L. J. Sham

Bio: L. J. Sham is an academic researcher from University of California, San Diego. The author has contributed to research in topics: Quantum dot & Spin polarization. The author has an hindex of 71, co-authored 333 publications receiving 60693 citations. Previous affiliations of L. J. Sham include Bell Labs & Lawrence Berkeley National Laboratory.

Self-Consistent Equations Including Exchange and Correlation Effects

Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.

Density-Functional Theory of the Energy Gap

Abstract: The energy-band gap of an insulator is obtained from the eigenvalues of the one-particle density-functional equation for the ground state and a finite correction due to the discontinuity of the functional derivative of the exchange and correlation energy. This correction is expressed in terms of the improper self-energy and the density-functional exchange-correlation potential. It is evaluated for a two-plane-wave model including exchange only.

Self-energy operators and exchange-correlation potentials in semiconductors

Abstract: We show how the density-functional theory (DFT) exchange-correlation potential ${V}_{\mathrm{xc}(\mathrm{r}}$) of a semiconductor is calculated from the self-energy operator \ensuremath{\Sigma}(r,r',\ensuremath{\omega}), and how \ensuremath{\Sigma} is obtained using the one-particle Green's function and the screened Coulomb interaction (the GW approximation). We discuss the nature of ${V}_{\mathrm{xc}}$ and the self-energy in real space, and investigate features and trends found in Si, GaAs, AlAs, and diamond. In each case the calculated quasiparticle band structure is in good agreement with experiment, while the DFT band structure is surprisingly similar to that with the common local-density approximation (LDA); in particular, about 80% of the severe LDA band-gap error is shown to be inherent in DFT calculations, being accounted for by the discontinuity \ensuremath{\Delta} in ${V}_{\mathrm{xc}}$ upon addition of an electron. The relationship of the calculated ${V}_{\mathrm{xc}}$ to the LDA and its extensions is also examined.

An All-Optical Quantum Gate in a Semiconductor Quantum Dot

Abstract: We report coherent optical control of a biexciton (two electron-hole pairs), confined in a single quantum dot, that shows coherent oscillations similar to the excited-state Rabi flopping in an isolated atom The pulse control of the biexciton dynamics, combined with previously demonstrated control of the single-exciton Rabi rotation, serves as the physical basis for a two-bit conditional quantum logic gate The truth table of the gate shows the features of an all-optical quantum gate with interacting yet distinguishable excitons as qubits Evaluation of the fidelity yields a value of 07 for the gate operation Such experimental capability is essential to a scheme for scalable quantum computation by means of the optical control of spin qubits in dots

One-particle properties of an inhomogeneous interacting electron gas.

Abstract: In previous publications (especially by Hohenberg, Kohn, and Sham), a theory of the ground state of an inhomogeneous interacting electron gas was developed, in which the electronic density $n(\mathrm{r})$ played a dominant role. The present paper extends this approach to the one-particle Green's function and physical properties related to it, such as single-particle-like excitations and, in the case of metals, the Fermi surface. The Dyson mass operator $\ensuremath{\Sigma}$ is studied as a function of its spatial arguments and as a functional of $n(\mathrm{r})$, and, in both senses, it is found to have important short-range properties. An approximation for $\ensuremath{\Sigma}$, which is exact for systems of slowly varying density, is proposed. This leads to simple, explicit, Schr\"odinger-like equations for the single-particle-like excitations, whose solution determines their energies and lifetimes. In particular, we show how to apply this procedure to metals.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Semiempirical GGA-type density functional constructed with a long-range dispersion correction.

Abstract: A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.