Non-adiabatic dynamics of electrons and atoms under non-equilibrium conditions

An approach to non-adiabatic dynamics of atoms in molecular and condensed matter systems under general non-equilibrium conditions is proposed. In this method interaction between nuclei and electrons is considered explicitly up to the second order in atomic displacements defined with respect to the mean atomic trajectory. This method enables one to consider movement of atoms beyond their simple vibrations. Both electrons and nuclei are treated fully quantum-mechanically using a combination of path integrals applied to nuclei and non-equilibrium Green's functions (NEGF) to elections. Our method is partition-less: initially, the entire system is coupled and assumed to be at thermal equilibrium. Then, the exact application of the Hubbard-Stratanovich transformation in mixed real and imaginary times enables us to obtain, without doing any additional approximations, an exact expression for the reduced density matrix for nuclei and hence an effective quantum Liouville equation for them, both containing Gaussian noises. It is shown that the time evolution of the expectation values for atomic positions is described by an infinite hierarchy of stochastic differential equations for atomic positions and momenta and their various fluctuations. The actual dynamics is obtained by sampling all stochastic trajectories. It is expected that applications of the method may include photo-induced chemical reactions (e.g. dissociation), electromigration, atomic manipulation in scanning tunneling microscopy, to name just a few.Comment: 30 pages, 1 fugur

Strongly localised molecular orbitals for α\alpha-quartz

A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich - physics/0401107) is applied to a perfect $\alpha$-quartz crystal characterised by an intermediate type of chemical bonding. The orbitals are constructed by applying various localisation methods to canonical Hartree-Fock orbitals calculated for a succession of finite molecular clusters of increased size with appropriate boundary conditions. The calculated orbitals span the same occupied Fock space as the canonical HF solutions, but have an advantage of reflecting the true chemical nature of the bonding in the system. The applicability of several localisation techniques as well as of a number of possible choices of localisation regions (structure elements) are discussed for this system in detail

Comparison of localization procedures for applications in crystal embedding

With the aim of future applications in quantum mechanical embedding in extended systems such as crystals, we suggest a simple and computationally efficient method which enables construction of a set of nonorthogonal highly localized one-electron orbitals for periodic nonmetallic crystals which reflect their chemical nature. The orbitals are also used to build up the Hartree-Fock (HF) electron density of the entire crystals. The simplicity of the method stems from the fact that it does not require usage and/or modification of periodic electronic structure codes, and is instead based on the HF calculation of a sequence of finite clusters with subsequent application of a localization procedure to transform the HF canonical molecular orbitals. Two extreme cases of chemical bonding, ionic (MgO crystal) and covalent (Si crystal), are considered for which a number of known localization schemes are applied and compared. With some modifications our method can also be applied to nonperiodic nonmetallic systems as well

Ferrogels cross-linked by magnetic particles: Field-driven deformation and elasticity studied using computer simulations

Ferrogels, i.e. swollen polymer networks into which magnetic particles are immersed, can be considered as "smart materials" since their shape and elasticity can be controlled by an external magnetic field. Using molecular dynamics simulations on the coarse-grained level we study a ferrogel in which the magnetic particles act as the cross-linkers of the polymer network. In a homogeneous external magnetic field the direct coupling between the orientation of the magnetic moments and the polymers by means of covalent bonds gives rise to a deformation of the gel, independent of the interparticle dipole-dipole interaction. In this paper we report quantitative measurements of this deformation, the gel's elastic moduli and its magnetic response. Our results demonstrate that these properties depend significantly on the topology of the polymer network

Structure and spectroscopy of surface defects from scanning force spectroscopy: theoetical predictions

A possibility to study surface defects by combining noncontact scanning force microscopy (SFM) imaging with atomically resolved optical spectroscopy is demonstrated by modeling an impurity Cr3+ ion at the MgO(001) surface with a SFM tip. Using a combination of the atomistic simulation and the ab initio electronic structure calculations, we predict a topographic noncontact SFM image of the defect and show that its optical transitions can be either enhanced or suppressed depending on the tip atomistic structure and its position relative to the defect. These effects should allow identification of certain impurity species through competition between radiative and nonradiative transitions

Calculation of the current response in a nanojunction for an arbitrary time-dependent bias: application to the molecular wire

Recently [Phys. Rev. B 91, 125433 (2015)] we derived a general formula for the time-dependent quantum electron current through a molecular junction subject to an arbitrary time-dependent bias within the Wide Band Limit Approximation (WBLA) and assuming a single particle Hamiltonian. Here we present an efficient numerical scheme for calculating the current and particle number. Using the Pad\'e expansion of the Fermi function, it is shown that all frequency integrals occurring in the general formula for the current can be removed analytically. Furthermore, when the bias in the reservoirs is assumed to be sinusoidal it is possible to manipulate the general formula into a form containing only summations over special functions. To illustrate the method, we consider electron transport through a one-dimensional molecular wire coupled to two leads subject to out-of-phase biases. We also investigate finite size effects in the current response and particle number that results from the switch-on of such a bias

Electrostatic energy calculation for the interpretation of scanning probe microscopy experiments

We discuss the correct expression for the classical electrostatic energy used while analysing scanning probe microscopy (SPM) experiments if either a conducting tip or a substrate or both are used in the experiment. For this purpose a general system consisting of an arbitrary arrangement of finite metallic conductors at fixed potentials (maintained by external sources) and a distribution of point charges in free space are considered using classical electrostatics. We stress the crucial importance of incorporating into the energy the contribution coming from the external sources (the `battery'). Using the Green function of the Laplace equation, we show in a very general case that the potential energy of point charges which are far away from metals is equally shared by their direct interaction and the polarization interaction due to charge induced in metals by the remote charges (the image interaction). When the charges are located close to the metals, there is an additional negative term in the energy entirely due to image interaction. The exact Hamiltonian of a quantum system interacting classically with polarized metal conductors is derived and its application in the Hartree-Fock and the density functional theories is briefly discussed. As an illustration of the theory, we consider an interaction of several point charges with a metal plane and a spherical tip, based on the set-up of a real SPM experiment. We show the significance of the image interaction for the force imposed on the tip