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Khokhlov D, Belov A. Low-Lying Excited States of Natural Carotenoids Viewed by Ab Initio Methods. J Phys Chem A 2022; 126:4376-4391. [PMID: 35767689 DOI: 10.1021/acs.jpca.2c02485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Low-lying excited states of carotenoids (the optically dark 2Ag- and bright 1Bu+) are deeply involved in energy transfer processes in photosynthetic antennas, such as light harvesting and non-photochemical quenching. Though any ab initio modeling of these phenomena has to rely on precise energies of the carotenoid electronic states, the accurate evaluation of these states remains a challenging problem due to their different natures. The paper aims to study the accuracy of the excitation energies of the low-lying excited states of certain open- and closed-chain carotenoids obtained by a state-of-the-art multireference approach for electronic structure calculation. Here, density matrix renormalization group SCF (DMRGSCF) and a perturbative approach based on driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2) were used to treat the static and dynamic correlation, respectively. Nuclear geometries of the electronic states were optimized with DFT-based approaches. It is demonstrated that spin-flip TD-DFT can replace multiconfigurational methods for the geometry optimization of the 2Ag- state but not for the calculation of the excitation energy. Adiabatic excitation energies to the 1Bu+ state were shown to be within a margin of 1000 cm-1 with an appropriate flow parameter value. Adiabatic excitation energies to the 2Ag- state for the open-chain carotenoids lie within a range of experimental values (taking into account the broad range of experimental estimates); for the closed-chain ones, the error does not exceed 2000 cm-1. Ab initio stationary (1Ag- → 1Bu+) and transient (2Ag- → 1Bu+) absorption spectra were modeled for violaxanthin and lycopene, and these spectra showed good agreement with the experimental ones both in terms of the vibronic structure and the transition energies.
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Affiliation(s)
- Daniil Khokhlov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Aleksandr Belov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
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Bondanza M, Jacquemin D, Mennucci B. Excited States of Xanthophylls Revisited: Toward the Simulation of Biologically Relevant Systems. J Phys Chem Lett 2021; 12:6604-6612. [PMID: 34251826 PMCID: PMC8311646 DOI: 10.1021/acs.jpclett.1c01929] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 07/08/2021] [Indexed: 06/13/2023]
Abstract
Xanthophylls are a class of oxygen-containing carotenoids, which play a fundamental role in light-harvesting pigment-protein complexes and in many photoresponsive proteins. The complexity of the manifold of the electronic states and the large sensitivity to the environment still prevent a clear and coherent interpretation of their photophysics and photochemistry. In this Letter, we compare cutting-edge ab initio methods (CC3 and DMRG/NEVPT2) with time-dependent DFT and semiempirical CI (SECI) on model keto-carotenoids and show that SECI represents the right compromise between accuracy and computational cost to be applied to real xanthophylls in their biological environment. As an example, we investigate canthaxanthin in the orange carotenoid protein and show that the conical intersections between excited states and excited-ground states are mostly determined by the effective bond length alternation coordinate, which is significantly tuned by the protein through geometrical constraints and electrostatic effects.
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Affiliation(s)
- Mattia Bondanza
- Dipartimento
di Chimica e Chimica Industriale, University
of Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Denis Jacquemin
- Université
de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Benedetta Mennucci
- Dipartimento
di Chimica e Chimica Industriale, University
of Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
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Khokhlov D, Belov A. Toward an Accurate Ab Initio Description of Low-Lying Singlet Excited States of Polyenes. J Chem Theory Comput 2021; 17:4301-4315. [PMID: 34125516 DOI: 10.1021/acs.jctc.0c01293] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
The low-lying excited states of carotenoids play a crucial role in many important biophysical processes such as photosynthesis. Most of these excited states are strongly correlated, which makes them both challenging for a qualitative ab initio description and an engaging model system for trying out emerging multireference methods. Among these methods, driven similarity renormalization group (DSRG) and its perturbative version (DSRG-MRPT2) are especially attractive in terms of both accuracy and moderate numerical complexity. In this paper, we applied density matrix renormalization group (DMRG) followed by DSRG-MRPT2 for the calculation of vertical and adiabatic excitation energies into the 2Ag-, 1Bu-, and 1Bu+ electronic states of polyenes containing from 8 to 13 conjugating double bonds acting as a model for natural carotenoids. It was shown that the DSRG flow parameter should be adjusted to ensure both the energy convergence with respect to it and the agreement with the experimental data. With the increased flow parameter, the proposed combination of methods provides a reasonable agreement with the experiment. The deviations of the adiabatic excitation energies are less than 1000 cm-1 for the 2Ag- and less than 3000 cm-1 for the excited states of the Bu symmetry, which in terms of accuracy significantly outperforms the N-electron valence state perturbation theory. At the same time, DSRG-MRPT2 is shown to be robust with respect to variation of quality of the DMRG reference wave function such as the orbital optimization or the number of electronic states in the averaging.
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Affiliation(s)
- Daniil Khokhlov
- Department of Chemistry, Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Aleksandr Belov
- Department of Chemistry, Lomonosov Moscow State University, Moscow, 119991, Russia
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Ye HZ, Tran HK, Van Voorhis T. Accurate Electronic Excitation Energies in Full-Valence Active Space via Bootstrap Embedding. J Chem Theory Comput 2021; 17:3335-3347. [PMID: 33957050 DOI: 10.1021/acs.jctc.0c01221] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Fragment embedding has been widely used to circumvent the high computational scaling of using accurate electron correlation methods to describe the electronic ground states of molecules and materials. However, similar applications that utilize fragment embedding to treat electronic excited states are comparably less reported in the literature. The challenge here is twofold. First, most fragment embedding methods are most effective when the property of interest is local, but the change of the wave function upon excitation is nonlocal in general. Second, even for local excitations, an accurate estimate of, for example, the excitation energy can still be challenging owing to the need for a balanced treatment of both the ground and the excited states. In this work, we show that bootstrap embedding (BE), a fragment embedding method developed recently by our group, is promising toward describing general electronic excitations. Numerical simulations show that the excitation energies in full-valence active space (FVAS) can be well-estimated by BE to an error of ∼0.05 eV using relatively small fragments, for both local excitations and the excitations of some large dye molecules that exhibit strong charge-transfer characters. We hence anticipate BE to be a promising solution to accurately describing the excited states of large chemical systems.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Henry K Tran
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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Optical Projection and Spatial Separation of Spin-Entangled Triplet Pairs from the S1 (21 Ag–) State of Pi-Conjugated Systems. Chem 2020. [DOI: 10.1016/j.chempr.2020.09.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
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Khokhlov D, Belov A. Ab Initio Study of Low-Lying Excited States of Carotenoid-Derived Polyenes. J Phys Chem A 2020; 124:5790-5803. [PMID: 32573233 DOI: 10.1021/acs.jpca.0c01678] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Knowledge about excited states of carotenoids is essential for understanding photophysical processes underlying photosynthesis. However, due to the presence of a large number of optically dark states, experimental study of the excited-state manifold is limited to a significant extent. In this paper, we apply high-level ab initio quantum chemical methods to study the low-lying excited states of polyenes containing from 8 to 13 conjugated double bonds, which serve as a model for natural carotenoids. Vertical and adiabatic excitation energies from the ground 1Ag- state to the excited 2Ag-, 1Bu+, and 1Bu- states were evaluated by means of density matrix renormalization group (DMRG) with NEVPT2 perturbative correction. The energies of all excited states are highly sensitive to nuclear geometry, especially the 2Ag- state. Thus, the 2Ag- and 1Bu+ states interchange their relative positions upon geometry relaxation, while the vertical excitation energy to the 2Ag- state is rather high. At the same time, the 1Bu- state energy is shown to be higher than other studied excited states at any geometry. With relaxed geometries of the excited states, absorption and transient absorption spectra were calculated within the Franck-Condon approximation bridging the gap between experimental spectroscopic data and computational results.
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Affiliation(s)
- Daniil Khokhlov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
| | - Aleksandr Belov
- Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
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Taffet EJ, Fassioli F, Toa ZSD, Beljonne D, Scholes GD. Uncovering dark multichromophoric states in Peridinin-Chlorophyll-Protein. J R Soc Interface 2020; 17:20190736. [PMID: 32183641 DOI: 10.1098/rsif.2019.0736] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
It has long been recognized that visible light harvesting in Peridinin-Chlorophyll-Protein is driven by the interplay between the bright (S2) and dark (S1) states of peridinin (carotenoid), along with the lowest-lying bright (Qy) and dark (Qx) states of chlorophyll-a. Here, we analyse a chromophore cluster in the crystal structure of Peridinin-Chlorophyll-Protein, in particular, a peridinin-peridinin and a peridinin-chlorophyll-a dimer, and present quantum chemical evidence for excited states that exist beyond the confines of single peridinin and chlorophyll chromophores. These dark multichromophoric states, emanating from the intermolecular packing native to Peridinin-Chlorophyll-Protein, include a correlated triplet pair comprising neighbouring peridinin excitations and a charge-transfer interaction between peridinin and the adjacent chlorophyll-a. We surmise that such dark multichromophoric states may explain two spectral mysteries in light-harvesting pigments: the sub-200-fs singlet fission observed in carotenoid aggregates, and the sub-200-fs chlorophyll-a hole generation in Peridinin-Chlorophyll-Protein.
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Affiliation(s)
- Elliot J Taffet
- Department of Chemistry, Princeton University, Washington Road, Princeton, NJ 08540, USA.,Department of Chemistry, University of Mons, 7000 Mons, Belgium
| | - Francesca Fassioli
- Department of Chemistry, Princeton University, Washington Road, Princeton, NJ 08540, USA.,SISSA - Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
| | - Zi S D Toa
- Department of Chemistry, Princeton University, Washington Road, Princeton, NJ 08540, USA
| | - David Beljonne
- Department of Chemistry, University of Mons, 7000 Mons, Belgium
| | - Gregory D Scholes
- Department of Chemistry, Princeton University, Washington Road, Princeton, NJ 08540, USA
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Taffet EJ, Lee BG, Toa ZSD, Pace N, Rumbles G, Southall J, Cogdell RJ, Scholes GD. Carotenoid Nuclear Reorganization and Interplay of Bright and Dark Excited States. J Phys Chem B 2019; 123:8628-8643. [PMID: 31553605 DOI: 10.1021/acs.jpcb.9b04027] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We report quantum chemical calculations using multireference perturbation theory (MRPT) with the density matrix renormalization group (DMRG) plus photothermal deflection spectroscopy measurements to investigate the manifold of carotenoid excited states and establish their energies relative to the bright state (S2) as a function of nuclear reorganization. We conclude that the primary photophysics and function of carotenoids are determined by interplay of only the bright (S2) and lowest-energy dark (S1) states. The lowest-lying dark state, far from being energetically distinguishable from the lowest-lying bright state along the entire excited-state nuclear reorganization pathway, is instead computed to be either the second or first excited state depending on what equilibrium geometry is considered. This result suggests that, rather than there being a dark intermediate excited state bridging a non-negligible energy gap from the lowest-lying dark state to the lowest-lying bright state, there is in fact no appreciable energy gap to bridge following photoexcitation. Instead, excited-state nuclear reorganization constitutes the bridge from S2 to S1, in the sense that these two states attain energetic degeneracy along this pathway.
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Affiliation(s)
- Elliot J Taffet
- Department of Chemistry , Princeton University , Princeton , New Jersey 08544 , United States
| | - Benjamin G Lee
- Chemical and Materials Science Center , National Renewable Energy Laboratory , Golden , Colorado 80401 , United States
| | - Zi S D Toa
- Department of Chemistry , Princeton University , Princeton , New Jersey 08544 , United States
| | - Natalie Pace
- Chemical and Materials Science Center , National Renewable Energy Laboratory , Golden , Colorado 80401 , United States
| | - Garry Rumbles
- Chemical and Materials Science Center , National Renewable Energy Laboratory , Golden , Colorado 80401 , United States
| | - June Southall
- Institute of Molecular, Cell and Systems Biology, College of Medical Veterinary and Life Sciences , University of Glasgow , University Avenue, Glasgow G12 8QQ , U.K
| | - Richard J Cogdell
- Institute of Molecular, Cell and Systems Biology, College of Medical Veterinary and Life Sciences , University of Glasgow , University Avenue, Glasgow G12 8QQ , U.K
| | - Gregory D Scholes
- Department of Chemistry , Princeton University , Princeton , New Jersey 08544 , United States
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Abstract
![]()
Fragment
embedding is one way to circumvent the high computational
scaling of accurate electron correlation methods. The challenge of
applying fragment embedding to molecular systems primarily lies in
the strong entanglement and correlation that prevent accurate fragmentation
across chemical bonds. Recently, Schmidt decomposition has been shown
effective for embedding fragments that are strongly coupled to a bath
in several model systems. In this work, we extend a recently developed
quantum embedding scheme, bootstrap embedding (BE), to molecular systems.
The resulting method utilizes the matching conditions naturally arising
from using overlapping fragments to optimize the embedding. Numerical
simulation suggests that the accuracy of the embedding improves rapidly
with fragment size for small molecules, whereas larger fragments that
include orbitals from different atoms may be needed for larger molecules.
BE scales linearly with system size (apart from an integral transform)
and hence can potentially be useful for large-scale calculations.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Nathan D Ricke
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Henry K Tran
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Troy Van Voorhis
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
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Liu Y, Kilby P, Frankcombe TJ, Schmidt TW. Electronic transitions of molecules: vibrating Lewis structures. Chem Sci 2019; 10:6809-6814. [PMID: 31391902 PMCID: PMC6657403 DOI: 10.1039/c9sc02534k] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Accepted: 06/02/2019] [Indexed: 11/21/2022] Open
Abstract
Since the conception of the electron pair bond, Lewis structures have been used to illustrate the electronic structure of a molecule in its ground state. But, for excited states, most descriptions rely on the concept of molecular orbitals. In this work we demonstrate a simple and intuitive description of electronic resonances in terms of localized electron vibrations. By partitioning the 3N-dimensional space of a many-electron wavefunction into hyper-regions related by permutation symmetry, chemical structures naturally result which correspond closely to Lewis structures, with identifiable single and double bonds, and lone pairs. Here we demonstrate how this picture of electronic structure develops upon the admixture of electronic wavefunctions, in the spirit of coherent electronic transitions. We show that π-π* transitions correspond to double-bonding electrons oscillating along the bond axis, and n-π* transitions reveal lone-pairs vibrating out of plane. In butadiene and hexatriene, the double-bond oscillations combine with in- and out-of-phase combinations, revealing the correspondence between electronic transitions and molecular normal mode vibrations. This analysis allows electronic excitations to be described by building upon ground state electronic structures, without the need for molecular orbitals.
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Affiliation(s)
- Yu Liu
- ARC Centre of Excellence in Exciton Science , School of Chemistry , UNSW Sydney , NSW 2052 , Australia . ; Tel: +61 439 386 109
| | - Philip Kilby
- Data 61 , Locked Bag 8001 , Canberra , ACT 2601 , Australia
| | | | - Timothy W Schmidt
- ARC Centre of Excellence in Exciton Science , School of Chemistry , UNSW Sydney , NSW 2052 , Australia . ; Tel: +61 439 386 109
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Ye HZ, Welborn M, Ricke ND, Van Voorhis T. Incremental embedding: A density matrix embedding scheme for molecules. J Chem Phys 2018; 149:194108. [PMID: 30466262 DOI: 10.1063/1.5053992] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding methods mainly focus on systems composed of weakly correlated parts and are insufficient when division across chemical bonds is unavoidable. Recently, density matrix embedding theory and other methods based on the Schmidt decomposition have emerged as a fresh approach to this problem. Despite their success on model systems, these methods can prove difficult for realistic systems because they rely on either a rigid, non-overlapping partition of the system or a specification of some special sites (i.e., "edge" and "center" sites), neither of which is well-defined in general for real molecules. In this work, we present a new Schmidt decomposition-based embedding scheme called incremental embedding that allows the combination of arbitrary overlapping fragments without the knowledge of edge sites. This method forms a convergent hierarchy in the sense that higher accuracy can be obtained by using fragments involving more sites. The computational scaling for the first few levels is lower than that of most correlated wave function methods. We present results for several small molecules in atom-centered Gaussian basis sets and demonstrate that incremental embedding converges quickly with fragment size and recovers most static correlation in small basis sets even when truncated at the second lowest level.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Matthew Welborn
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Nathan D Ricke
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Taffet EJ, Scholes GD. Peridinin Torsional Distortion and Bond-Length Alternation Introduce Intramolecular Charge-Transfer and Correlated Triplet Pair Intermediate Excited States. J Phys Chem B 2018; 122:5835-5844. [DOI: 10.1021/acs.jpcb.8b02504] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Elliot J. Taffet
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Gregory D. Scholes
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
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