Comparing the performance of TD‐DFT and SAC‐CI methods in the description of excited states potential energy surfaces: An excited state proton transfer reaction as case study

The performances, in the description of excited state potential energy surfaces, of several density functional approximations representative of the currently most applied exchange correlation functionals’ families have been tested with respect to post Hartree‐Fock references (here Symmetry Adapted Cluster‐Configuration Interaction results). An experimentally well‐characterized intermolecular proton transfer reaction has been considered as test case. The computed potential energy profiles were analyzed both in the gas phase and in toluene solution, here represented as a polarizable continuum model. The presence of intermolecular (dark) and intramolecular (bright) charge transfer excited states, whose polarity strongly differs along the reaction pathway, makes clear that only subtle compensation between spurious electronic effects—related to the incorrect asymptotic behavior of the functional—and solvent stabilization of polar states leads to the overall correct description of this excited state reaction when using global hybrids with low percentage of Hartree Fock exchange. © 2017 Wiley Periodicals, Inc.

[1]  Hiroshi Nakatsuji,et al.  EXCITED AND IONIZED STATES OF FREE BASE PORPHIN STUDIED BY THE SYMMETRY ADAPTED CLUSTER-CONFIGURATION INTERACTION (SAC-CI) METHOD , 1996 .

[2]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[3]  Donald G Truhlar,et al.  Density functional for spectroscopy: no long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states. , 2006, The journal of physical chemistry. A.

[4]  Darío J. R. Duarte,et al.  Intermolecular perturbation in the self-assembly of melamine , 2016, Theoretical Chemistry Accounts.

[5]  M. Head‐Gordon,et al.  Systematic optimization of long-range corrected hybrid density functionals. , 2008, The Journal of chemical physics.

[6]  V. Barone,et al.  Proton transfer in model hydrogen-bonded systems by a density functional approach , 1994 .

[7]  Carlo Adamo,et al.  A Qualitative Index of Spatial Extent in Charge-Transfer Excitations. , 2011, Journal of chemical theory and computation.

[8]  Masahiro Ehara,et al.  Excited-State Geometries of Heteroaromatic Compounds: A Comparative TD-DFT and SAC-CI Study. , 2013, Journal of chemical theory and computation.

[9]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[10]  Weitao Yang,et al.  Many-electron self-interaction error in approximate density functionals. , 2006, The Journal of chemical physics.

[11]  M. Head‐Gordon,et al.  Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. , 2008, Physical chemistry chemical physics : PCCP.

[12]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[13]  M. Head‐Gordon,et al.  Failure of time-dependent density functional theory for long-range charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and bacteriochlorophyll-spheroidene complexes. , 2004, Journal of the American Chemical Society.

[14]  I. Ciofini,et al.  Exploring the metric of excited state proton transfer reactions. , 2013, The journal of physical chemistry. B.

[15]  P. Cimino,et al.  On the different strength of photoacids , 2016, Theoretical Chemistry Accounts.

[16]  Paul G. Mezey,et al.  A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions , 1989 .

[17]  D. Truhlar,et al.  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 , 2008 .

[18]  Hiroshi Nakatsuji,et al.  Cluster expansion of the wavefunction. Calculation of electron correlations in ground and excited states by SAC and SAC CI theories , 1979 .

[19]  Donald G Truhlar,et al.  Comparative DFT study of van der Waals complexes: rare-gas dimers, alkaline-earth dimers, zinc dimer, and zinc-rare-gas dimers. , 2006, The journal of physical chemistry. A.

[20]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[21]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[22]  Vincenzo Barone,et al.  Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models , 1998 .

[23]  Kimihiko Hirao,et al.  Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory , 1978 .

[24]  Andreas Dreuw,et al.  Single-reference ab initio methods for the calculation of excited states of large molecules. , 2005, Chemical reviews.

[25]  M. Frisch,et al.  Singularity-free analytical energy gradients for the SAC/SAC-CI method: coupled perturbed minimum orbital-deformation (CPMOD)approach , 2003 .

[26]  Masahiro Ehara,et al.  Chemically intuitive indices for charge‐transfer excitation based on SAC‐CI and TD‐DFT calculations , 2013, J. Comput. Chem..

[27]  A. Becke Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[28]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[29]  Masahiro Ehara,et al.  Benchmark Study on the Triplet Excited-State Geometries and Phosphorescence Energies of Heterocyclic Compounds: Comparison Between TD-PBE0 and SAC-CI. , 2014, Journal of chemical theory and computation.

[30]  John P. Perdew,et al.  Comment on ``Significance of the highest occupied Kohn-Sham eigenvalue'' , 1997 .

[31]  T. Bally,et al.  INCORRECT DISSOCIATION BEHAVIOR OF RADICAL IONS IN DENSITY FUNCTIONAL CALCULATIONS , 1997 .

[32]  Gustavo E. Scuseria,et al.  A novel form for the exchange-correlation energy functional , 1998 .

[33]  Ting Yuan,et al.  A new four-dimensional ab initio potential energy surface and predicted infrared spectra for the He–CS2 complex , 2015, Theoretical Chemistry Accounts.

[34]  G. Scuseria,et al.  An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules , 1998 .

[35]  Brian P. Mehl,et al.  Base-induced phototautomerization in 7-hydroxy-4-(trifluoromethyl)coumarin. , 2012, The journal of physical chemistry. B.

[36]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[37]  Correct dissociation behavior of radical ions such as H2+ in density functional calculations , 2001 .

[38]  Jan M. L. Martin,et al.  Development of density functionals for thermochemical kinetics. , 2004, The Journal of chemical physics.

[39]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[40]  E. Gross,et al.  Density-Functional Theory for Time-Dependent Systems , 1984 .

[41]  Hermann Stoll,et al.  Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr , 1989 .

[42]  Adrienn Ruzsinszky,et al.  Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+. , 2007, The Journal of chemical physics.

[43]  G. Scuseria,et al.  Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits. , 2005, The Journal of chemical physics.

[44]  Hiroshi Nakatsuji,et al.  Cluster expansion of the wavefunction. Electron correlations in ground and excited states by SAC (symmetry-adapted-cluster) and SAC CI theories , 1979 .

[45]  G. Scuseria,et al.  Assessment of a long-range corrected hybrid functional. , 2006, The Journal of chemical physics.

[46]  Vincenzo Barone,et al.  Toward reliable adiabatic connection models free from adjustable parameters , 1997 .

[47]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[48]  G. Scuseria,et al.  Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional , 1999 .

[49]  I. Ciofini,et al.  Intrinsic and dynamical reaction pathways of an excited state proton transfer. , 2015, The journal of physical chemistry. B.

[50]  J. Tomasi,et al.  Electronic excitation energies of molecules in solution within continuum solvation models: investigating the discrepancy between state-specific and linear-response methods. , 2005, The Journal of chemical physics.

[51]  A. Becke A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[52]  W. Domcke,et al.  Ab initio potential-energy functions for excited state intramolecular proton transfer: a comparative study of o-hydroxybenzaldehyde, salicylic acid and 7-hydroxy-1-indanone , 1999 .

[53]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[54]  S. Patchkovskii,et al.  Improving ``difficult'' reaction barriers with self-interaction corrected density functional theory , 2002 .

[55]  M. Barbatti,et al.  Excited-state diproton transfer in [2,2'-bipyridyl]-3,3'-diol: the mechanism is sequential, not concerted. , 2009, The journal of physical chemistry. A.

[56]  Masahiro Ehara,et al.  Efficiency of perturbation‐selection and its orbital dependence in the SAC‐CI calculations for valence excitations of medium‐size molecules , 2014, J. Comput. Chem..

[57]  G. Scuseria,et al.  Tests of functionals for systems with fractional electron number. , 2007, The Journal of chemical physics.

[58]  Masahiro Ehara,et al.  Symmetry-adapted cluster and symmetry-adapted cluster-configuration interaction method in the polarizable continuum model: theory of the solvent effect on the electronic excitation of molecules in solution. , 2010, The Journal of chemical physics.

[59]  G. Scuseria,et al.  Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals. , 2006, The Journal of chemical physics.

[60]  Hiroshi Nakatsuji,et al.  Energy gradient method for the ground, excited, ionized, and electron-attached states calculated by the SAC (symmetry-adapted cluster)/SAC–CI (configuration interaction) method , 1999 .

[61]  Alberto Vela,et al.  Charge-Transfer Complexes: Stringent Tests for Widely Used Density Functionals , 1996 .

[62]  Weitao Yang,et al.  A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons , 1998 .

[63]  Xin Xu,et al.  From The Cover: The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[64]  Modeling of charge transfer processes to understand photophysical signatures: The case of Rhodamine 110 , 2014 .

[65]  Marcus Lundberg,et al.  Quantifying the effects of the self-interaction error in DFT: when do the delocalized states appear? , 2005, The Journal of chemical physics.

[66]  Masahiro Ehara,et al.  Exploring excited states using Time Dependent Density Functional Theory and density-based indexes , 2015 .

[67]  David J. Tozer,et al.  Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials , 2001 .

[68]  Jacopo Tomasi,et al.  Geometries and properties of excited states in the gas phase and in solution: theory and application of a time-dependent density functional theory polarizable continuum model. , 2006, The Journal of chemical physics.

[69]  I. Ciofini,et al.  Intermolecular proton shuttling in excited state proton transfer reactions: insights from theory. , 2014, Physical chemistry chemical physics : PCCP.

[70]  Hiroshi Nakatsuji,et al.  Formulation and implementation of direct algorithm for the symmetry-adapted cluster and symmetry-adapted cluster-configuration interaction method. , 2008, The Journal of chemical physics.