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Latest developments in multiconfigurational range-separated density-functional theory: on many-body perturbation theory and actinide chemistry

Emmanuel Fromager

Center for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, 9037 Tromsø, NORWAY, http://www.ctcc.uit.no/people/manu/

A progress report on the development of multiconfigurational range-separated DFT, simply referred to as short-range DFT (srDFT) in the following, is presented. Two different topics are addressed.

(i) The description of dispersion interaction effects in srDFT by means of self-consistent many-body perturbation theory techniques. A general formalism (i.e.valid for any zeroth-order hamiltonian), which is based on the one-electron reduced density matrix, is proposed for the derivation of computable expressions through any order of perturbation [1]. Two applications are then presented: the derivation of a second-order Moeller-Plesset-type one-electron reduced density matrix and a range-separated optimized effective potential method based on second-order Goerling-Levy-type perturbation theory.

(ii) The application of a Multi-Configurational Self-Consistent Field-srDFT (MCSCF-srDFT) approach to actinide chemistry. We focuse on the neptunyl (VII) NpO2+++ ion which has, according to wave-function theory-based calculations, a linear equilibrium geometry. However, due to significant static correlation effects, standard functionals such as LDA, PBE or B3LYP give an equilibrium geometry that is bent. We address this bending problem within the MCSCF-srDFT approach [2].

References:

[1] E. Fromager and H. J. Aa. Jensen, submitted to Phys. Rev. A (2008). "Self-consistent many-body perturbation theory in range-separated density-functional theory: a one-electron reduced density matrix-based formulation"

[2] E. Fromager, F. Real, P. Waahlin, U. Wahlgren and H. J. Aa. Jensen, to be submitted to J. Chem. Phys. (2008). "On the universality of the long/short-range separation in multiconfigurational density-functional theory. II. Investigating f0 actinide species"

Conical Intersections in TDDFT

Mark E. Casida

Laboratoire de Chimie Théorique, Département de Chimie Molécularie (DCM, UMR CNRS/UJF 5250), Institut de Chimie Moléculaire de Grenoble (ICMG, FR-2607), Université Joseph Fourier (Grenoble I), 301 rue de la Chimie, BP 53, F-38041 Grenoble Cedex 9, FRANCE, mark.casida@ujf-grenoble.fr, http://dcm.ujf-grenoble.fr/PERSONNEL/CT/casida/

Over 20 years ago, Runge and Gross proved that the external potential is determined up to an additive spatially-constant function of time by the time-dependent charge density and the initial wave function (which is itself a functional of thedensity if the system starts in its ground stationary state). [RG84] About a decade ago, the linear response form of time-dependent density-functional theory (LR-TDDFT) was introduced into quantum chemistry as a formally rigorous way to obtain information about excited states [C95] and, with few exceptions, has now become the dominant single-determinant method for treating excited states in medium- and large-sized molecules. This has led to obvious hopes that LR-TDDFT could also be used to model photochemical reactions. [C01] However it became clear in the 1990s that many (if not most)photochemical reactions pass through conical intersections (CXs) and many of these have biradicloid character which is normally not easily described by DFT. In fact, Levine et al. have argued that (S0,S1) CXs cannot occur in TDDFT in the adiabatic approximation. Their reasoning will be reviewed and the results of our investigation of the ability of TDDFT to describe a critical (S0,S1) CX in oxirane will be presented. [CDI+07,TTR+08] Important issues will be raised concerning holes below the Fermi level, how to treat two-electron excitations explicitly, and where a multiconfigurational TDDFT could be useful.

References

[RG84] E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)."Density functional theory for time-dependent systems"

[C95] M.E. Casida in Recent Advances in Density Functional Methods, Part I, D.P. Chong, editor (World Scientific:Singapore, 1995), p. 155."Time-dependent density-functional response theory for molecules"

[C01] M.E. Casida, in Accurate Description of Low-Lying Molecular States and Potential Energy Surfaces, ACS Symposium Series 828, edited by Mark R. Hoffmann and Kenneth G. Dyall (ACS Press: Washington, D.C., 2002), ISBN 0-8412-3792-1, (Proceedings of ACS Symposium, San Diego, Calif., 2001), pp. 199-220."Jacob's ladder for time-dependent density-functional theory: Some rungs on the way to photchemical heaven"

[LKQM06] B.G. Levine, C. Ko, J. Quenneville, and T.J. Martinez, Molec. Phys. 104, 1039 (2006)."Conical intersections and double excitations in time-dependent density functional theory"

[CDI+07] F. Cordova, L.J. Doriol, A. Ipatov, M.E. Casida, C. Filippi, and A. Vela, J. Chem. Phys. 127, 164111 (2007)."Troubleshooting time-dependent density-functional theory for photochemical applications"

[TTR+08] E. Tapavicza, I. Tavernelli, U. Röthlisberger, C. Filippi, and M.E. Casida, in preparation."Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry"

[TDDFT for excited states, book chapter, 2008 |Image:Casida 07042008.pdf]

Range-separation in exponential orbital translation: exchange integrals

Philip E. Hoggan

LASMEA UMR 6602 CNRS, Clermont University, 63177 AUBIERE, FRANCE

Range separation in the sense of Ewald's expression of the Coulomb operator may be applied to exchange integrals over exponential type orbitals (ETOs)[1]. This talk concentrates on integrands which are not analytic closed forms. This is generally the case for exchange integrals involving at least one displaced center. The ETOs must then be translated using expressions derived from the Gegenbauer addition theorem [2]. These lead to the definition of so-called Barnett-Coulson-Loewdin Functions (BCLFs) [3]. Naturally, two ranges are involved (in the expansion), according to whether the electron position variable is greater than or less than the translation parameter 'a' (usually a bond distance, fixed by the molecular geometry). Two problems will be discussed: first, how the BCLFs can be used with Ewald range separation (extension of [1]) and second, how are BCLFs related to single range translation procedures [4].

References:

[1] J. Angyan et al, J. Phys. A. 39 (2006) 8613.

[2] G. N. Watson, A treatise on the Theory of Bessel Functions, CUP, Cambridge, UK, 1944 (see p366).

[3] M.P. Barnett and Coulson. The evaluation of integrals occuring in the theory of molecular structures. Part I and II. Philos. Trans; R. Soc. London, Ser. A, 243 (1951) 221.

[4] BCLFs. P. E. Hoggan and D. Pinchon, Working note. 10 may 2007 (pdf available).

Local range-separated hybrids

Gustavo E. Scuseria

Rice University, USA.

I will discuss the work done by my student Aliaksandr Krukau in collaboration with John Perdew and Andreas Savin. Tom Henderson and Ben Janesko have also made valuable contributions to this project. We are developing range-separated hybrids (for exchange) with a screening parameter w that is a function of space w=w(r), ie, the value of w can be different at each and every point in space. Think of this as an approximation to the microscopic dielectric function that gives the "right answer for the right reason "within a Green's Function approach. Our local-range-separation (LRS) or locally-range-separated hybrid is a frequency independent version of this microscopic dielectric function. The implementation of such a beast is non-trivial and require some key approximations. While the idea of a LRS hybrid is something that Andreas and I have talked about for a long time, we needed John to come up with some crucial ingredient to make this thing realizable. Let me say that simple forms of w(r) based on dimensional analysis yield very promising results. I hope to have lots of data to show you in a few weeks by the time we all meet in Paris. For the details of how one goes around implementing this LRS, you will need to come to my talk!

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