The limitations of Slater's element-dependent exchange functional from analytic density functional theory

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density and the one body effective potential of density functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method,where variationality then refers to the error in each two electron integral and not to the total energy. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in the Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gaspar-Kohn-Sham exchange-correlation potential around each atom in the system. Of several ways of choosing the scaling factors (Slater's exchange parameters), two most obvious are the Hartree-Fock (HF), alpha_HF, values and the exact atomic, alpha_EA, values. The performance of this simple analytic model with both sets for atomization energies of G2 set of 148 molecules is better than the local density approximation or the HF theory, although the errors in atomization energy are larger than the target chemical accuracy. To improve peformance for atomization energies, the SR method is reparametrized to give atomization energies of 148 molecules to be comparbale to those obtained by one of the most widely used generalized gradient approximations. The mean absolute error in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 Angstrom. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.Comment: 33 pages, Uses RevTex, to appear in The Journal of Chemical Physic

Exchange coupling between silicon donors: the crucial role of the central cell and mass anisotropy

Donors in silicon are now demonstrated as one of the leading candidates for implementing qubits and quantum information processing. Single qubit operations, measurements and long coherence times are firmly established, but progress on controlling two qubit interactions has been slower. One reason for this is that the inter donor exchange coupling has been predicted to oscillate with separation, making it hard to estimate in device designs. We present a multivalley effective mass theory of a donor pair in silicon, including both a central cell potential and the effective mass anisotropy intrinsic in the Si conduction band. We are able to accurately describe the single donor properties of valley-orbit coupling and the spatial extent of donor wave functions, highlighting the importance of fitting measured values of hyperfine coupling and the orbital energy of the $1s$ levels. Ours is a simple framework that can be applied flexibly to a range of experimental scenarios, but it is nonetheless able to provide fast and reliable predictions. We use it to estimate the exchange coupling between two donor electrons and we find a smoothing of its expected oscillations, and predict a monotonic dependence on separation if two donors are spaced precisely along the [100] direction.Comment: Published version. Corrected b and B values from previous versio

Truth and tractability: compromising between accuracy and computational cost in quantum computational chemistry methods for noncovalent interactions and metal-salen catalysis

Computational chemists are concerned about two aspects when choosing between the myriad of theoretical methodologies: the accuracy (the "truth") and the computational cost (the tractability). Among the least expensive methods are the Hartree-Fock (HF), density functional theory (DFT), and second-order Moller-Plesset perturbation theory (MP2) methods. While each of these methods yield excellent results in many cases, the inadequate inclusion of certain types of electron correlation (either high-orders or nondynamical) can produce erroneous results. The compromise for the computation of noncovalent interactions often comes from empirically scaling DFT and/or MP2 methods to fit benchmark data sets. The DFT method with an empirically fit dispersion term (DFT-D) often yields semi-quantitative results. The spin-component scaled MP2 (SCS-MP2) method parameterizes the same- and opposite-spin correlation energies and often yields less than 20% error for prototype noncovalent systems compared to chemically accurate CCSD(T) results. There is no simple fix for cases with a large degree of nondynamical correlation (such as transition metal-salen complexes). While testing standard and new DFT functionals on the spin-state energy gaps of transition metal-salen complexes, no DFT method produced reliable results compared to very robust CASPT3 results. Therefore each metal-salen complex must be evaluated on a case-by-case basis to determine which methods are the most reliable. Utilizing a combination of DFT-D and SCS-MP2 methods, the reaction mechanism for the addition of cyanide to unsaturated imides catalyzed by the Al(Cl)-salen complex was performed. Various experimental observations are rationalized through this mechanism.Ph.D.Committee Chair: Sherrill, C. David; Committee Member: Bredas, Jean-luc; Committee Member: Brown, Kenneth; Committee Member: Ludovice, Peter; Committee Member: Orlando, Thoma

A comparison between quantum chemistry and quantum Monte Carlo techniques for the adsorption of water on the (001) LiH surface

We present a comprehensive benchmark study of the adsorption energy of a single water molecule on the (001) LiH surface using periodic coupled cluster and quantum Monte Carlo theories. We benchmark and compare different implementations of quantum chemical wave function based theories in order to verify the reliability of the predicted adsorption energies and the employed approximations. Furthermore we compare the predicted adsorption energies to those obtained employing widely-used van der Waals density-functionals. Our findings show that quantum chemical approaches are becoming a robust and reliable tool for condensed phase electronic structure calculations, providing an additional tool that can also help in potentially improving currently available van der Waals density-functionals

Consistent Scenarios for Cosmic-Ray Excesses from Sommerfeld-Enhanced Dark Matter Annihilation

Anomalies in direct and indirect detection have motivated models of dark matter consisting of a multiplet of nearly-degenerate states, coupled by a new GeV-scale interaction. We perform a careful analysis of the thermal freezeout of dark matter annihilation in such a scenario. We compute the range of "boost factors" arising from Sommerfeld enhancement in the local halo for models which produce the correct relic density, and show the effect of including constraints on the saturated enhancement from the cosmic microwave background (CMB). We find that boost factors from Sommerfeld enhancement of up to ~800 are possible in the local halo. When the CMB bounds on the saturated enhancement are applied, the maximal boost factor is reduced to ~400 for 1-2 TeV dark matter and sub-GeV force carriers, but remains large enough to explain the observed Fermi and PAMELA electronic signals. We describe regions in the DM mass-boost factor plane where the cosmic ray data is well fit for a range of final states, and show that Sommerfeld enhancement alone is enough to provide the large annihilation cross sections required to fit the data, although for light mediator masses (less than ~200 MeV) there is tension with the CMB constraints in the absence of astrophysical boost factors from substructure. Additionally, we consider the circumstances under which WIMPonium formation is relevant and find for heavy WIMPs (greater than ~2 TeV) and soft-spectrum annihilation channels it can be an important consideration; we find regions with dark matter mass greater than 2.8 TeV that are consistent with the CMB bounds and have ~600-700 present-day boost factors.Comment: Related web application at http://astrometry.fas.harvard.edu/mvogelsb/sommerfeld . v2: added brief clarification regarding propagation parameters, plots now show effect of relaxing CMB bounds. 35 pages in JCAP format, 4 figures. Accepted for publication in JCA