Assessment of double-hybrid energy functionals for pi-conjugated systems.

There have been tremendous efforts in the past decade on the use of computational methods for conjugated systems. Their properties and energetics are often described by density functional theory calculations which, however, are known to face a challenge when dealing with these systems since serious and systematic errors with popular density functionals occur, specially in the case of having stacked or sterically overcrowded aromatic systems, and discourage their use as a black box technique. We overcome here this shortcoming by applying recently developed dispersion-corrected double-hybrid density functionals (B2PLYP) in search of greater yet wide accuracy with little more computational effort. Interestingly, we have derived a related method (B2piPLYP), which has been thoroughly assessed against a set of databases and reactions of the most interest, and works better for this subclass of systems. The deviations with respect to benchmark or experimental values are found to be in the reasonably low range of 1-2 kcal/mol when a correction for the dispersion interactions is added and, most importantly, without suffering the large and systematic errors that are common in former yet conventional methods.

[1]  Clémence Corminboeuf,et al.  Systematic errors in computed alkane energies using B3LYP and other popular DFT functionals. , 2006, Organic letters.

[2]  K. Baldridge,et al.  Implementation and Performance of DFT-D with Respect to Basis Set and Functional for Study of Dispersion Interactions in Nanoscale Aromatic Hydrocarbons. , 2008, Journal of chemical theory and computation.

[3]  Donald G Truhlar,et al.  Density functionals with broad applicability in chemistry. , 2008, Accounts of chemical research.

[4]  Kimihiko Hirao,et al.  A density-functional study on pi-aromatic interaction: benzene dimer and naphthalene dimer. , 2005, The Journal of chemical physics.

[5]  Mikael P. Johansson,et al.  Torsional Barriers and Equilibrium Angle of Biphenyl: Reconciling Theory with Experiment. , 2008, Journal of chemical theory and computation.

[6]  M. Kertész,et al.  Single-Bond Torsional Potentials in Conjugated Systems: A Comparison of ab Initio and Density Functional Results , 1997 .

[7]  George C Schatz,et al.  Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics. , 2008, The journal of physical chemistry. A.

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

[9]  Donald G. Truhlar,et al.  Multi-coefficient extrapolated density functional theory for thermochemistry and thermochemical kinetics , 2005 .

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

[11]  Donald G Truhlar,et al.  Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions. , 2005, The journal of physical chemistry. A.

[12]  D. Truhlar,et al.  Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions. , 2008, Journal of chemical theory and computation.

[13]  F. Neese,et al.  Double-hybrid density functional theory for excited electronic states of molecules. , 2007, The Journal of chemical physics.

[14]  Gustavo E. Scuseria,et al.  Local hybrid functionals , 2003 .

[15]  Donald G Truhlar,et al.  Multicoefficient extrapolated density functional theory studies of pi...pi interactions: the benzene dimer. , 2005, The journal of physical chemistry. A.

[16]  J. Sancho‐García,et al.  Anchoring the Torsional Potential of Biphenyl at the ab Initio Level:  The Role of Basis Set versus Correlation Effects. , 2005, Journal of chemical theory and computation.

[17]  G. Orlova,et al.  Practical failures from the inclusion of exact exchange: how much exact exchange is appropriate? , 2002 .

[18]  D. Langreth,et al.  Van Der Waals Interactions In Density Functional Theory , 2007 .

[19]  S. Grimme,et al.  Theoretical thermodynamics for large molecules: walking the thin line between accuracy and computational cost. , 2008, Accounts of chemical research.

[20]  Pedro Alexandrino Fernandes,et al.  General performance of density functionals. , 2007, The journal of physical chemistry. A.

[21]  Dana Vuzman,et al.  Double-hybrid functionals for thermochemical kinetics. , 2008, The journal of physical chemistry. A.

[22]  T. Van Voorhis,et al.  Self-consistent implementation of a nonlocal van der Waals density functional with a Gaussian basis set. , 2008, The Journal of chemical physics.

[23]  S. Grimme,et al.  Towards chemical accuracy for the thermodynamics of large molecules: new hybrid density functionals including non-local correlation effects. , 2006, Physical chemistry chemical physics : PCCP.

[24]  Marco Häser,et al.  Auxiliary basis sets to approximate Coulomb potentials , 1995 .

[25]  D. Truhlar,et al.  Assessment of density functionals for pi systems: Energy differences between cumulenes and poly-ynes; proton affinities, bond length alternation, and torsional potentials of conjugated polyenes; and proton affinities of conjugated Shiff bases. , 2006, The journal of physical chemistry. A.

[26]  Jean-Luc Brédas,et al.  Charge transport in organic semiconductors. , 2007, Chemical reviews.

[27]  Ferdinand C. Grozema,et al.  Mechanism of charge transport in self-organizing organic materials , 2008 .

[28]  S. Grimme Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies , 2003 .

[29]  A. Becke,et al.  A unified density-functional treatment of dynamical, nondynamical, and dispersion correlations. , 2007, The Journal of chemical physics.

[30]  Kazumasa Honda,et al.  High-level ab initio computations of structures and interaction energies of naphthalene dimers: origin of attraction and its directionality. , 2004, The Journal of chemical physics.

[31]  J. Sancho‐García Assessing a new nonempirical density functional: difficulties in treating pi-conjugation effects. , 2006, The Journal of chemical physics.

[32]  J. Sancho‐García,et al.  Assessment of recently developed exchange-correlation functionals for the description of torsion potentials in pi-conjugated molecules. , 2004, The Journal of chemical physics.

[33]  Á. Pérez‐Jiménez,et al.  Exchange and correlation interplay in density functional theory under test: the relative stability of C3H isomers , 2002 .

[34]  I. Ciofini,et al.  Assessment of recently developed density functional approaches for the evaluation of the bond length alternation in polyacetylene , 2005 .

[35]  D. Truhlar,et al.  A Prototype for Graphene Material Simulation : Structures and Interaction Potentials of Coronene Dimers , 2008 .

[36]  J. Ángyán,et al.  London dispersion forces by range-separated hybrid density functional with second order perturbational corrections: the case of rare gas complexes. , 2007, The Journal of chemical physics.

[37]  S. Grimme,et al.  How to compute isomerization energies of organic molecules with quantum chemical methods. , 2007, The Journal of organic chemistry.

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

[39]  Gregory S. Tschumper,et al.  Probing the effects of heterogeneity on delocalized pi...pi interaction energies. , 2008, Physical chemistry chemical physics : PCCP.

[40]  Á. Pérez‐Jiménez,et al.  Improved accuracy with medium cost computational methods for the evaluation of bond length alternation of increasingly long oligoacetylenes. , 2007, Physical chemistry chemical physics : PCCP.

[41]  Clémence Corminboeuf,et al.  How accurate are DFT treatments of organic energies? , 2007, Organic letters.

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

[43]  T. Takatani,et al.  Performance of spin-component-scaled Møller-Plesset theory (SCS-MP2) for potential energy curves of noncovalent interactions. , 2007, Physical chemistry chemical physics : PCCP.

[44]  T. Crawford,et al.  Conformations of [10]Annulene: More Bad News for Density Functional Theory and Second-Order Perturbation Theory , 1999 .

[45]  Jan K. Labanowski,et al.  Density Functional Methods in Chemistry , 1991 .

[46]  M. Kaupp,et al.  Local hybrid functionals: an assessment for thermochemical kinetics. , 2007, The Journal of chemical physics.

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

[48]  P. Schreiner,et al.  Many density functional theory approaches fail to give reliable large hydrocarbon isomer energy differences. , 2006, Organic letters.

[49]  Donald G. Truhlar,et al.  Doubly Hybrid Meta DFT: New Multi-Coefficient Correlation and Density Functional Methods for Thermochemistry and Thermochemical Kinetics , 2004 .

[50]  S. Grimme Semiempirical hybrid density functional with perturbative second-order correlation. , 2006, The Journal of chemical physics.

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

[52]  M. Kertész,et al.  Conjugated polymers and aromaticity. , 2005, Chemical reviews.

[53]  A. Becke,et al.  A unified density-functional treatment of dynamical, nondynamical, and dispersion correlations. II. Thermochemical and kinetic benchmarks. , 2008, The Journal of chemical physics.

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

[55]  S. Grimme,et al.  Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability. , 2007, Physical chemistry chemical physics : PCCP.

[56]  Axel D. Becke,et al.  Density‐functional thermochemistry. IV. A new dynamical correlation functional and implications for exact‐exchange mixing , 1996 .

[57]  Robert A. Wolkow,et al.  Application of 25 density functionals to dispersion-bound homomolecular dimers , 2004 .

[58]  Andreas Savin,et al.  Combining long-range configuration interaction with short-range density functionals , 1997 .

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

[60]  S. Grimme,et al.  Stereoelectronic Substituent Effects in Saturated Main Group Molecules:  Severe Problems of Current Kohn-Sham Density Functional Theory. , 2007, Journal of chemical theory and computation.

[61]  Donald G Truhlar,et al.  Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions. , 2006, Journal of chemical theory and computation.

[62]  J. Brédas,et al.  A multimode analysis of the gas-phase photoelectron spectra in oligoacenes. , 2004, The Journal of chemical physics.

[63]  W. Goddard,et al.  Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics , 2009, Proceedings of the National Academy of Sciences.

[64]  F. Neese,et al.  Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method. , 2009, The Journal of chemical physics.

[65]  Donald G Truhlar,et al.  Assessment of Model Chemistries for Noncovalent Interactions. , 2006, Journal of chemical theory and computation.

[66]  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.

[67]  S. Grimme,et al.  Computation of accurate excitation energies for large organic molecules with double-hybrid density functionals. , 2009, Physical chemistry chemical physics : PCCP.

[68]  Donald G Truhlar,et al.  How well can new-generation density functional methods describe stacking interactions in biological systems? , 2005, Physical chemistry chemical physics : PCCP.

[69]  Thomas M Henderson,et al.  The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach. , 2008, The Journal of chemical physics.

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

[71]  Giovanni Scalmani,et al.  Assessment of the efficiency of long-range corrected functionals for some properties of large compounds. , 2007, The Journal of chemical physics.

[72]  P. Schreiner Relative energy computations with approximate density functional theory--a caveat! , 2007, Angewandte Chemie.

[73]  Stefan Grimme,et al.  The importance of inter- and intramolecular van der Waals interactions in organic reactions: the dimerization of anthracene revisited. , 2006, Angewandte Chemie.

[74]  F. Neese,et al.  Analytic derivatives for perturbatively corrected "double hybrid" density functionals: theory, implementation, and applications. , 2007, The Journal of chemical physics.

[75]  S. Grimme On the importance of electron correlation effects for the pi-pi interactions in cyclophanes. , 2004, Chemistry.

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

[77]  Ernest R Davidson Modern Electronic Structure Theory And Applications In Organic Chemistry , 1997 .

[78]  Frank Neese,et al.  An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix , 2003, J. Comput. Chem..

[79]  M. Dion,et al.  van der Waals density functional for general geometries. , 2004, Physical review letters.

[80]  C David Sherrill,et al.  Oscillations in meta-generalized-gradient approximation potential energy surfaces for dispersion-bound complexes. , 2009, The Journal of chemical physics.

[81]  Benjamin G. Janesko,et al.  Long-range-corrected hybrid density functionals including random phase approximation correlation: application to noncovalent interactions. , 2009, The Journal of chemical physics.

[82]  M. Kaupp,et al.  Local hybrid exchange-correlation functionals based on the dimensionless density gradient , 2007 .

[83]  S. Grimme Seemingly simple stereoelectronic effects in alkane isomers and the implications for Kohn-Sham density functional theory. , 2006, Angewandte Chemie.

[84]  Thomas M Henderson,et al.  Screened hybrid density functionals for solid-state chemistry and physics. , 2009, Physical chemistry chemical physics : PCCP.

[85]  Á. Pérez‐Jiménez,et al.  A theoretical study of the molecular structure and torsional potential of styrene , 2002 .

[86]  A. Cohen,et al.  Influence of Coulomb-attenuation on exchange-correlation functional quality. , 2006, Physical chemistry chemical physics : PCCP.

[87]  J. Brédas,et al.  Assessment of the reliability of the Perdew–Burke–Ernzerhof functionals in the determination of torsional potentials in π-conjugated molecules , 2003 .

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

[89]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[90]  A. Savin,et al.  Is size-consistency possible with density functional approximations? , 2009 .

[91]  Donald G Truhlar,et al.  A density functional that accounts for medium-range correlation energies in organic chemistry. , 2006, Organic letters.

[92]  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 .

[93]  Stefan Grimme,et al.  Noncovalent Interactions between Graphene Sheets and in Multishell (Hyper)Fullerenes , 2007 .

[94]  F. Moscardó,et al.  New approach to the design of density functionals , 2001 .

[95]  Thomas M Henderson,et al.  Long-range-corrected hybrids including random phase approximation correlation. , 2009, The Journal of chemical physics.

[96]  D. Truhlar,et al.  The DBH24/08 Database and Its Use to Assess Electronic Structure Model Chemistries for Chemical Reaction Barrier Heights. , 2009, Journal of chemical theory and computation.

[97]  J. Sancho‐García Assessment of recently developed multicoefficient strategies for the treatment of pi-conjugated molecules. , 2005, The journal of physical chemistry. A.

[98]  J. Sancho‐García,et al.  Theoretical approach to the conformational analysis of heteroaromatic dimers: 2-(2-Thienyl)pyrrole, 2-(2-thienyl)furan, and 2-(2-furyl)pyrrole , 2009 .

[99]  H. Schaefer,et al.  Problematic Energy Differences between Cumulenes and Poly-ynes: Does This Point to a Systematic Improvement of Density Functional Theory? , 2002 .

[100]  L. Gladden,et al.  Modulating the Selectivity for CO and Butane Oxidation over Heterogeneous Catalysis through Amorphous Catalyst Coatings , 2008 .

[101]  G. Scuseria,et al.  Assessment of a Middle-Range Hybrid Functional. , 2008, Journal of chemical theory and computation.

[102]  J. Sancho‐García Assessment of density-functional models for organic molecular semiconductors: The role of Hartree–Fock exchange in charge-transfer processes , 2007 .

[103]  J. Perdew,et al.  Improved Description of Stereoelectronic Effects in Hydrocarbons Using Semilocal Density Functional Theory. , 2008, Journal of chemical theory and computation.

[104]  Á. Pérez‐Jiménez,et al.  A systematic and accurate study of singlet propynylidene 1 Part of this work was done at the J. Heyr , 2000 .

[105]  J. Perdew Size-Consistency, Self-Interaction Correction, and Derivative Discontinuity in Density Functional Theory , 1990 .

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