface of the parallel-displaced benzene dimer. This method was further critically compared to high-level calculations recently reported in the literature for a range of pi-stacked complexes, including monosubstituted benzene-benzene dimers, along with DNA and RNA bases, and generally agrees with MP2 and/or CCSD(T) results to within +/-2 kJ mol(-1). We also show that the resulting BH&H binding energy is closely related to the electron density in the intermolecular region. The net result is that the BH&H functional, presumably due to fortuitous cancellation of errors, provides a pragmatic, computationally efficient quantum mechanical tool for the study of large pi-stacked systems such as DNA.     

On the influence of microsolvation by argon atoms on the electron affinity properties of water dimer

This work provides a comparison of neutral (H2O)2Ar(n) and negatively charged (H2O)(2-)Ar(n) complexes. The excess electron stabilizes the complexes and leads to the trans to cis rearrangement within the water dimer core. In the case of small complexes (n < or = 4) the microsolvation of the dimer by argon atoms arises on the trans side with respect to the donor water molecule. The stabilization of an excess electron is enhanced by the delocalization of the electronic charge density due to microsolvation. The process of cis to trans rotation is induced by the electric field of the approaching negative charge. The interaction energy decomposition suggests a more ionic character of binding in the negatively charged complexes. The attachment of an electron is controlled by the correlation energy.     

Effect of CO on the Oxidative Addition of Arene C?H Bonds by Cationic Rhodium Complexes

Sequential addition of CO molecules to cationic aryl–hydrido Rh^III complexes of phosphine‐based (PCP) pincer ligands was found to lead first to C? H reductive elimination and then to C? H oxidative addition, thereby demonstrating a dual role of CO. DFT calculations indicate that the oxidative addition reaction is directly promoted by CO, in contrast to the commonly accepted view that CO hinders such reactions. This intriguing effect was traced to repulsive π interactions along the aryl‐Rh‐CO axis, which are augmented by the initially added CO ligand (due to antibonding interactions between occupied Rh d_π orbitals and occupied π orbitals of both CO and the arene moiety), but counteracted by the second CO ligand (due to significant π back‐donation). These repulsive interactions were themselves linked to significant weakening of the π‐acceptor character of CO in the positively charged rhodium complexes, which is concurrent with an enhanced σ‐donating capability. Replacement of the phosphine ligands by an analogous phosphinite‐based (POCOP) pincer ligand led to significant changes in reactivity, whereby addition of CO did not result in C? H reductive elimination, but yielded relatively stable mono‐ and dicarbonyl aryl–hydrido POCOP–Rh^III complexes. DFT calculations showed that the stability of these complexes arises from the higher electrophilicity of the POCOP ligand, relative to PCP, which leads to partial reduction of the excessive π‐electron density along the aryl‐Rh‐CO axis. Finally, comparison between the effects of CO and acetonitrile on C? H oxidative addition revealed that they exhibit similar reactivity, despite their markedly different electronic properties. However, DFT calculations indicate that the two ligands operate by different mechanisms.     

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.     

Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.     

On the short-time limit of ring polymer molecular dynamics

We examine the short-time accuracy of a class of approximate quantum dynamical techniques that includes the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) methods. Both of these methods are based on the path integral molecular dynamics (PIMD) technique for calculating the exact static equilibrium properties of quantum mechanical systems. For Kubo-transformed real-time correlation functions involving operators that are linear functions of positions or momenta, the RPMD and (adiabatic) CMD approximations differ only in the choice of the artificial mass matrix of the system of ring polymer beads that is employed in PIMD. The obvious ansatz for a general method of this type is therefore to regard the elements of the PIMD (or Parrinello-Rahman) mass matrix as an adjustable set of parameters that can be chosen to improve the accuracy of the resulting approximation. We show here that this ansatz leads uniquely to the RPMD approximation when the criterion that is used to select the mass matrix is the short-time accuracy of the Kubo-transformed correlation function. In particular, we show that the leading error in the RPMD position autocorrelation function is O(t(8)) and the error in the velocity autocorrelation function is O(t(6)), for a general anharmonic potential. The corresponding errors in the CMD approximation are O(t(6)) and O(t(4)), respectively.     

Configuration interaction based on constrained density functional theory: a multireference method

Existing density functional theory (DFT) methods are typically very effective in capturing dynamic correlation, but run into difficulty treating near-degenerate systems where static correlation becomes important. In this work, we propose a configuration interaction (CI) method that allows one to use a multireference approach to treat static correlation but incorporates DFT's efficacy for the dynamic part as well. The new technique uses localized charge or spin states built by a constrained DFT approach to construct an active space in which the effective Hamiltonian matrix is built. These local configurations have significantly less static correlation compared to their delocalized counterparts and possess an essentially constant amount of self-interaction error. Thus their energies can be reliably calculated by DFT with existing functionals. Using a small number of local configurations as different references in the active space, a simple CI step is then able to recover the static correlation missing from the localized states. Practical issues of choosing configurations and adjusting constraint values are discussed, employing as examples the ground state dissociation curves of H(2) (+), H(2), and LiF. Excellent results are obtained for these curves at all interatomic distances, which is a strong indication that this method can be used to accurately describe bond breaking and forming processes.     

Driving forces for self-organized coadsorption: C6H6/2O and C6H6/2CO on Ni[111

The self-organized (2log3 x 2log3) coadsorbed phases of C(6)H(6) with O and with CO are investigated within first-principles density functional theory. The main driving force for formation of the C(6)H(6)/2O phase is found to be the reduction of O adatom repulsive interactions, while for the C(6)H(6)/2CO phase it is the interspecies attractive interactions and benzene-benzene repulsive interactions which are most important.     

Further evidences of the quality of double-hybrid energy functionals for π-conjugated systems

Despite numerous interesting efforts along decades to improve the accuracy of density functionals with broad applicability, such as B3LYP, there are still large sets of molecular systems where improvements are badly needed. We select π-conjugated systems as an example of the latter due to the subtle interplay between some physical effects affecting possibly most of the calculations: self-interaction or delocalization error, medium-range correlation signatures, dispersive-like weak interactions, and static correlation effects. We further assess a recently proposed modification of the B2-PLYP double-hybrid functional, called B2π-PLYP, that is expected to yield substantial progress for this kind of systems. Generally speaking, when compared with other more popular and older density functionals, double hybrids behave particularly accurate for π-conjugated systems without suffering the large errors that are common in former yet conventional methods.     

Long-Range Interaction Forces between Polymer-Supported Lipid Bilayer Membranes

Much of the short-range forces and structures of softly supported DMPC bilayers has been described previously. However, one interesting feature of the measured force-distance profile that remained unexplained is the presence of a long-range exponentially decaying repulsive force that is not observed between rigidly supported bilayers on solid mica substrate surfaces. This observation is discussed in detail here based on recent static and dynamic surface force experiments. The repulsive forces in the intermediate distance regime (mica-mica separations from 15 to 40 nm) are shown to be due not to an electrostatic force between the bilayers but to compression (deswelling) of the underlying soft polyelectrolyte layer, which may be thought of as a model cytoskeleton. The experimental data can be fit by simple theoretical models of polymer interactions from which the elastic properties of the polymer layer can be deduced.