F. G. Eich

Density-matrix-power functional: Performance for finite systems and the homogeneous electron gas

An exchange-correlation energy functional involving fractional power of the one-body reduced density matrix [S. Sharma, J. K. Dewhurst, N. N. Lathiotakis, and E. K. U. Gross, Phys. Rev. B 78, 201103(R) (2008)] is applied to finite systems and to the homogeneous electron gas. The performance of the functional is assessed for the correlation and atomization energies of a large set of molecules and for the correlation energy of the homogeneous electron gas. High accuracy is found for these two very different types of systems.

Transverse spin-gradient functional for noncollinear spin-density-functional theory.

We present a novel functional for spin-density-functional theory aiming at the description of noncollinear magnetic structures. The construction of the functional employs the spin-spiral-wave state of the uniform electron gas as reference system. We show that the functional depends on transverse gradients of the spin magnetization; i.e., in contrast with the widely used local spin density approximation, the functional is sensitive to local changes of the direction of the spin magnetization. As a consequence the exchange-correlation magnetic field is not parallel to the spin magnetization and a local spin torque is present in the ground state of the Kohn-Sham system. As a proof of principle, we apply the functional to a Chromium monolayer in the noncollinear 120°-Néel state.

The adiabatic limit of the exact factorization of the electron-nuclear wave function

We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model of proton-coupled electron transfer in different non-adiabatic regimes.

Transverse and longitudinal gradients of the spin magnetization in spin-density-functional theory

We derive the gradient expansion for the exchange energy of a spin-polarized electron gas by perturbing the uniformly spin polarized state and thus inducing a small non-collinearity that is slowly varying in space. We show that the exchange-energy contribution due to the induced longitudinal gradient of the spin polarization to the exchange energy differs from the contribution due to the transverse gradient. The difference is present at any non-vanishing spin polarization and becomes larger with increasing spin polarization. We argue that improved generalized gradient approximations of Spin-Density-Functional Theory must account for the difference between the longitudinal and transverse spin stiffness.

Density-functional theory of thermoelectric phenomena.

We introduce a nonequilibrium density-functional theory of local temperature and associated local energy density that is suited for the study of thermoelectric phenomena. The theory rests on a local temperature field coupled to the energy-density operator. We identify the excess-energy density, in addition to the particle density, as the basic variable, which is reproduced by an effective noninteracting Kohn-Sham system. A novel Kohn-Sham equation emerges featuring a time-dependent and spatially varying mass which represents local temperature variations. The adiabatic contribution to the Kohn-Sham potentials is related to the entropy viewed as a functional of the particle and energy density. Dissipation can be taken into account by employing linear response theory and the thermoelectric transport coefficients of the electron gas.

Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory

We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative.

Transient Charge and Energy Flow in the Wide-Band Limit

The wide-band limit is a commonly used approximation to analyze transport through nanoscale devices. In this work we investigate its applicability to the study of charge and heat transport through molecular break junctions exposed to voltage biases and temperature gradients. We find by comparative simulations that while the wide-band-limit approximation faithfully describes the long-time charge and heat transport, it fails to characterize the short-time behavior of the junction. In particular, we show that the charge current flowing through the device shows a discontinuity when a temperature gradient is applied, while the energy flow is discontinuous when a voltage bias is switched on and even diverges when the junction is exposed to both a temperature gradient and a voltage bias. We provide an explanation for this pathological behavior and propose two possible solutions to this problem.

U(1)×SU(2) gauge invariance made simple for density functional approximations

A semi-relativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for non-collinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local U(1)

Functional theories of thermoelectric phenomena.

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Temperature-driven transient charge and heat currents in nanoscale conductors

SU(2) gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here, we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple {\it minimal substitution} on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet non-empirical functionals, which do not assume weak inhomogeneity and should therefore have a wide range of applicability in atomic, molecular and condensed matter physics.