Combining linear interpolation with extrapolation methods in range-separated ensemble density functional theory

ABSTRACT The combination of a recently proposed linear interpolation method (LIM), which enables the calculation of weight-independent excitation energies in range-separated ensemble density functional approximations, with the extrapolation scheme of Savin is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter μ when the latter is large. As a result, the extrapolation scheme, which is usually applied to long-range interacting energies, can be adapted straightforwardly to LIM. This extrapolated LIM (ELIM) has been tested on a small test set consisting of He, Be, H2 and HeH+. Relatively accurate results have been obtained for the first singlet excitation energies with the typical μ = 0.4 value. The improvement of LIM after extrapolation is remarkable, in particular for the doubly excited 21Σ+g state in the stretched H2 molecule. Three-state ensemble calculations in H2 also show that ELIM does not necessarily improves relative excitation energies, even though individual excitation energies are more accurate after extrapolation. Finally, an alternative decomposition of the short-range ensemble exchange–correlation energy is proposed in order to correct for ghost-interaction errors in multi-determinant range-separated ensemble density functional theory calculations. The implementation and calibration of such a scheme are currently in progress.

[1]  A K Theophilou,et al.  The energy density functional formalism for excited states , 1979 .

[2]  G. Paragi,et al.  Investigation of exchange-correlation potentials in ensemble density functional theory: parameter fitting and excitation energy , 2001 .

[3]  K. Pernal,et al.  Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle , 2013 .

[4]  A. Savin,et al.  Short-Range Exchange-Correlation Energy of a Uniform Electron Gas with Modified Electron-Electron Interaction , 2004, cond-mat/0611559.

[5]  E. Gross,et al.  Spurious interactions, and their correction, in the ensemble-Kohn-Sham scheme for excited States. , 2002, Physical review letters.

[6]  M. E. Casida,et al.  Progress in time-dependent density-functional theory. , 2011, Annual review of physical chemistry.

[7]  Oliveira,et al.  Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom. , 1988, Physical review. A, General physics.

[8]  Saverio Moroni,et al.  Local-spin-density functional for multideterminant density functional theory , 2006 .

[9]  Á. Nagy.  Local ensemble exchange potential , 1996 .

[10]  A. Savin,et al.  Excitation energies along a range-separated adiabatic connection. , 2014, The Journal of chemical physics.

[11]  E. Baerends,et al.  Excitation energies of dissociating H2: A problematic case for the adiabatic approximation of time-dependent density functional theory , 2000 .

[12]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[13]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[14]  Stefan Knecht,et al.  Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states , 2015, 1504.06477.

[15]  Trygve Helgaker,et al.  Calculating excitation energies by extrapolation along adiabatic connections , 2015 .

[16]  H. Werner,et al.  A short-range gradient-corrected density functional in long-range coupled-cluster calculations for rare gas dimers. , 2005, Physical chemistry chemical physics : PCCP.

[17]  Jorge M. Seminario,et al.  Recent developments and applications of modern density functional theory , 1996 .

[18]  Stefan Knecht,et al.  Multi-configuration time-dependent density-functional theory based on range separation. , 2012, The Journal of chemical physics.

[19]  David E. Woon,et al.  Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties , 1994 .

[20]  Luca Frediani,et al.  The Dalton quantum chemistry program system , 2013, Wiley interdisciplinary reviews. Computational molecular science.

[21]  J. Toulouse,et al.  Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory. , 2013, The Journal of chemical physics.

[22]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[23]  A. Savin,et al.  On degeneracy, near-degeneracy and density functional theory , 1996 .

[24]  Andreas Savin,et al.  Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence , 2006 .

[25]  O. Franck,et al.  Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H2 molecule , 2013, 1308.4596.

[26]  P. Gori-Giorgi,et al.  A short-range correlation energy density functional with multi-determinantal reference , 2005, physics/0611200.

[27]  M. Filatov,et al.  Ensemble density functional theory method correctly describes bond dissociation, excited state electron transfer, and double excitations. , 2015, The Journal of chemical physics.

[28]  Andreas Savin,et al.  Towards a systematic way to correct density functional approximations. , 2014, The Journal of chemical physics.

[29]  Michael Filatov,et al.  Spin‐restricted ensemble‐referenced Kohn–Sham method: basic principles and application to strongly correlated ground and excited states of molecules , 2015 .

[30]  Walter Thiel,et al.  Assessment of approximate computational methods for conical intersections and branching plane vectors in organic molecules. , 2014, The Journal of chemical physics.

[31]  Ensemble density variational methods with self- and ghost-interaction-corrected functionals. , 2014, The Journal of chemical physics.

[32]  E. Gross,et al.  Time-dependent density functional theory. , 2004, Annual review of physical chemistry.

[33]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[34]  Julien Toulouse,et al.  On the universality of the long-/short-range separation in multiconfigurational density-functional theory. , 2007, The Journal of chemical physics.

[35]  Á. Nagy.  Optimized potential method for ensembles of excited states , 1998 .

[36]  Oliveira,et al.  Rayleigh-Ritz variational principle for ensembles of fractionally occupied states. , 1988, Physical review. A, General physics.

[37]  Kieron Burke,et al.  Excitations and benchmark ensemble density functional theory for two electrons. , 2014, The Journal of chemical physics.

[38]  Kieron Burke,et al.  Exact and approximate Kohn-Sham potentials in ensemble density-functional theory , 2014 .

[39]  Andreas Savin,et al.  Long-range/short-range separation of the electron-electron interaction in density functional theory , 2004 .

[40]  Kieron Burke,et al.  Double excitations within time-dependent density functional theory linear response. , 2004, The Journal of chemical physics.

[41]  G. Paragi,et al.  Investigation of exchange potentials for excited states by parameter fitting , 2000 .

[42]  Paweł Sałek,et al.  Dalton, a molecular electronic structure program, Release Dalton2011 , 2011 .

[43]  Oliveira,et al.  Density-functional theory for ensembles of fractionally occupied states. I. Basic formalism. , 1988, Physical review. A, General physics.