Prediction of Excited-State Energies and Singlet–Triplet Gaps of Charge-Transfer States Using a Restricted Open-Shell Kohn–Sham Approach

Hait, Diptarka; Zhu, Tianyu; McMahon, David P.; Voorhis, Troy Van

doi:10.1021/acs.jctc.6b00426

Cited by 88 publications

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“…16 These effects originally stem from errors in the ground state DFT solution like delocalization error 17,18 or spin symmetry breaking, 19,20 but the linear response protocol augments these deficiencies in the reference to catastrophic levels in excited states, on account of insufficient orbital relaxation. [21][22][23][24]…”

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Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

Hait

Head‐Gordon

2020

J. Chem. Theory Comput.

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We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse.The resulting Square Gradient Minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach.SGM is applied to both single determinant ∆SCF and spin-purified Restricted Open-Shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the Maximum Overlap Method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ∆SCF/ROKS predict highly accurate excitation 1 arXiv:1911.04709v1 [physics.chem-ph] 12 Nov 2019 energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems. IntroductionAccurate quantum chemical methods for modeling electronic excited states are essential for gaining insight into the photophysics and photochemistry of molecules and materials. The most widely used technique for excited state calculations at present is time dependent density functional theory (TDDFT), 1-5 on account of its relatively low computational complexity (O(N 2−3 ), where N is the molecule size) and reasonable accuracy for many problems. 6,7 TDDFT excited states are computed via determining the linear response of a ground state DFT solution to time-dependent external electric fields, 5 permitting simultaneous modeling of multiple excited states. In principle, TDDFT is formally exact 1 when the exact exchangecorrelation (xc) ground state functional is employed, although lack of that functional, and the need for the widely used adiabatic local density approximation 3-5 (ALDA) prevents this from being the case in practice. ALDA in fact restricts utility of TDDFT to single excitations out of the reference alone, with large errors arising whenever the target excited state has significant double (or higher) excitation character. 8-11 Furthermore, TDDFT is known to systematically underestimate excitation energies for charge-transfer 5,12-14 and Rydberg 8,15 states, and yields qualitatively erroneous potential energy surfaces along single bond dissociation coordinates. 16 These effects originally stem from errors in the ground state DFT solution like delocalization error 17,18 or spin symmetry breaking, 19,20 but the linear response protocol augments these deficiencies in the reference to catastrophic levels in excited states, on account of insufficient or...

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confidence: 99%

“…and is excellent for CT state energies in systems where TDDFT fails catastrophically 24. However, the implementation described in Ref 28 is restricted to the lowest excited singlet (S 1 ) state alone.…”

mentioning

confidence: 99%

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

Hait

Head‐Gordon

2020

J. Chem. Theory Comput.

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165

297

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“…This general overdelocalization behavior leads to catastrophes like incorrect asymptotics in dissociation curves for charged species 20 (as shown in the right panel of Fig 1), fractional electrons dissociating from anions 21 or spurious fractional charges at the dissociation limit for polar bonds [22][23][24][25] . It also causes other complications like lowering of barrier heights [26][27][28] , reduction of band gaps 29,30 and dramatic underestimation of excited state energies with linear response time dependent density functional theory (TDDFT) [31][32][33][34] . Self-repulsion alone is however an inadequate explanation for deviation from Eqn 2 27,35 .…”

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Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number

Hait

Head‐Gordon

2018

J. Phys. Chem. Lett.

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Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps and excitation energies. We present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C 12 H 14 polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge based data point could therefore permit fitting/tuning of functionals with lower delocalization error.The central idea behind density functional theory (DFT) is that there exists a functional which maps the ground state electron density of an electron distribution to its energy 1-5 . The existence of this exact functional was formally proven by Hohenberg and Kohn in 1964 1 , but it remains computationally inaccessible for realistic systems. It is however possible to express the total energy E as :where the non-interacting kinetic energy E T , the electron-external potential interaction energy E ext (which includes electron-nuclear attraction energy) and the quasi-classical electron repulsion E J are exactly known, leaving behind the exchange correlation energy E xc as the only unknown term 2 . The practical use of DFT typically involves employing some of the hundreds of density functional approximations (DFAs) for E xc that have been proposed over the last few decades 5 . DFAs deviate from the exact functional in many (at times, predictable) regards and there is often substantial variation in predictions from different DFAs. Despite these shortcomings, DFT has found wide use in chemistry, physics and material science as an often adequately accurate and computationally efficient theory that permits exploration of systems well beyond the reach of more expensive wave function approaches. There are however certain known properties of the exact functional that most modern DFAs deviate from. Using statistical mixture, Perdew et.al. 6 showed that the electronic energy of a system with fractional charge is exactly determined by a linear interpolation between the energies corresponding to the two closest integer electron numbers. Mathematically, therefore, the energy E of a system with N − x electrons (where N is a nonnegative integer and x lies between 0 and 1) is given by:Eqn. 2 therefore specifies that the electronic energy is piecewise linear with respect to the electro...

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“…[49][50][51] As a result, our SCF procedure to converge molecular orbitals in Section 2.3 will also be similar to the one for converging ROKS calculations. [49][50][51] As a result, our SCF procedure to converge molecular orbitals in Section 2.3 will also be similar to the one for converging ROKS calculations.…”

Section: Spin-adiabatic Statesmentioning

confidence: 99%

Constructing spin‐adiabatic states for the modeling of spin‐crossing reactions. I. A shared‐orbital implementation

Tao

Pei

Bellonzi

et al. 2019

Int J of Quantum Chemistry

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In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spincrossing reactions (predissociation of N 2 O, singlet-triplet conversion in CH 2 , and CO addition to Fe(CO) 4 ), the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (ie, a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces. K E Y W O R D Schemical reactions, spin-adiabatic surface, spin-crossing reaction | INTRODUCTIONIn most chemical reactions, the total electron spin is conserved. However, if a reaction involves high-spin species, such as oxygen ( 3 P) and nitrogen ( 4 N) atoms, molecular oxygen ( 3 O 2 ), and transition metals, [1][2][3][4][5][6][7][8] a change in the electron spin might occur during the transition from the reactant to the product. Such spin-crossing reactions are known to be enabled by the spin-orbit coupling (SOC) between different spin states. [9,10] While usually slower than their spin-conserved counterparts (especially in cases with a weak SOC), spin-crossing reactions can play an important role in biochemical processes, homogeneous/heterogeneous catalysis, energy storage/conversion, etc.In the study of spin-crossing reactions, one can explore either the spin-diabatic or spin-adiabatic potential energy surfaces. In the spindiabatic approach, the central task is to reach the crossing seam of two spin-diabatic potential energy surfaces, and then locate the minimum energy crossing point (MECP) on the crossing seam. [11][12][13][14] This is illustrated in Figure 1A for a triplet-to-singlet reaction. Once the MECP is found, Yunwen Tao and Zheng Pei contributed equally to this study.

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Prediction of Excited-State Energies and Singlet–Triplet Gaps of Charge-Transfer States Using a Restricted Open-Shell Kohn–Sham Approach

Cited by 88 publications

References 59 publications

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number

Constructing spin‐adiabatic states for the modeling of spin‐crossing reactions. I. A shared‐orbital implementation

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