arXiv subjects

Morrel H. Cohen

Publications and source records attributed to Morrel H. Cohen.

At least 19 recordsLinked to original sources

arXiv2016

A well-scaling natural orbital theory

We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix.

physics.chem-ph↗

arXiv2015

A favorably-scaling natural-orbital functional theory based on higher-order occupation probabilities

We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The functional derives from a sequence of controlled approximations to the two-particle density matrix. Algebraic scaling of computational cost with electron number is obtainable in general, and Hartree-Fock scaling in the seniority-zero version of the theory. Results obtained with the latter version for saturated small molecular systems are compared with those of highly-accurate quantum-chemical computations. The numerical results are variational, capturing most of the correlation energy from equilibrium to dissociation. Their accuracy is considerably greater than that obtainable with current density-functional theory approximations and with current functionals of the one-particle density matrix only.

physics.chem-ph↗

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

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↗

arXiv2007

Self assembly of a model multicellular organism resembling the Dictyostelium slime molds

The evolution of multicellular organisms from monocellular ancestors represents one of the greatest advances of the history of life. The assembly of such multicellular organisms requires signalling and response between cells: over millions of years these signalling processes have become extremely sophisticated and refined by evolution, such that study of modern organisms may not be able to shed much light on the original ancient processes . Here we are interested in determining how simple a signalling method can be, while still achieving self-assembly. In 2D a coupled cellular automaton/differential equation approach models organisms and chemotaxic chemicals, producing spiralling aggregation. In 3D Lennard-Jones-like particles are used to represent single cells, and their evolution in response to signalling is followed by molecular dynamics. It is found that if a single cell is able to emit a signal which induces others to move towards it, then a colony of single-cell organisms can assemble into shapes as complex as a tower, a ball atop a stalk, or a fast-moving slug. The similarity with the behaviour of modern Dictyostelium slime molds signalling with cyclic adenosine monophosphate (cAMP) is striking.

q-bio.CB↗

arXiv2007

Nanoscale Smoothing and the Analysis of Interfacial Charge and Dipolar Densities

The interface properties of interest in multilayers include interfacial charge densities, dipole densities, band offsets, and screening-lengths, among others. Most such properties are inaccesible to direct measurements, but are key to understanding the physics of the multilayers. They are contained within first-principles electronic structure computations but are buried within the vast amount of quantitative information those computations generate. Thus far, they have been extracted from the numerical data by heuristic nanosmoothing procedures which do not necessarily provide results independent of the smoothing process. In the present paper we develop the theory of nanosmoothing, establishing procedures for both unpolarized and polarized systems which yield interfacial charge and dipole densities and band offsets invariant to the details of the smoothing procedures when the criteria we have established are met. We show also that dipolar charge densities, i. e. the densities of charge transferred across the interface, and screening lengths are not invariant. We illustrate our procedure with a toy model in which real, transversely averaged charge densities are replaced by sums of Gaussians.

cond-mat.mtrl-sci↗

arXiv2005

N-representability and stationarity in time-dependent density functional theory

To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are $N$-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schrödinger equation. The original Runge-Gross (RG) formulation is subsumed within the new formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.

cond-mat.other↗

arXiv2004

Towards a first principles description of phonons in Ni$_{50}$Pt$_{50}$ disordered alloys: the role of relaxation

Using a combination of density-functional perturbation theory and the itinerant coherent potential approximation, we study the effects of atomic relaxation on the inelastic incoherent neutron scattering cross sections of disordered Ni$_{50}$Pt$_{50}$ alloys. We build on previous work, where empirical force constants were adjusted {\it ad hoc} to agree with experiment. After first relaxing all structural parameters within the local-density approximation for ordered NiPt compounds, density-functional perturbation theory is then used to compute phonon spectra, densities of states, and the force constants. The resulting nearest-neighbor force constants are first compared to those of other ordered structures of different stoichiometry, and then used to generate the inelastic scattering cross sections within the itinerant coherent potential approximation. We find that structural relaxation substantially affects the computed force constants and resulting inelastic cross sections, and that the effect is much more pronounced in random alloys than in ordered alloys.

cond-mat.mtrl-sci↗

arXiv2003

Extrinsic models for the dielectric response of CaCu{3}Ti{4}O{12}

The large, temperature-independent, low-frequency dielectric constant recently observed in single-crystal CaCu{3}Ti{4}O{12} is most plausibly interpreted as arising from spatial inhomogenities of its local dielectric response. Probable sources of inhomogeneity are the various domain boundaries endemic in such materials: twin, Ca-ordering, and antiphase boundaries. The material in and neighboring such boundaries can be insulating or conducting. We construct a decision tree for the resulting six possible morphologies, and derive or present expressions for the dielectric constant for models of each morphology. We conclude that all six morphologies can yield dielectric behavior consistent with observations and suggest further experiments to distinguish among them.

cond-mat.mtrl-sci↗

arXiv2002

Classical Langevin Dynamics for Model Hamiltonians

We propose a scheme for extending the model Hamiltonian method developed originally for studying the equilibrium properties of complex perovskite systems to include Langevin dynamics. The extension is based on Zwanzig's treatment of nonlinear generalized Langevin's equations. The parameters entering the equations of motion are to be determined by mapping from first-principles calculations, as in the original model Hamiltonian method. The scheme makes possible, in principle, the study of the dynamics and kinetics of structural transformations inaccessible to the original model Hamiltonian method. Moreover, we show that the equilibrium properties are governed by an effective Hamiltonian which differs from that used in previous work by a term which captures the coherent part of the previously ignored dynamical interaction with the omitted degrees of freedom. We describe how the additional information required for the Langevin equations can be obtained by a minor extension of the previous mapping.

cond-mat.mtrl-sci↗

arXiv2002

Risk and Utility in Portfolio Optimization

Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to alleviate that weakness which, typically, combine utility and risk. We present here a modification of MPT based on the inclusion of separate risk and utility criteria. We define risk as the probability of failure to meet a pre-established investment goal. We define utility as the expectation of a utility function with positive and decreasing marginal value as a function of yield. The emphasis throughout is on long investment horizons for which risk-free assets do not exist. Analytic results are presented for a Gaussian probability distribution. Risk-utility relations are explored via empirical stock-price data, and an illustrative portfolio is optimized using the empirical data.

cond-mat.stat-mech↗

arXiv2002

Lattice dielectric response of CdCu{3}Ti{4}O{12} and of CaCu{3}Ti{4}O{12} from first principles

Structural, vibrational, and lattice dielectric properties of CdCu{3}Ti{4}O{12} are studied using density-functional theory within the local spin-density approximation, and the results are compared with those computed previously for CaCu{3}Ti{4}O{12}. Replacing Ca with Cd is found to leave many calculated quantities largely unaltered, although significant differences do emerge in zone-center optical phonon frequencies and mode effective charges. The computed phonon frequencies of CdCu{3}Ti{4}O{12} are found to be in excellent agreement with experiment, and the computed lattice contribution to the intrinsic static dielectric constant (~60) also agrees exceptionally well with a recent optical absorption experiment. These results provide further support for a picture in which the lattice dielectric response is essentially conventional, suggesting an extrinsic origin for the anomalous low-frequency dielectric response recently observed in both materials.

cond-mat.mtrl-sci↗

arXiv2002

Phonons in random alloys: the itinerant coherent-potential approximation

We present the itinerant coherent-potential approximation(ICPA), an analytic, translationally invariant and tractable form of augmented-space-based, multiple-scattering theory in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni_{55} Pd_{45} and Ni_{50} Pt_{50} alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation(CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.

cond-mat.mtrl-sci↗

arXiv2002

A first-principles study of the structure and lattice dielectric response of CaCu{3}Ti{4}O{12}

Structural and electronic properties of CaCu{3}Ti{4}O{12} have been calculated using density-functional theory within the local spin-density approximation. After an analysis of structural stability, zone-center optical phonon frequencies are evaluated using the frozen-phonon method, and mode effective charges are determined from computed Berry-phase polarizations. Excellent agreement between calculated and measured phonon frequencies is obtained; calculated mode effective charges are in poorer agreement with experiment, although they are of the correct order of magnitude; and the lattice contribution to the static dielectric constant is calculated to be ~40. On the basis of these results, various mechanisms are considered for the enormous dielectric response reported in recent experiments. No direct evidence is found for intrinsic lattice or electronic mechanisms, suggesting that increased attention should be given to extrinsic effects.

cond-mat.mtrl-sci↗

arXiv2001

Flat branches and pressure amorphization

After summarizing the phenomenology of pressure amorphization (PA), we present a theory of PA based on the notion that one or more branches of the phonon spectrum soften and flatten with increasing pressure. The theory expresses the anharmonic dynamics of the flat branches in terms of local modes, represented by lattice Wannier functions, which are in turn used to construct an effective Hamiltonian. When the low-pressure structure becomes metastable with respect to the high-pressure equilibrium phase and the relevant branches are sufficiently flat, transformation into an amorphous phase is shown to be kinetically favored because of the exponentially large number of both amorphous phases and reaction pathways. In effect, the critical-size nucleus for the first-order phase transition is found to be reduced to a single unit cell, or nearly so. Random nucleation into symmetrically equivalent local configurations characteristic of the high-pressure structure is then shown to overwhelm any possible domain growth, and an ``amorphous'' structure results.

cond-mat↗

arXiv2000

Monoclinic and triclinic phases in higher-order Devonshire theory

Devonshire theory provides a successful phenomenological description of many cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of the free energy in the polar order parameter. However, the recent discovery of a novel monoclinic ferroelectric phase in the PZT system by Noheda et al. (Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we confirm that the sixth-order Devonshire theory cannot support a monoclinic phase, and consider extensions of the theory to higher orders. We show that an eighth-order theory allows for three kinds of equilibrium phases in which the polarization is confined not to a symmetry axis but to a symmetry plane. One of these phases provides a natural description of the newly observed monoclinic phase. Moreover, the theory makes testable predictions about the nature of the phase boundaries between monoclinic, tetragonal, and rhombohedral phases. A ferroelectric phase of the lowest (triclinic) symmetry type, in which the polarization is not constrained by symmetry, does not emerge until the Devonshire theory is carried to twelfth order. A topological analysis of the critical points of the free-energy surface facilitates the discussion of the phase transition sequences.

cond-mat.mtrl-sci↗

arXiv2000

Theoretical Investigation of Water Formation on Rh and Pt Surfaces

In this report we present a theoretical investigation of the potential-energy diagram for water formation from adsorbed O and H species on Rh(111) and Pt(111) surfaces. The study is based on accurate first-principles calculations applying density-functional theory. Our results are compared to the potential-energy diagram for this reaction inferred from experimental data by Hickman and Schmidt The calculations essentially reproduce the scheme of Hickman and Schmidt for water formation on Rh(111) with the important difference that the OH molecule is significantly more stable than assumed by Hickman and Schmidt. On Pt(111) surfaces, however, the calculations predict a barrier to OH formation very similar to that found on Rh(111). In particular, the calculated barrier to OH formation of about 20 kcal/mol seems to contradict the small 2.5 kcal/mol barrier assumed in the Hickman-Schmidt scheme and the observed large rate of water formation on Pt. A possible explanation for the apparent discrepancy between the large calculated barrier for OH formation on Pt and the experimentally observed rapid formation of water even at low temperatures is that the active sites for water formation on Pt are at "defect" sites and not on the ideally flat terraces. A similar conclusion has been reached by Verheij and Comsa, who did detailed experimental work on water formation on Pt surfaces. Analyzing our results, we develop an explicit picture of the interaction processes governing the formation of OH groups. This picture rationalizes the calculated weak dependence of OH formation on substrate material. An important conclusion from this work is that good catalysts for the partial oxidation of hydrocarbons should resist defect formation at their surfaces.

cond-mat.mtrl-sci↗