Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Hole–hole Tamm–Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/5.0003985· OSTI ID:1656599
 [1];  [1];  [1];  [1]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States). Photon Ultrafast Laser Science and Engineering Inst. (PULSE); Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole–hole Tamm–Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole–hole counterpart to the more established particle–particle TDA (pp-TDA) method, both of which are derived from the particle–particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. Furthermore, the treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. Additionally, we show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states—particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.
Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; Leopoldina Fellowship Program; AMOS Program
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1656599
Alternate ID(s):
OSTI ID: 1637988
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 2 Vol. 153; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (94)

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach journal April 2003
The complete active space SCF method in a fock-matrix-based super-CI formulation journal March 1980
Density-functional theory of the superconducting state journal January 1991
Turbomole
  • Furche, Filipp; Ahlrichs, Reinhart; Hättig, Christof
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 2 https://doi.org/10.1002/wcms.1162
journal July 2013
Spin-restricted ensemble-referenced Kohn-Sham method: basic principles and application to strongly correlated ground and excited states of molecules journal November 2014
The DFT/MRCI method journal July 2018
The influence of polarization functions on molecular orbital hydrogenation energies journal January 1973
Excited state direct dynamics of benzene with reparameterized multi-reference semiempirical configuration interaction methods journal September 2004
A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) journal July 2004
Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems journal December 2016
Combining Wave Function Methods with Density Functional Theory for Excited States journal April 2018
Improved Complete Active Space Configuration Interaction Energies with a Simple Correction from Density Functional Theory journal February 2017
On-the-Fly CASPT2 Surface-Hopping Dynamics journal July 2017
Accurate Treatment of Charge-Transfer Excitations and Thermally Activated Delayed Fluorescence Using the Particle–Particle Random Phase Approximation journal May 2018
Dynamical Correlation Effects on Photoisomerization: Ab Initio Multiple Spawning Dynamics with MS-CASPT2 for a Model trans -Protonated Schiff Base journal November 2015
Conical Intersections from Particle–Particle Random Phase and Tamm–Dancoff Approximations journal June 2016
Dual-Functional Tamm–Dancoff Approximation: A Convenient Density Functional Method that Correctly Describes S 1 /S 0 Conical Intersections journal April 2017
α-CASSCF: An Efficient, Empirical Correction for SA-CASSCF To Closely Approximate MS-CASPT2 Potential Energy Surfaces journal May 2017
Single, Double Electronic Excitations and Exciton Effective Conjugation Lengths in π-Conjugated Systems journal June 2018
The Simplest Possible Approach for Simulating S 0S 1 Conical Intersections with DFT/TDDFT: Adding One Doubly Excited Configuration journal May 2019
Theoretical Studies of Electronically Excited States of Molecular Systems Using Multiconfigurational Perturbation Theory journal February 1999
Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules journal November 2005
Atomic and Molecular Electron Affinities:  Photoelectron Experiments and Theoretical Computations journal January 2002
Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections journal November 2012
Quantum Chemistry on Graphical Processing Units. 1. Strategies for Two-Electron Integral Evaluation journal January 2008
Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation journal March 2009
Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules journal August 2009
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields journal November 1994
Competitive Decay at Two- and Three-State Conical Intersections in Excited-State Intramolecular Proton Transfer journal April 2005
Ab Initio Molecular Dynamics of Excited-State Intramolecular Proton Transfer Using Multireference Perturbation Theory journal November 2007
Role of Rydberg States in the Photochemical Dynamics of Ethylene journal December 2011
Singlet–Triplet Energy Gaps for Diradicals from Particle–Particle Random Phase Approximation journal April 2015
Photophysics of the π,π* and n,π* States of Thymine: MS-CASPT2 Minimum-Energy Paths and CASSCF on-the-Fly Dynamics journal September 2009
Ab Initio Multiple Spawning Dynamics Using Multi-State Second-Order Perturbation Theory journal December 2009
Configuration Interaction-Corrected Tamm–Dancoff Approximation: A Time-Dependent Density Functional Method with the Correct Dimensionality of Conical Intersections journal January 2014
Probing ultrafast ππ*/nπ* internal conversion in organic chromophores via K-edge resonant absorption journal June 2017
Theoretical study of the photodissociation dynamics of ClOOCl journal January 2001
Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy journal January 2005
Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states journal January 2008
The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies journal January 2013
Excited states using the simplified Tamm–Dancoff-Approach for range-separated hybrid density functionals: development and application journal January 2014
Analytic gradients, geometry optimization and excited state potential energy surfaces from the particle-particle random phase approximation journal January 2015
The spin–flip approach within time-dependent density functional theory: Theory and applications to diradicals journal March 2003
A spin-complete version of the spin-flip approach to bond breaking: What is the impact of obtaining spin eigenfunctions? journal May 2003
Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules journal January 1971
Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules journal March 1972
Can coupled-cluster theory treat conical intersections? journal July 2007
Systematic optimization of long-range corrected hybrid density functionals journal February 2008
Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3 journal April 2008
The spin-flip extended single excitation configuration interaction method journal August 2008
The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach journal December 2008
A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states journal February 2009
Ultrafast internal conversion in ethylene. I. The excited state lifetime journal June 2011
An efficient internally contracted multiconfiguration–reference configuration interaction method journal November 1988
Fully optimized contracted Gaussian basis sets for atoms Li to Kr journal August 1992
A new mixing of Hartree–Fock and local density‐functional theories journal January 1993
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr journal April 1994
Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals journal November 1997
Toward reliable density functional methods without adjustable parameters: The PBE0 model journal April 1999
A combination of Kohn–Sham density functional theory and multi-reference configuration interaction methods journal October 1999
Equivalence of particle-particle random phase approximation correlation energy and ladder-coupled-cluster doubles journal September 2013
Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory journal September 2013
Benchmark tests and spin adaptation for the particle-particle random phase approximation journal November 2013
Double, Rydberg and charge transfer excitations from pairing matrix fluctuation and particle-particle random phase approximation journal December 2013
Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation journal May 2014
Linear-response time-dependent density-functional theory with pairing fields journal May 2014
Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O ( r6 ) to O ( r4 ) journal July 2014
Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies journal September 2014
Spin-flip, tensor equation-of-motion configuration interaction with a density-functional correction: A spin-complete method for exploring excited-state potential energy surfaces journal December 2015
Ultra-fast computation of electronic spectra for large systems by tight-binding based simplified Tamm-Dancoff approximation (sTDA-xTB) journal August 2016
Charge transfer excitations from particle-particle random phase approximation—Opportunities and challenges arising from two-electron deficient systems journal March 2017
Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism journal July 2017
Excitation energies from particle-particle random phase approximation with accurate optimized effective potentials journal October 2017
Crossing conditions in coupled cluster theory journal October 2017
Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. II. Ab initio multiple spawning simulations journal April 2018
State-interaction pair-density functional theory journal July 2018
Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction journal July 2018
Nature of ground and electronic excited states of higher acenes journal August 2016
Understanding band gaps of solids in generalized Kohn–Sham theory journal March 2017
Conical intersections and double excitations in time-dependent density functional theory journal March 2006
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
A correlation-energy density functional for multideterminantal wavefunctions journal June 1997
Optimization of Semiempirical Quantum Chemistry Methods via Multiobjective Genetic Algorithms: Accurate Photodynamics for Larger Molecules and Longer Time Scales journal June 2007
Density-functional exchange-energy approximation with correct asymptotic behavior journal September 1988
Orbital spaces and density-functional theory journal March 2007
Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation journal September 2013
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density journal January 1988
Ab initio theory of superconductivity. I. Density functional formalism and approximate functionals journal July 2005
Density-Functional Theory for Superconductors journal June 1988
Generalized Gradient Approximation Made Simple journal October 1996
Spin-state energetics of iron(II) porphyrin from the particle-particle random phase approximation journal November 2018
Time-Dependent Density Functional Response Theory for Molecules book November 1995
Assessment of the Potential Energy Hypersurfaces in Thymine within Multiconfigurational Theory: CASSCF vs. CASPT2 journal December 2016