Session Q28: Focus Session: New Frontiers in Electronic Structure Theory IV

Predictive Electronic Structure Methods for Model Charge Transfer Systems

Ionization of non-covalent dimers (such as pi-stacked or hydrogen-bonded nucleobases) changes the bonding pattern from non-covalent to covalent, which induces significant structural and spectroscopic changes. The high density of states and open-shell character of the wave functions presents a challenge for ab initio methodology. Robust electronic structure methods will be discussed, and their relative strengths and weaknesses will be demonstrated by examples (water, benzene, uracil cations and their respective dimers).   

Exploiting explicitly correlated electronic structure methods for accurate molecular calculations involving heavy main group elements

Recent advances in explicitly correlated electronic structure methods, namely MP2-F12 and CCSD(T)-F12, have demonstrated significant improvements in accuracy and efficiency due to the much improved convergence with respect to the one-particle basis set. Recent work in our group involving the heavy post-d main group elements will be presented, including new F12-optimized Gaussian basis sets and benchmark molecular calculations.   

Bethe-Salpeter equation without empty electronic states applied to charge-transfer excitations

We present an approach to compute optical absorption spectra of molecules and nanostructures from first principles, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator. This is equivalent to solving the Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on Density Functional Perturbation Theory [1,2]. In this way, full absorption spectra may be obtained with a computational workload comparable to ground state Hartree-Fock calculations. Applications to the description of charge transfer excitations are presented. [1] D.Rocca, D.Lu and G.Galli (submitted) [2] H. Wilson, F. Gygi and G. Galli, Phys. Rev. B , 78, 113303, 2008;H. Wilson, D. Lu, F. Gygi and G. Galli, Phys. Rev. B, 79, 245106,2009.   

Efficient evaluation of dielectric response functions and calculations of ground and excited state properties beyond local Density Functional approaches

A recently developed technique to diagonalize iteratively dielectric matrices [1], is used to carry out efficient, ab-initio calculations of dispersion interactions, and excited state properties of nanostructures. In particular, we present results for the binding energies of weakly bonded molecular crystals [2], obtained at the EXX/RPA level of theory, and for absorption spectra of semiconducting clusters, obtained by an iterative solution of the Bethe-Salpeter equations [3]. We show that the ability to obtain the eigenmodes of dielectric matrices from Density Functional perturbation theory, without computing single particle excited states, greatly improves the efficiency of both EXX/RPA and many body perturbation theory [3,4] calculations and opens the way to large scale computations. [1] H. Wilson, F. Gygi and G. Galli, Phys. Rev. B , 78, 113303, 2008; and H. Wilson, D. Lu, F. Gygi and G. Galli, Phys. Rev. B, 79, 245106, 2009. [2] D. Lu, Y. Li, D. Rocca and G. Galli, Phys. Rev. Lett, 102, 206411, 2009; and Y. Li, D. Lu, V. Nguyen and G. Galli, J. Phys. Chem. C (submitted) [3] D. Rocca, D. Lu and G. Galli, submitted. [4] D. Lu, F. Gygi and G. Galli, Phys. Rev. Lett. 100, 147601, 2008. Work was funded by DOE/Scidac DE-FC02-06ER25794 and DOE/BES DE-FG02-06ER46262.   

Ab-initio calculations of absorption spectra of Si nanostructures using iterative techniques to solve the Bethe-Salpeter Equation

A first principle approach to solve the Bethe Salpeter equation has been recently proposed [1], that does not require the calculation of excited single particle orbitals, and thus opens the way to calculations of absorption spectra of relatively large systems. We show that the efficiency of this approach can be further improved: (i) by exploiting localization properties of the eigenvectors of the dielectric matrix entering the expression of the screened Coulomb interaction; and (ii) by adopting appropriate truncation schemes that allows one to accurately describe the dielectric matrix [2] with a small number of eigenvectors and eigenvalues . Applications to the calculation of absorption spectra of semiconducting clusters and Si nanorods will be presented. [1]D.Rocca, D.Lu and G.galli (submitted) [2]H.Wilson, F.Gygi and G.Galli, Phys. Rev. B 78, 113303 (2008); and H. Wilson, D. Lu, F. Gygi and G. Galli, Phys. Rev. B, 79, 245106, 2009.   

Widths of Autoionizing Resonances from TDDFT

Autoionizing resonances arising from a bound single excitation lying in the continuum can be captured with the usual adiabatic approximations for the exchange-correlation kernel of time-dependent density functional theory, but those arising from a double excitation cannot. We test a recently derived frequency-dependent kernel [Phys. Chem. Chem. Phys. 11, 4655 (2009)] for the width of the He atom 2s$^2$ resonance, and explore the sensitivity on the ground-state approximation used.   

Explicitly-Correlated Electronic-Structure Methods for Single-Reference and Multi-Reference Systems

Predictive computation of energy differences and properties related to them (equilibrium constants, reaction rates, rovibrational spectra) demand convergent series of high-level wave function models in combination with specially-designed basis set sequences. Unfortunately, the use of practical basis sets results in unacceptably-large basis set errors. For example, the mean absolute and maximum basis set error of heats of formations of small closed and open-shell molecules in the HEAT testset are 9.1 and 25.2 kJ/mol when using the correlation-consistent triple-zeta basis set. Reliable predictions of chemical accuracy (defined as 1 kcal/mol = 4.2 kJ/mol) clearly requires more extensive basis sets and computational costs increased by orders of magnitude. The cause of the large basis set errors is fundamental: the qualitatively incorrect behavior of the standard wave functions when electrons approach each other closely. Although carefully designed basis set sequences allow to reduce the basis set error of molecular energies by empirical extrapolation, such approaches are often not reliable and cannot be easily extended to properties. Explicitly correlated R12 wave function methods account for the basis set challenge from first principles. In R12 methods the two-electron basis includes products $f(r_{ij}) |ij \rangle$, where $f(r_{ij})$ is a function of an interelectronic distance that models the short-range correlation of the electrons. The many-electron integrals that appear in explicitly correlated methods are simplified by systematic approximations based on the resolution of the identity (RI). At the MP2 level the use of R12 approach allows to reduce the basis set error by an order of magnitude, with a disproportionately-small increase in computational cost. I will first discuss our recent progress in extension of R12 approach to the highly-accurate coupled-cluster (CC) methods for ground and excited states. The rigorous R12 extension of the CC method is formally straightforward but the resulting equations are immensely complex and are not suited for manual implementation. To derive, manipulate, and implement these equations we employed an automated compiler that can handle the more general algebraic structure of the CC-R12 equations, isolate the special R12 intermediates, factorize the resulting tensor expressions, and generate efficient computer codes. Evaluation of the nonstandard two-electron integrals is also carried out by a high-performance computer code produced by a specialized compiler. These developments have allowed us for the first time to investigate a range of unprecedented ground-state CC-R12 methods through CCSDTQ-R12. Application of these novel methods to small polyatomic molecules results in absolute electronic energies of chemical accuracy and without any extrapolation. A more practical approach to R12 coupled-cluster methods is to introduce explicit correlation by perturbation theory. My group has developed a family of CC-R12 methods that treat geminal terms alone (CCSD(2)$_{\rm R12}$), or in conjunction with triple excitations (CCSD(T)$_{\rm R12}$), in a manner similar the workings of the ``gold standard'' CCSD(T) method. The advantage of the perturbative route is that the standard CC equations are not modified, and technical changes to the MP2-R12 code are minor. We demonstrated that the CCSD(T)$_{\rm R12}$ method is a practical R12 variant of the CCSD(T) method with performance similar to the rigorous CCSD(T)-R12 counterpart. For the aforementioned HEAT example, the use of the CCSD(T)$_{\rm R12}$ method allows to reduce the basis set error to 2.8 kJ/mol in mean absolute sense and to 7.2 kJ/mol at most, all with the same triple-zeta basis set. Thus, the CCSD(T)$_{\rm R12}$ method with only a triple-zeta basis set seems to reach chemical accuracy on average. I will finally discuss how the R12 approach can be applied to any electronic state for which low-order reduced density matrices are available. This development allowed us to couple the R12 method with the multi-reference configuration-interaction (MR-CI) in an efficient and robust manner. Preliminary investigations of potential energy surfaces of hydrogen fluoride and nitrogen molecules at the MRCI singles and doubles indicate that with the universal R12 correction only a double-zeta basis is necessary to compute correlation energies of a quadruple-zeta quality, or better. The proposed R12 correction can in principle be combined with any single- and multi-reference method in use today.   

Resonance Lifetimes from Complex Densities

The \emph{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. Using one and two electron examples, we illustrate a method for extracting the lifetime from the complex density and explore a Kohn-Sham analog for resonances.   

Time-dependent density functional theory for open quantum systems using unitary dynamics

We extend the Runge-Gross theorem for a very general class of Markovian and non-Markovian open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) Time-Dependent Density Functional Theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential, thus placing the interactions between the particles of the system and the coupling to the environment on the same footing. A Markovian bath functional inspired by the theory of nonlinear Schrodinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.   

Importance of cusps in TDDFT

Density cusp is the most prominent feature of Coulombic systems, as the Coulobmic potential is dominately strong at these points. In our recent paper[J. Chem. Phys. 131, 114308(2009)], we discussed how the nuclear cusp determines the asymptotic form of the oscillator strength of ground-state Kohn-Sham systems, and here we apply the analysis to time-dependent systems. By studying 1d model systems with turn-on perturbations both with linear response theory and propagating in real time, we find the density cusp in space generates singularity in time. We discuss the implications of these t-singularities on TDDFT.   

Time-dependent density-functional approach for exciton binding energies

Optical processes in insulators and semiconductors, including excitonic effects, can be described using time-dependent density-functional theory (TDDFT) in linear response, provided one uses suitable long-range exchange-correlation (XC) kernels. We derive a conceptually and computationally simple formalism for calculating exciton binding energies with TDDFT which is convenient for testing different XC kernels. The formalism is based on a linearization of the TDDFT semiconductor Bloch equations within a two-band model and gives rise to an eigenvalue equation in momentum space which directly yields exciton binding energies; these can be accurate even if the underlying Kohn-Sham band gap is not. Exciton binding energies are calculated for several direct-gap semiconductors and insulators using exchange-only and model XC kernels.