Measuring electron sharing between atoms in first-principle simulations

Calculations of large scale electronic structure within periodic boundary conditions, mostly based on solid state physics, allow the modeling of atomic forces and molecular dynamics for atomic assemblies of 100–1000 atoms, thus providing complementary information in material and macromolecular sciences. Nevertheless, these methods lack connections with the chemistry of simple molecules as isolated entities. In order to contribute to establish a conceptual connection between solid state physics and chemistry, the calculation of the extent of electron sharing between atoms, also known as delocalization index, is performed on simple molecules and on complexes with transition metal atoms, using density functional calculations where the Kohn–Sham molecular orbitals are represented in terms of plane waves and in periodic boundary conditions. These applications show that the useful measure of electron sharing between atomic pairs can be recovered from density functional calculations using the same set-up applied to large atomic assemblies in condensed phases, with no projections of molecular orbitals onto atomic orbitals.     

The influence of temperature and density functional models in ab initio molecular dynamics simulation of liquid water

The performance of density functional theory methods for the modeling of condensed aqueous systems is hard to predict and validation by ab initio molecular simulation of liquid water is absolutely necessary. In order to assess the reliability of these tests, the effect of temperature on the structure and dynamics of liquid water has been characterized with 16 simulations of 20 ps in the temperature range of 280-380 K. We find a pronounced influence of temperature on the pair correlation functions and on the diffusion constant including nonergodic behavior on the time scale of the simulation in the lower temperature range (which includes ambient temperature). These observations were taken into account in a consistent comparison of a series of density functionals (BLYP, PBE, TPSS, OLYP, HCTH120, HCTH407). All simulations were carried out using an ab initio molecular dynamics approach in which wave functions are represented using Gaussians and the density is expanded in an auxiliary basis of plane waves. Whereas the first three functionals show similar behavior, it is found that the latter three functionals yield more diffusive dynamics and less structure.     

DFT calculations with the symmetrized kohn–sham formalism for the electronic structure of the high-energy states of nitrogen dioxide

Quantum-chemical calculations of the electronic structure of the high-energy states of NO₂ were performed by the density functional method with symmetrized Kohn–Sham formalism. The results from the DFT calculation of the NO₂^* NO_2^* excited states agree well with experimental data and ab initio calculations. The reactivity of the long-lived excited state NO₂^*( [(C)\tilde]²A" ) NO_2^*\left( {{{\tilde{C}}^2}A'} \right) during photochemical conversion to NO₃ was investigated.     

Ab initio dynamics with wave-packets and density matrices

Efficient methodologies to conduct simultaneous dynamics of electrons and nuclei are discussed. Particularly, attention is directed to a recent development that combines quantum dynamics with ab initio molecular dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. An approach to conduct quantum dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator is highlighted with suitable review of other related approaches. One notable feature of the method is that all important quantum dynamical effects including zero-point effects, tunneling as well as over-barrier reflections are accurately treated. Computational methodologies for improved efficiency of the quantum dynamics are also discussed. There exists a number of ways to carry out simultaneous ab initio molecular dynamics (such as Born–Oppenheimer dynamics and extended Lagrangian dynamics, Car–Parrinello dynamics being a prime example of the latter); our prime focus remains on atom-centered density-matrix propagation and Born–Oppenheimer dynamics. The electronic degrees of freedom are handled at accurate levels of density functional theory, using hybrid or gradient corrected approximations. Benchmark calculations are provided for a prototypical proton transfer system. Future generalizations and goals are discussed.     

Hydrated hydride anion clusters

On the basis of density functional theory (DFT) and high level ab initio theory, we report the structures, binding energies, thermodynamic quantities, IR spectra, and electronic properties of the hydride anion hydrated by up to six water molecules. Ground state DFT molecular dynamics simulations (based on the Born-Oppenheimer potential surface) show that as the temperature increases, the surface-bound hydride anion changes to the internally bound structure. Car-Parrinello molecular dynamics simulations are also carried out for the spectral analysis of the monohydrated hydride. Excited-state ab initio molecular dynamics simulations show that the photoinduced charge-transfer-to-solvent phenomena are accompanied by the formation of the excess electron-water clusters and the detachment of the H radical from the clusters. The dynamics of the detachment process of a hydrogen radical upon the excitation is discussed.     

Iterative solution of Bloch-type equations: stability conditions and chaotic behavior

Two different form of nonperturbative Bloch-type equations are studied: one for the wave operator of the N-electron Schr?dinger equation, another one for obtaining first-order density matrix P in one-electron theories (Hartree–Fock or Kohn–Sham). In both cases, we investigate the possibility of an iterative solution of the nonlinear Bloch equation. To have a closer view on convergence features, we determine the stability matrix of the iterative procedures and determine the Ljapunov exponents from its eigenvalues. For some of the cases when not every exponents are negative, chaotic solutions can be identified, which should of course be carefully avoided in practical iterations.     

First principles calculation of the thermodynamic properties of silicon clusters

The thermodynamic properties of Si clusters are calculated using first principles quantum methods combined with molecular dynamics for simulating the trajectories of clusters. A plane wave basis is used with ab initio pseudo potentials and the local density approximation for determining the electronic energies and forces. Langevin molecular dynamics simulates thermal contact with a constant temperature reservoir. Vibrational spectra, moments of inertia, anharmonic corrections, and free energies are predicted for Si₂ through Si₅. The translational contribution is based on the ideal gas limit. The rotation contribution is approximated using a classical rigid rotator. Vibrational modes are determined from the dynamical matrix in the harmonic approximation. Corrections due to anharmonicity and coupling between rotational and vibrational modes are fit from the molecular dynamics simulations. Received: 17 September 1997 / Accepted: 14 October 1997     

Does an exact local exchange potential exist?

In Kohn–Sham density functional theory, equations for occupied orbital functions of a model state are derived from the exact ground‐state energy functional of Hohenberg and Kohn. The exchange‐correlation potential in these exact Kohn–Sham equations is commonly assumed to be a local potential function rather than a more general linear operator. This assumption is tested and shown to fail for the exchange potential in a Hartree–Fock model for atoms, for which accurate solutions are known. This revised version was published online in July 2006 with corrections to the Cover Date.     

Strategies for computing chemical reactivity indices

 Two recent articles [(2000) J Am Chem Soc 122: 2010, (2001) J Am Chem Soc 123: 2007] have explored electron-density-based and external-potential-based chemical reactivity indices. In this article, methods are presented for computing these indices from the output of a Kohn–Sham density functional theory calculation. Received: 18 October 2000 / Accepted: 4 April 2001 / Published online: 9 August 2001     

Electrostatic exchange-correlation charge density in Be and Ne: quantal density functional theoretic analysis

Using classical electrostatics, the total effective integrated charge-density function is calculated for Be and Ne using the multiplicative potentials derived from (1) Hartree and (2) Hartree–Fock approximation to quantal density functional theory (3)exchange-only optimized effective potential and (4) Kohn–Sham exchange-correlation potential using the quantum Monte Carlo density. The evolution of effective integrated charge-density function for these atoms is examined as the electron correlation is built up stepwise from its absence to the stage of its near complete presence. These results provide a deeper understanding of the Kohn–Sham exchange-correlation potential in terms the correspondingly defined integrated charge-density functions based on the Poisson equation. This paper is dedicated to Professor Karl Jug on the occasion of his 65th Birthday     

Generalized Christoffel–Darboux formulae and the frontier Kohn–Sham molecular orbitals

The Christoffel–Darboux formula for classical orthogonal polynomials is generalized to arbitrary sets of orthogonal functions in three dimensions, yielding an explicit link between frontier Kohn–Sham molecular orbitals and the Kohn–Sham density matrix. Methods using this result could significantly accelerate Kohn–Sham density functional theory calculations, as only a subset of the Kohn–Sham equations would need to be addressed. The result can also be seen as an explicit justification for the utility of frontier molecular orbital theory.     

Magnetic Properties and Electronic Structure of Neptunyl(VI) Complexes: Wavefunctions,Orbitals, and Crystal‐Field Models

The electronic structure and magnetic properties of neptunyl(VI), NpO₂²⁺, and two neptunyl complexes, [NpO₂(NO₃)₃]^? and [NpO₂Cl₄]^2?, were studied with a combination of theoretical methods: ab initio relativistic wavefunction methods and density functional theory (DFT), as well as crystal‐field (CF) models with parameters extracted from the ab initio calculations. Natural orbitals for electron density and spin magnetization from wavefunctions including spin–orbit coupling were employed to analyze the connection between the electronic structure and magnetic properties, and to link the results from CF models to the ab initio data. Free complex ions and systems embedded in a crystal environment were studied. Of prime interest were the electron paramagnetic resonance g‐factors and their relation to the complex geometry, ligand coordination, and nature of the nonbonding 5f orbitals. The g‐factors were calculated for the ground and excited states. For [NpO₂Cl₄]^2?, a strong influence of the environment of the complex on its magnetic behavior was demonstrated. Kohn–Sham DFT with standard functionals can produce reasonable g‐factors as long as the calculation converges to a solution resembling the electronic state of interest. However, this is not always straightforward.     

Global geometry optimization of small silicon clusters at the level of density functional theory

By an application to small silicon clusters Si _N (with N = 4,5,7,10) it is shown that truly global geometry optimization on an ab initio or density functional theory level can be achieved, at a computational cost of approximately 1–5 traditional local optimization runs (depending on cluster size). This extends global optimization from the limited area of empirical potentials into the realm of ab initio quantum chemistry. Received: 24 February 1998 / Accepted: 6 March 1998 / Published online: 17 June 1998     

A small-core multiconfiguration Dirac–Hartree–Fock-adjusted pseudopotential for Tl – application to TlX (X = F, Cl, Br, I)

 A relativistic pseudopotential of the energy-consistent variety simulating the Tl²¹⁺ (1s– 4f) core has been generated by adjustment to multiconfiguration Dirac–Hartree–Fock data based on the Dirac–Coulomb–Breit Hamiltonian. Valence ab initio calculations using this pseudopotential have been performed for atomic excitation energies and for spectroscopic constants of the X0⁺ and A0⁺ states of TlX (X = F, Cl, Br, I). Comparison is made to experiment and to four-component density functional results. Received: 22 June 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

Favorable performance of the DFT methods in predicting the minimum‐energy structure of the lowest triplet state of WF4

The tetrahedral structure of the lowest triplet state of the WF₄ complex was examined using different variants of the density functional theory (DFT) and conventional ab initio methods. The low‐level, conventional, ab initio methods, such as SCF, MP2, MP3, and CISD, predict the tetrahedral structure to be a minimum, whereas the DFT schemes predict an imaginary frequency for the e vibrational mode. Only after recovering electron correlation effects at the MP4 and higher levels, the conventional electronic structure methods also predict the T_d structure to be a second‐order stationary point. This is not the correlation but the exchange part of the DFT functionals which is responsible for the discrepancy between the DFT and low‐level, conventional, ab initio predictions. The lowering of symmetry to C_2v leads to a minimum on the lowest triplet potential energy surface and the electronic energy difference between the T_d and C_2v stationary points amounts to 0.85 and 0.96 kcal/mol at the B3LYP and CCSD(T) levels, respectively. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 369–375, 1999     

On-the-fly localization of electronic orbitals in Car-Parrinello molecular dynamics

The ab initio molecular-dynamics formalism of Car and Parrinello is extended to preserve the locality of the orbitals. The supplementary term in the Lagrangian does not affect the nuclear dynamics, but ensures "on the fly" localization of the electronic orbitals within a periodic supercell in the Gamma-point approximation. The relationship between the resulting equations of motion and the formation of a gauge-invariant Lagrangian combined with a gauge-fixing procedure is briefly discussed. The equations of motion can be used to generate a very stable and easy to implement numerical integration algorithm. It is demonstrated that this algorithm can be used to compute the trajectory of the maximally localized orbitals, known as Wannier orbitals, in ab initio molecular dynamics with only a modest increase in the overall computer time. In the present paper, the new method is implemented within the generalized gradient approximation to Kohn-Sham density-functional theory employing plane wave basis sets and atomic pseudopotentials. In the course of the presentation, we briefly discuss how the present approach can be combined with localized basis sets to design fast linear scaling ab initio molecular-dynamics methods.     

Diabatic and adiabatic potential-energy surfaces for azomethane photochemistry

We propose an analytic form to represent the intersecting potential energy surfaces (PES) of the first two singlet states of azomethane. The aim is to run semiclassical simulations of photochemical events such as fragmentation and isomerization. The PES are based on ab initio calculations and corrected on the basis of available experimental data. We resort to a quasi-diabatic representation, suitable to deal with the S₀-S₁ conical intersection and to include the essential information about electronic couplings in a 2 × 2 effective hamiltonian matrix. Received: 18 February 1999 / Accepted: 12 April 1999 / Published online: 14 July 1999     

Radiochemical challenges in the study of endohedral fullerenes and MD simulation

The formation of atom-doped fullerenes has been investigated by using several types of radionuclides produced by nuclear reactions. From the trace of the radioactivities after high performance liquid chromatography (HPLC), it was found that formation of endohedral fullerenes (or heterofullerene) with small atoms (Be, Li), noble-gas atoms (Kr, Xe) and 4B–6B elements (Ge, As, Se, Sb, Te etc.) is possible by a recoil process following the nuclear reaction. In order to show the possibility of creating endohedral fullerenes by inserting a foreign atom with a suitably high kinetic energy into C₆₀, we have carried out large-scale ab initio molecular dynamics simulations on the basis of the all-electron mixed-basis approach with atomic orbitals and plane waves for Li, Be, N, O, Na, S, Cl, K, V, Cu, As, Se, Sb, Te, Kr, Xe. This revised version was published online in July 2006 with corrections to the Cover Date.     

α-Al2O3(0001)表面弛豫及其对表面电子态的影响

The relaxation and electronic structure of the α-Al2O3 (0001) super-cell (2×2) surface with single Al atoms layer-terminated are studied using ab initio quantum-mechanical calculations based on the density functional theory and pseudo potential method. The calculations employ slab geometry and periodic boundary conditions, with the occupied orbitals expanded in plane waves. It is found that the surface relaxation results in the change of surface electronic states by investigating the relaxation and the population of the Al-O atoms of the surface. By analyzing the difference of the density of state and electron charge density between the unrelaxed and relaxed surface, it is obvious that the α-Al2O3 (0001) crystal surface appears on the O-surface state from which is most contribution to the O2p states, and the surface electronic density plotted by electron localization function (ELF) shows the characteristics of surface bonding atoms. The ELF indicates the outmost Al-O ionic bonds of the relaxed surface are much stronger than that of the unrelaxed surface.