Electron Density Matrix Research Articles

Hydrodynamic tensor density functional theory with correct susceptibility

In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work the authors assumed that the cumulants vanish above a certain order (N). Here the authors show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a nonperturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained, while the Thomas-Fermi and von Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate the author's previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.

Negative long wavelength dielectric constant in semiconductor QWs

AbstractIn this work we present an analytical and numerical result of the dielectric function of electronic systems with Rashba spin‐orbit interaction. By solving the quantum equation of motion for the electron density matrix, we obtained the dielectric function in the mean‐field approximation. It is shown that when the momentum transfer q for an electronic transition is smaller than a critical value characterized by the spin‐orbit interaction, the static dielectric function increases with q, indicating on‐set of a new collective state. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

First-principles dynamics treatment of light emission in collisions between alkali-metal atoms and noble-gas atoms at10keV

Collision-induced light emission during the interaction of an alkali-metal atom and a noble-gas atom is treated within a first-principles, or direct, dynamics approach that calculates a time-dependent electric dipole for the whole system, and spectral emission cross sections from its Fourier transform. These cross sections are very sensitive to excited diatomic potentials and a source of information on their shape. The coupling between electronic transitions and nuclear motions is treated with atomic pseudopotentials and an electronic density matrix coupled to trajectories for the nuclei. A recently implemented pseudopotential parametrization scheme is used here for the ground and excited states of the LiHe system, and to calculate state-to-state dipole moments. To verify the accuracy of our new parameters, we recalculate the integral cross sections for the LiHe system in the keV energy regime and obtain agreement with other results from theory and experiment. We further present results for the emission spectrum from $10\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ $\mathrm{Li}(2s)+\mathrm{He}$ collisions, and compare them to experimental values available in the region of light emitted at $300--900\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$.

Infrared and Raman spectra ofβ−BC2Nfrom first principles calculations

We present the study on the infrared and nonresonant Raman spectra of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{C}}_{2}\mathrm{N}$ within the framework of ab initio pseudopotential density functional perturbation theory in a four-atom orthorhombic unit cell. The Raman tensors are calculated from the second-order response of the electronic density matrix with respect to a uniform electric field. Comparison between experiments and calculations for cubic BN is presented to test our method in reproducing all the measured features quantitatively. The LO/TO splitting is well imposed by adding the nonanalytical part deduced from the Born effective charge and macroscopic dielectric constant. Finally, different Raman experiment configurations for $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{C}}_{2}\mathrm{N}$ are discussed.

Testing of the analytical anisotropic algorithm for photon dose calculation

The analytical anisotropic algorithm (AAA) was implemented in the Eclipse (Varian Medical Systems) treatment planning system to replace the single pencil beam (SPB) algorithm for the calculation of dose distributions for photon beams. AAA was developed to improve the dose calculation accuracy, especially in heterogeneous media. The total dose deposition is calculated as the superposition of the dose deposited by two photon sources (primary and secondary) and by an electron contamination source. The photon dose is calculated as a three-dimensional convolution of Monte-Carlo precalculated scatter kernels, scaled according to the electron density matrix. For the configuration of AAA, an optimization algorithm determines the parameters characterizing the multiple source model by optimizing the agreement between the calculated and measured depth dose curves and profiles for the basic beam data. We have combined the acceptance tests obtained in three different departments for 6, 15, and 18 MV photon beams. The accuracy of AAA was tested for different field sizes (symmetric and asymmetric) for open fields, wedged fields, and static and dynamic multileaf collimation fields. Depth dose behavior at different source-to-phantom distances was investigated. Measurements were performed on homogeneous, water equivalent phantoms, on simple phantoms containing cork inhomogeneities, and on the thorax of an anthropomorphic phantom. Comparisons were made among measurements, AAA, and SPB calculations. The optimization procedure for the configuration of the algorithm was successful in reproducing the basic beam data with an overall accuracy of 3%, 1 mm in the build-up region, and 1%, 1 mm elsewhere. Testing of the algorithm in more clinical setups showed comparable results for depth dose curves, profiles, and monitor units of symmetric open and wedged beams below dmax. The electron contamination model was found to be suboptimal to model the dose around dmax, especially for physical wedges at smaller source to phantom distances. For the asymmetric field verification, absolute dose difference of up to 4% were observed for the most extreme asymmetries. Compared to the SPB, the penumbra modeling is considerably improved (1%, 1 mm). At the interface between solid water and cork, profiles show a better agreement with AAA. Depth dose curves in the cork are substantially better with AAA than with SPB. Improvements are more pronounced for 18 MV than for 6 MV. Point dose measurements in the thoracic phantom are mostly within 5%. In general, we can conclude that, compared to SPB, AAA improves the accuracy of dose calculations. Particular progress was made with respect to the penumbra and low dose regions. In heterogeneous materials, improvements are substantial and more pronounced for high (18 MV) than for low (6 MV) energies.

On the definition of the effectively unpaired electron density matrix: A similarity measure approach

The mathematical concepts of similarity and distance in metric spaces are used to relate Takatsuka et al. and Head-Gordon definitions of the effectively unpaired electron density matrix. This approach opens the possibility of new suitable definitions of this quantity to given purposes.

Effects of geometry and impurities on quantum rings in magnetic fields

We investigate the effects of impurities and changing ring geometry on the energetics of quantum rings under different magnetic field strengths. We show that as the magnetic field and/or the electron number are/is increased, both the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become insensitive to whether the ring is circular or square in shape. This is in qualitative agreement with experiments. However, we also find that the Aharonov-Bohm oscillation can be greatly phase shifted by only a few impurities and can be completely obliterated by a high level of impurity density. In the many-electron calculations we use a recently developed fourth-order imaginary time projection algorithm that can exactly compute the density matrix of a free electron in a uniform magnetic field.

Current–voltage curves for molecular junctions computed using all-electron basis sets

We present current–voltage ( I– V) curves computed using all-electron basis sets on the conducting molecule. The all-electron results are very similar to previous results obtained using effective core potentials (ECP). A hybrid integration scheme is used that keeps the all-electron calculations cost competitive with respect to the ECP calculations. By neglecting the coupling of states to the contacts below a fixed energy cutoff, the density matrix for the core electrons can be evaluated analytically. The full density matrix is formed by adding this core contribution to the valence part that is evaluated numerically. Expanding the definition of the core in the all-electron calculations significantly reduces the computational effort and, up to biases of about 2 V, the results are very similar to those obtained using more rigorous approaches. The convergence of the I– V curves and transmission coefficients with respect to basis set is discussed. The addition of diffuse functions is critical in approaching basis set completeness.

Density matrix calculations of gaseous and adsorbate dynamics in electronically excited molecular systems

AbstractThis contribution deals with two approaches for localized phenomena in excited many‐atom systems. The first approach develops a quantum quasi‐classical treatment for the density operator, including all atoms. It is based on a partial Wigner representation and is illustrated with applications to photodissociation of NaI, and to light emission of excited Li interacting with a He cluster. This second application describes the direct dynamics with a time‐dependent electronic density matrix, expanded in a basis set of atomic functions. It shows that such an approach can deal with electronically excited many‐atom systems involving tens of quantum states and hundreds of classical variables. The second approach makes use of the reduced density operator description for a system in a medium. This allows for dissipative dynamics, which can be instantaneous or delayed. An application is presented for femtosecond photodesorption using a Markovian dissipation and construction of the density operator from density amplitudes, for CO/Cu(001). A second application of a reduced density operator has been made to vibrational relaxation of adsorbates, solving integrodifferential equations to compare delayed, instantaneous, and Markovian dissipation. It is concluded that delayed dissipation is needed at short times and that a Markovian treatment is suitable for the interpretation of cross‐sectional measurements that involve long‐term dynamics. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Interchain interactions in charged diacetylenic oligomers carrying bulk substituents revisited

We are studying how the electronic properties of an aggregate, built with conjugated oligomers carrying bulk substituents, are affected by intermolecular interactions. In this paper we apply the CEO (Collective Electronic Oscillator) method, on the basis of the semiempirical INDO/S Hamiltonian, to compute the electronic density matrix modifications following the photon absorption in a doubly charged cluster of two units of a fully carbazolyl-substituted oligodiacetylene tetramer, taken as a model system. The picture that had emerged from our previous calculations based on the less sophisticated CIS (Configuration Interaction including Singles) approach is seen to be confirmed. Despite the large separation between the backbones, a through-space charge transfer occurs between the two oligomers due to the fact that the excess charge, contrary to what is generally believed, is not localized on the conjugated backbone, but is spread out over the carbazolyl moieties of the charged molecule. Consideration of this kind of interaction improves the theoretical results obtained for the isolated charged oligomer chain, and aids in better explaining some features of the experimental photoinduced spectra of the corresponding polymer.

A reduced density-matrix theory of absorption line shape of molecular aggregate

A theory for the absorption line shape of molecular aggregates in condensed phase is formulated based on a reduced density-matrix approach. Intermolecular couplings in the aggregates are assumed to be weak (Förster type of energy transfer mechanism). The spin-Boson model is employed to include the effect of electron-phonon coupling. Using the projection operator technique, we derive kinetic equations for the reduced electronic density matrix associated with the absorption spectrum. General expressions of time-dependent rate constants in the kinetic equations are derived by using the cumulant expansion technique. The resulting time-dependent kinetic equations are solved numerically. We illustrate the applicability of the present theory by calculating the line shape of a dimer (a pair of donor and acceptor of energy transfer). For a J-aggregate type of molecular pair (with excitonic redshift), a tail appears on the blue side of the absorption spectrum due to the existence of inhomogeneity in electronic state mixing which is originated from the electron-phonon coupling.

Casimir-Polder forces: A nonperturbative approach

Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.

Atoms near Magnetodielectric Bodies: van der Waals Energy and the Casimir–Polder Force

Based on macroscopic QED in linear, causal media, a consistent theory for the Casimir-Polder force acting on an atom positioned near dispersing and absorbing magnetodielectric bodies is presented. The perturbative result for the van der Waals energy is shown to exhibit interesting new features in the presence of magnetodielectric bodies. To go beyond perturbation theory, we start with the center-of-mass equation of motion and derive a dynamical expression for the Casimir-Polder force acting on an atom prepared in an arbitrary electronic state. For a nondriven atom in the weak coupling regime, the force as a function of time is shown to be a superposition of force components that are related to the electronic density matrix elements at a chosen time. These force components depend on the position-dependent polarizability of the atom, which correctly accounts for the body-induced level shifts and broadenings.

Nuclear moments and electron density matrices in atoms

AbstractAn electron density matrix approach for the determination of nuclear multipole moments is presented. The electronic matrix elements entering the expressions of the experimentally observed hyperfine coupling constants of atoms are expressed as functionals of the electron charge or spin density matrices. In principle, the calculation of these functionals could be made using any (relativistic or not) molecular orbital (MO) or DFT method. The electronic matrix elements for all possible hyperfine interaction operators, including the yet unobserved magnetic octupole couplings, are considered. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Technique for incorporating the density functional Hessian into the geometry optimization of biomolecules, solvated molecules, and large floppy molecules.

Traditional geometry optimization methods require the gradient of the potential surface, together with a Hessian which is often approximated. Approximation of the Hessian causes difficulties for large, floppy molecules, increasing the number of steps required to reach the minimum. In this article, the costly evaluation of the exact Hessian is avoided by expanding the density functional to second order in both the nuclear and electronic variables, and then searching for the minimum of the quadratic functional. The quadratic search involves the simultaneous determination of both the geometry step and the associated change in the electron density matrix. Trial calculations on Taxol indicate that the cost of the quadratic search is comparable to the cost of the density functional energy plus gradient. While this procedure circumvents the bottleneck coupled-perturbed step in the evaluation of the full Hessian, the second derivatives of the electron-repulsion integrals are still required for atomic-orbital-based calculations, and they are presently more expensive than the energy plus gradient. Hence, we anticipate that the quadratic optimizer will initially find application in fields in which existing optimizers breakdown or are inefficient, particularly biochemistry and solvation chemistry.

Hybrid Ab-Initio/Empirical Molecular Dynamics: Combining the ONIOM Scheme with the Atom-Centered Density Matrix Propagation (ADMP) Approach

A new methodology to perform hybrid empirical/ab-initio molecular dynamics is presented. The method combines the well-established hybrid ONIOM scheme with the recently developed ADMP (Atom-Centered Density Matrix Propagation) approach, where the one electron density matrix expanded in an atom-centered Gaussian basis set is propagated as electronic variables along with the classical nuclear degrees of freedom via an extended Lagrangian procedure. The unified and single-valued ONIOM expressions for the energy and energy derivatives allow for an implementation of conservative dynamics. It is found that atom-centered basis sets large enough to provide good chemical accuracy can be used even when electronic embedding is adopted in the QM/MM scheme, and this does not affect the well-behaved and conservative nature of the dynamics. The method contains very appealing features for the study of biological systems, including the ability to employ accurate density functionals, the freedom to choose a periodic or a cluster boundary condition for the system under study, asymptotic O(N) scaling through established techniques, and the ability to use reasonably large time-steps through the tensorial fictitious mass scheme. The general ADMP/ONIOM formalism is illustrated through a series of test calculations. A simulated study of proton hopping inside the gramicidin A ion channel is also presented, to show the potential of the method in describing reactivity in large systems.

Electron Density Calculation Using the Contact Block Reduction Method

A novel efficient method to calculate the ballistic quantum transport in two or three dimensional multi-terminal devices of arbitrary geometry, potential profile and number of leads has been presented. In this work we show that the method termed contact block reduction (CBR) allows calculation of not only the transmission function, but the electron density and density matrix of the device as well. The calculation costs are mainly determined by the size of the contact boundaries of the device.

Introductory lecture: nonadiabatic effects in chemical dynamics.

Recent progress in the theoretical treatment of electronically nonadiabatic processes is discussed. First we discuss the generalized Born-Oppenheimer approximation, which identifies a subset of strongly coupled states, and the relative advantages and disadvantages of adiabatic and diabatic representations of the coupled surfaces and their interactions are considered. Ab initio diabatic representations that do not require tracking geometric phases or calculating singular nonadiabatic nuclear momentum coupling will be presented as one promising approach for characterizing the coupled electronic states of polyatomic photochemical systems. Such representations can be accomplished by methods based on functionals of the adiabatic electronic density matrix and the identification of reference orbitals for use in an overlap criterion. Next, four approaches to calculating or modeling electronically nonadiabatic dynamics are discussed: (1) accurate quantum mechanical scattering calculations, (2) approximate wave packet methods, (3) surface hopping, and (4) self-consistent-potential semiclassical approaches. The last two of these are particularly useful for polyatomic photochemistry, and recent refinements of these approaches will be discussed. For example, considerable progress has been achieved in making the surface hopping method more applicable to the study of systems with weakly coupled electronic states. This includes introducing uncertainty principle considerations to alleviate the problem of classically forbidden surface hops and the development of an efficient sampling algorithm for low-probability events. A topic whose central importance in a number of quantum mechanical fields is becoming more widely appreciated is the introduction of decoherence into the quantal degrees of freedom to account for the effect of the classical treatment on the other degrees of freedom, and we discuss how the introduction of such decoherence into a self-consistent-potential approximation leads to a reasonably accurate but very practical trajectory method for electronically nonadiabatic processes. Finally, the performances of several dynamical methods for Landau-Zener-type and Rosen-Zener-Demkov-type reactive scattering problems are compared.

Many-body effects in molecular photoionization in intense laser fields; time-dependent Hartree-Fock simulations.

The time evolution of the reduced single electron density matrix for eight electrons in a one-dimensional finite box potential driven by an intense laser field is calculated by numerically integrating the time-dependent Hartree-Fock equations. We study the effects of the Coulomb interaction, field intensity, and frequency on the time profile of the ionization process. Our computed saturation ionization intensity (Isat) is in good agreement with experimental results for decatetraene [Ivanov et al. J. Chem. Phys. 117, 1575 (2002)].

Transferable group contributions for a variety of chemical phenomena and compounds

An approximate method for calculating molecular electrostatic potential (MEP) maps and atomic point charge models for large molecules in a reduced computational time is proposed and tested for two widely used basis sets (STO-3G and 6–31G*). The method avoids the molecular orbital calculation of the whole system by expressing its first order electronic density matrix in terms of transferable localized orbitals (TLO), previously determined on model molecules, via a localization process followed by the cutting of the tails, and stored in two databases (one for each basis set). For systems with a canonic electronic structure TLO are made of a single vector, involving either two nuclei (to describe the covalent bond between those atoms) or one nucleus (to describe lone pairs and inner shells). Conversely, delocalized π systems require many-center TLO, formed by a suitable number of vectors. Density functions of large chemical compounds can thus be built up automatically from a code that recognizes which fragments are contained in the system of interest, extracts them from the chosen database, reorders the atoms consistently with the pertinent TLO and places them in the correct position and orientation on the relevant atoms. A great number of chemical groups were parameterized and the efficiency of the method was evaluated on different systems, including aliphatic hydrocarbons. Numerical calculations on several molecules revealed that this approximation brought no significant loss of accuracy with respect to the corresponding Hartree-Fock (HF) values for the examined properties. Although the method is specifically designed to produce approximate wavefunctions, the point charge models obtained by fitting the corresponding MEP represent a viable alternative when ab initio HF calculations are not affordable, and can be used in connection with any popular force field.