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Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT. COMPUTATION 2022. [DOI: 10.3390/computation10020013] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The lowest-energy singlet (S1) and triplet (T1) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying on the exchange-correlation functional employed. However, there are challenging cases for which this cannot be the case, due to the fact that those excited states are not exclusively formed by single excitations and/or are affected by marked correlation effects, and thus TD-DFT might fall short. We will tackle here a set of molecules belonging to the azaphenalene family, for which research recently documented an inversion of the relative energy of S1 and T1 excited states giving rise to a negative energy difference (ΔEST) between them and, thereby, contrary to most of the systems thus far treated by TD-DFT. Since methods going beyond standard TD-DFT are not extensively applied to excited-state calculations and considering how challenging this case is for the molecules investigated, we will prospectively employ here a set of non-standard methods (Multi-Configurational Pair Density Functional Theory or MC-PDFT) and correlation functionals (i.e., Lie–Clementi and Colle–Salvetti) relying not only on the electronic density but also on some modifications considering the intricate electronic structure of these systems.
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2
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Abstract
Kohn-Sham density functional theory with the available exchange-correlation functionals is less accurate for strongly correlated systems, which require a multiconfigurational description as a zero-order function, than for weakly correlated systems, and available functionals of the spin densities do not accurately predict energies for many strongly correlated systems when one uses multiconfigurational wave functions with spin symmetry. Furthermore, adding a correlation functional to a multiconfigurational reference energy can lead to double counting of electron correlation. Multiconfiguration pair-density functional theory (MC-PDFT) overcomes both obstacles, the second by calculating the quantum mechanical part of the electronic energy entirely by a functional, and the first by using a functional of the total density and the on-top pair density rather than the spin densities. This allows one to calculate the energy of strongly correlated systems efficiently with a pair-density functional and a suitable multiconfigurational reference function. This article reviews MC-PDFT and related background information.
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Affiliation(s)
- Prachi Sharma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA;
| | - Jie J Bao
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA;
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA;
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, USA;
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Salvitti G, Negri F, Pérez-Jiménez ÁJ, San-Fabián E, Casanova D, Sancho-García JC. Investigating the (Poly)Radicaloid Nature of Real-World Organic Compounds with DFT-Based Methods. J Phys Chem A 2020; 124:3590-3600. [DOI: 10.1021/acs.jpca.0c01239] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Giovanna Salvitti
- Department of Physical Chemistry, University of Alicante, E-03080 Alicante, Spain
- Dipartimento di Chimica “Giacomo Ciamician”, Università di Bologna, IT-40126 Bologna, Italy
| | - Fabrizia Negri
- Dipartimento di Chimica “Giacomo Ciamician”, Università di Bologna, IT-40126 Bologna, Italy
- INSTM UdR Bologna, 40136 Bologna, Italy
| | | | - Emilio San-Fabián
- Department of Physical Chemistry, University of Alicante, E-03080 Alicante, Spain
| | - David Casanova
- Donostia International Physics Center (DIPC), E-20018 Donostia, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
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King AW, Baskerville AL, Cox H. Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2017.0153. [PMID: 29431681 DOI: 10.1098/rsta.2017.0153] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/25/2017] [Indexed: 06/08/2023]
Abstract
An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be ZHFC=1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'.
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Affiliation(s)
- Andrew W King
- Department of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UK
| | - Adam L Baskerville
- Department of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UK
| | - Hazel Cox
- Department of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UK
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Pérez-Guardiola A, Sandoval-Salinas ME, Casanova D, San-Fabián E, Pérez-Jiménez AJ, Sancho-García JC. The role of topology in organic molecules: origin and comparison of the radical character in linear and cyclic oligoacenes and related oligomers. Phys Chem Chem Phys 2018; 20:7112-7124. [DOI: 10.1039/c8cp00135a] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We discuss the nature of electron-correlation effects in carbon nanorings and nanobelts by a combined approach based on FT-DFT and RAS-SF methods.
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Affiliation(s)
- A. Pérez-Guardiola
- Department of Physical Chemistry
- University of Alicante
- E-03080 Alicante
- Spain
| | - M. E. Sandoval-Salinas
- Departament de Ciéncia de Materials i Química Física
- Institut de Química Teòrica i Computacional (IQTCUB)
- Universitat de Barcelona
- E-08028 Barcelona
- Spain
| | - D. Casanova
- Kimika Fakultatea
- Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC)
- E-20018 Donostia
- Spain
- IKERBASQUE
| | - E. San-Fabián
- Department of Physical Chemistry
- University of Alicante
- E-03080 Alicante
- Spain
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Sancho-García JC, Pérez-Jiménez AJ, Savarese M, Brémond E, Adamo C. Importance of Orbital Optimization for Double-Hybrid Density Functionals: Application of the OO-PBE-QIDH Model for Closed- and Open-Shell Systems. J Phys Chem A 2016; 120:1756-62. [DOI: 10.1021/acs.jpca.6b00994] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- J. C. Sancho-García
- Departamento
de Química Física, Universidad de Alicante, 03080 Alicante, Spain
| | - A. J. Pérez-Jiménez
- Departamento
de Química Física, Universidad de Alicante, 03080 Alicante, Spain
| | - M. Savarese
- CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa, Italy
| | - E. Brémond
- CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa, Italy
| | - C. Adamo
- CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa, Italy
- Institut de Recherche
de Chimie Paris, IRCP CNRS UMR-8247, Chimie ParisTech, École Nationale Superieure de Chimie de Paris, 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France
- Institut Universitaire de France, 103 Boulevard Saint Michel, F-75005 Paris, France
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Abstract
It is commonly accepted in the scientific literature that the static correlation energy, Estat, of a system can be defined as the exact correlation energy of its valence electrons in a minimal basis. Unfortunately, the computational cost of calculating the exact correlation energy within a fully optimized minimal basis grows exponentially with system size, making such calculations intractable for all but the smallest systems. However, analogous to single-reference methods, it is possible to systematically approximate both the treatment of electron correlation and flexibility of the minimal basis to reduce computational cost. This yields a hierarchy of methods for calculating Estat, ranging from coupled cluster methods in a minimal atomic basis up to full valence complete active space methods with a minimal molecular orbital basis constructed from a near-complete atomic orbital basis. By examining a variety of dissociating diatomics, along with equilibrium and transition structures for polyatomic systems, we show that standard coupled cluster models with minimal atomic basis sets (e.g., STO-3G) offer a convenient and cost-effective hierarchy of black box estimates for Estat in small- to medium-sized systems near their equilibrium geometries. To properly describe homolytic bond dissociation, it is better to use a more flexible basis set expansion so that each atomic orbital can effectively adapt to its molecular environment.
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Sancho-García JC, Adamo C. Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds. Phys Chem Chem Phys 2013; 15:14581-94. [DOI: 10.1039/c3cp50907a] [Citation(s) in RCA: 85] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Sancho-García JC. Further evidences of the quality of double-hybrid energy functionals for π-conjugated systems. J Chem Phys 2011; 134:234102. [DOI: 10.1063/1.3598482] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
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Demel O, Shamasundar KR, Kong L, Nooijen M. Application of Double Ionization State-Specific Equation of Motion Coupled Cluster Method to Organic Diradicals. J Phys Chem A 2008; 112:11895-902. [PMID: 18956856 DOI: 10.1021/jp800577q] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ondřej Demel
- Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1 Canada
| | - K. R. Shamasundar
- Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1 Canada
| | - Liguo Kong
- Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1 Canada
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1 Canada
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Sancho-García JC, Pérez-Jiménez AJ. Dependence of Charge-Transport Parameters on Static Correlation and Self-Interaction Energy: The Case of a 1,4-Bis(Phenylethynyl)Benzene Derivative Conjugated Molecule. J Phys Chem A 2008; 112:10325-32. [DOI: 10.1021/jp802160b] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- J. C. Sancho-García
- Departamento de Química Física, Universidad de Alicante, E-03080 Alicante, Spain
| | - A. J. Pérez-Jiménez
- Departamento de Química Física, Universidad de Alicante, E-03080 Alicante, Spain
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Weimer M, Della Sala F, Görling A. Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation. J Chem Phys 2008; 128:144109. [DOI: 10.1063/1.2868755] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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Pérez-Jiménez AJ, Pérez-Jordá JM, Sancho-García JC. Combining two-body density correlation functionals with multiconfigurational wave functions using natural orbitals and occupation numbers. J Chem Phys 2007; 127:104102. [PMID: 17867732 DOI: 10.1063/1.2770713] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a procedure that combines multiconfigurational (MC) wave functions with two-body density correlation functionals by transforming the latter into functionals of the MC natural orbitals and occupation numbers. The method is tested with the spectroscopic constants of a set of 11 diatomics, the diradical-involved automerization barrier of cyclobutadiene, the energy difference between triplet and open-shell singlet states in He and the methylene molecule, and the magnetic coupling constants of several systems, such as NiO, KNiF(3), K(2)NiF(4), La(2)CuO(4), alpha-4-dehydrotoluene, 1,1('),5,5(')-tetramethyl-6,6(')-dioxo-3,3(')-biverdazyl, [Cu(2)Cl(6)](-2), copper(II) acetate monohidrate and H-He-H. The procedure is applied to the Colle-Salvetti [Theor. Chim. Acta 37, 329 (1975); 53, 55 (1979)], functional and to a size-consistent functional depending on the on-top pair density (F1-5-N(eff)). On average, the best results are provided by the transformed F1-5-N(eff) [J. Chem. Phys. 114, 2022 (2001)] functional.
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Pérez-Jiménez AJ, Sancho-García JC, Pérez-Jordá JM. Torsional potential of 4,4'-bipyridine: ab initio analysis of dispersion and vibrational effects. J Chem Phys 2007; 123:134309. [PMID: 16223290 DOI: 10.1063/1.2043107] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ab initio calculations using restricted Hartree-Fock, second-order Møller-Plesset perturbation theory (MP2), density-functional theory (DFT), and coupled-cluster methods have been done to obtain the torsional potential-energy profile of the aza-aromatic molecule 4,4'-bipyridine. The torsional potential is evaluated adiabatically by fixing the normalized sum of the dihedral angles through the C-C inter-ring bond at several values along the torsional path and relaxing the remaining degrees of freedom. Previous discrepancies between MP2 and DFT internal rotation barrier heights are removed, and seen to be mostly due to the underestimation of the dispersion energy in the coplanar conformer by MP2 when using relatively small basis sets. The calculations indicate that the barrier height between the twisted global minimum and the 0 degrees conformer is around 1.5-1.8 kcal mol-1 while that corresponding to the 90 degrees one is about 2.0-2.2 kcal mol-1. This same relative energy ordering of the coplanar and perpendicular conformers was experimentally derived from nuclear magnetic resonance (NMR) measurements of 1H dipolar couplings on 4,4'-bipyridine solutions in a nematic liquid crystal, although the barrier heights are much lower than those estimated from NMR experiments in the gas phase. The DFT infrared spectrum and zero-point vibrational energy corrections to the torsional energy profile have also been calculated, the latter having a small influence on the torsional potential-energy profiles.
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Abstract
This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.
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Affiliation(s)
- Donald G Truhlar
- Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, Minnesota 55455-0431, USA.
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Levchenko SV, Wang T, Krylov AI. Analytic gradients for the spin-conserving and spin-flipping equation-of-motion coupled-cluster models with single and double substitutions. J Chem Phys 2005; 122:224106. [PMID: 15974650 DOI: 10.1063/1.1877072] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Analytic gradient expressions for the spin-conserving and spin-flipping equation-of-motion coupled-cluster models with single and double substitutions are derived using a Lagrangian approach for the restricted and unrestricted Hartree-Fock references, both for the case of all orbitals being active in correlated calculations and for the frozen core and/or virtual orbitals. Details of the implementation within the Q-CHEM electronic structure package are discussed. The capabilities of the new code are demonstrated by application to cyclobutadiene.
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Affiliation(s)
- Sergey V Levchenko
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
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Gräfenstein J, Cremer * D. Development of a CAS-DFT method covering non-dynamical and dynamical electron correlation in a balanced way. Mol Phys 2005. [DOI: 10.1080/00268970512331318858] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Gusarov S, Malmqvist * PÅ, Lindh R. Using on-top pair density for construction of correlation functionals for multideterminant wave functions. Mol Phys 2004. [DOI: 10.1080/00268970410001734297] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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