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Adam Wasserman

Publications and source records attributed to Adam Wasserman.

At least 37 records · Page 2Linked to original sources
arXiv2015

Time-dependent Electronic Populations in Fragment-based Time-dependent Density Functional Theory

Conceiving a molecule as composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences, and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient algorithms can be proposed to address problems in the description of chemical bond formation and breaking. We present a formally exact time-dependent density-functional theory for the electronic dynamics of molecular fragments with variable number of electrons. This new formalism is an extension of previous work [Phys. Rev. Lett. {\bf 111}, 023001 (2013)]. We also introduce a stable density-inversion method that is applicable to time-dependent and ground-state density-functional theory, and their extensions, including those discussed in this work.

physics.chem-ph↗
arXiv2014

Integer Discontinuity of Density Functional Theory

Density functional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a non-integer number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any density functional approximation. Our formalism derives from a formula for the exact energy functional and a new constrained search functional that recovers the linear dependence of the energy on the number of electrons.

physics.chem-ph↗
arXiv2013

Stark Ionization of Atoms and Molecules within Density Functional Resonance Theory

We show that the energetics and lifetimes of resonances of finite systems under an external electric field can be captured by Kohn--Sham density functional theory (DFT) within the formalism of uniform complex scaling. Properties of resonances are calculated self-consistently in terms of complex densities, potentials and wavefunctions using adapted versions of the known algorithms from DFT. We illustrate this new formalism by calculating ionization rates using the complex-scaled local density approximation and exact exchange. We consider a variety of atoms (H, He, Li and Be) as well as the hydrogen molecule. Extensions are briefly discussed.

cond-mat.mtrl-sci↗
arXiv2013

Fragment-based Time-dependent Density-functional Theory

Using the Runge-Gross theorem that establishes the foundation of Time-dependent Density Functional Theory (TDDFT) we prove that for a given electronic Hamiltonian, choice of initial state, and choice of fragmentation, there is a unique single-particle potential (dubbed time-dependent partition potential) which, when added to each of the pre-selected fragment potentials, forces the fragment densities to evolve in such a way that their sum equals the exact molecular density at all times. This uniqueness theorem suggests new ways of computing time-dependent properties of electronic systems via fragment-TDDFT calculations. We derive a formally exact relationship between the partition potential and the total density, and illustrate our approach on a simple model system for binary fragmentation in a laser field.

physics.chem-ph↗
arXiv2012

Density Functional Resonance Theory: complex density functions, convergence, orbital energies, and functionals

Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett. \textbf{107}, 163002 (2011)], a recently developed complex-scaled version of ground-state Density Functional Theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, $θ$. In Kohn-Sham DFRT, it is shown that almost all $θ$-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to a physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling constant system.

quant-ph↗
arXiv2011

Density Functional Theory for Fractional Particle Number: Derivative Discontinuity of the Energy at the Maximum Number of Bound Electrons

The derivative discontinuity in the exact exchange-correlation potential of ensemble Density Functional Theory (DFT) is investigated at the specific integer number that corresponds to the maximum number of bound electrons, $J_{max}$. A recently developed complex-scaled analog of DFT is extended to fractional particle numbers and used to study ensembles of both bound and metastable states. It is found that the exact exchange-correlation potential experiences discontinuous jumps at integer particle numbers including $J_{max}$. For integers below $J_{max}$ the jump is purely real because of the real shift in the chemical potential. At $J_{max}$, the jump has a non-zero imaginary component reflecting the finite lifetime of the $(J_{max}+1)$ state.

quant-ph↗
arXiv2011

Molecular Binding Energies from Partition Density Functional Theory

Approximate molecular calculations via standard Kohn-Sham Density Functional Theory are exactly reproduced by performing self-consistent calculations on isolated fragments via Partition Density Functional Theory [Phys. Rev. A 82, 024501 (2010)]. We illustrate this with the binding curves of small diatomic molecules. We find that partition energies are in all cases qualitatively similar and numerically close to actual binding energies. We discuss qualitative features of the associated partition potentials.

cond-mat.other↗
arXiv2011

Density Functional Resonance Theory of Unbound Electronic Systems

Density Functional Resonance Theory (DFRT) is a complex-scaled version of ground-state Density Functional Theory (DFT) that allows one to calculate the resonance energies and lifetimes of metastable anions. In this formalism, the exact energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex "density" that can be obtained via complex-coordinate scaling. This complex density is used as the primary variable in a DFRT calculation just as the ground-state density would be used as the primary variable in DFT. As in DFT, there exists a mapping of the N-electron interacting system to a Kohn-Sham system of N non-interacting particles in DFRT. This mapping facilitates self consistent calculations with an initial guess for the complex density, as illustrated with an exactly-solvable model system. Whereas DFRT yields in principle the exact resonance energy and lifetime of the interacting system, we find that neglecting the complex-correlation contribution leads to errors of similar magnitude to those of standard scattering close-coupling calculations under the bound-state approximation.

quant-ph↗
arXiv2009

Resonance Lifetimes from Complex Densities

The ab-initio calculation of resonance lifetimes of metastable anions challenges modern quantum-chemical methods. The exact lifetime of the lowest-energy resonance is encoded into a complex "density" that can be obtained via complex-coordinate scaling. We illustrate this with one-electron examples and show how the lifetime can be extracted from the complex density in much the same way as the ground-state energy of bound systems is extracted from its ground-state density.

cond-mat.other↗
arXiv2009

Partition Density Functional Theory

Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment densities. An example is given and consequences discussed.

cond-mat.other↗
arXiv2008

Charge Transfer in Partition Theory

The recently proposed Partition Theory (PT) [J.Phys.Chem.A 111, 2229 (2007)] is illustrated on a simple one-dimensional model of a heteronuclear diatomic molecule. It is shown that a sharp definition for the charge of molecular fragments emerges from PT, and that the ensuing population analysis can be used to study how charge redistributes during dissociation and the implications of that redistribution for the dipole moment. Interpreting small differences between the isolated parts' ionization potentials as due to environmental inhomogeneities, we gain insight into how electron localization takes place in H2+ as the molecule dissociates. Furthermore, by studying the preservation of the shapes of the parts as different parameters of the model are varied, we address the issue of transferability of the parts. We find good transferability within the chemically meaningful parameter regime, raising hopes that PT will prove useful in chemical applications.

cond-mat.other↗
arXiv2007

Time-dependent Density Functional calculation of e-H scattering

Phase shifts for single-channel elastic electron-atom scattering are derived from time-dependent density functional theory. The H$^-$ ion is placed in a spherical box, its discrete spectrum found, and phase shifts deduced. Exact-exchange yields an excellent approximation to the ground-state Kohn-Sham potential, while the adiabatic local density approximation yields good singlet and triplet phase shifts.

cond-mat.mtrl-sci↗
arXiv2007

Investigating interaction-induced chaos using time-dependent density functional theory

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbour level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.

cond-mat.other↗
arXiv2007

Partition theory: A very simple illustration

We illustrate the main features of a recently proposed method based on ensemble density functional theory to divide rigorously a complex molecular system into its parts [M.H. Cohen and A. Wasserman, J. Phys. Chem. A 111, 2229 (2007)]. The illustrative system is an analog of the hydrogen molecule for which analytic expressions for the densities of the parts (hydrogen "atoms") are found along with the "reactivity potential" that enters the theory. While previous formulations of Chemical Reactivity Theory lead to zero, or undefined, values for the chemical hardness of the isolated parts, we demonstrate they can acquire a finite and positive hardness within the present formulation.

cond-mat.other↗
arXiv2006

Hohenberg-Kohn theorem for the lowest-energy resonance of unbound systems

We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT) can be extended to the lowest-energy resonance of unbound systems. Using the Gel'fand Levitan theorem, the extended version of the HKT can also be applied to systems that support a finite number of bound states. The extended version of the HKT provides an adequate framework to carry out DFT calculations of negative electron affinities.

cond-mat.other↗
arXiv2005

Rydberg transition frequencies from the Local Density Approximation

A method is given that extracts accurate Rydberg excitations from LDA density functional calculations, despite the short-ranged potential. For the case of He and Ne, the asymptotic quantum defects predicted by LDA are in less than 5% error, yielding transition frequency errors of less than 0.1eV.

cond-mat.other↗
arXiv2005

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He$^+$ scattering.

cond-mat.other↗