Conical Intersections from Particle–Particle Random Phase and Tamm–Dancoff Approximations

Yang, Yang; Shen, Lin; Zhang, Du; Yang, Weitao

doi:10.1021/acs.jpclett.6b00936

Cited by 29 publications

(39 citation statements)

References 27 publications

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“…However, as previously shown (not duplicated here), 3,11 KSDFT and TDDFT calculations result in a spurious curved seam of intersections due to incorrect dimensionality. Furthermore, these calculations also suffer from convergence and instability issues with imaginary eigenvalues.…”

Section: Photodissociation Of Ammoniasupporting

confidence: 75%

Beyond Kohn–Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory

Gao

Grofe

Ren

et al. 2016

J. Phys. Chem. Lett.

202

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A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn–Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections.

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Section: Photodissociation Of Ammoniasupporting

confidence: 75%

Beyond Kohn–Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory

Gao

Grofe

Ren

et al. 2016

J. Phys. Chem. Lett.

202

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show abstract

“…Because the ground and excited states are treated on equal footing, pp-RPA and pp-TDA based on an (N-2)electron reference are able to predict the correct topography around conical intersections, as has been shown explicitly for H3 and NH3. 53 This is a major advance over conventional ph-TDDFT and CIS methods, which cannot reproduce conical intersections involving the ground state. 2 In 2014, Peng et al derived the pp-RPA equations from linear response theory by choosing a pairing field perturbation (termed TDDFT-P, see below in Section II.A).…”

Section: Introductionmentioning

confidence: 99%

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

Bannwarth

Hohenstein

et al. 2020

The Journal of Chemical Physics

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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 (CASSCF) 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 Nelectron 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. The treatment of dynamic correlation is introduced through the use of commonly-employed density functional approximations to the exchange-correlation potential. 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 pp* and np* 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.

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“…Both of these eigenvalue problems are guaranteed to have real eigenvalues only and are thus more robust than the full pp-RPA case, which can have complex solutions. While the pp-TDA method has been proposed by Yang and coworkers as a method to describe low-lying excited states and S0/S1 conical intersections, 42 hh-TDA has not been treated in detail until now. In this work, we suggest hh-TDA as an alternative and very efficient DFT-based method capable of computing low-lying excited states while remaining applicable in cases where a robust treatment of static correlation is essential.…”

Section: C! the Hole-hole Tamm-dancoff Approximated Pp-rpa Methodsmentioning

confidence: 99%

“…[34][35] Recently, the particle-particle random phase approximation (pp-RPA) [36][37][38][39][40][41] and its Tamm-Dancoff approximation (pp-TDA) 40,42 have been proposed as a class of methods for describing both static and dynamic correlation while requiring minimal parameterization (i.e., no active space selection) at a computational cost comparable to the simplest excited state methods, e.g., TDDFT and configuration interaction singles (CIS). By performing two electron attachments to a doubly cationic (N-2) reference, the N-electron ground state and excited states from the highest occupied Although the pp-TDA methods have been explored in a series of papers by Yang and coworkers, [39][40]42 the complementing hole-hole (hh) scheme has so far been almost 37,41 entirely ignored. In this paper, we describe the hole-hole Tamm-Dancoff approximation (hh-TDA) as an efficient and robust electronic structure method that incorporates dynamic and static correlation in ground and low-lying excited states.…”

Section: Introductionmentioning

confidence: 99%

Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory: A Highly Efficient Electronic Structure Method Incorporating Dynamic and Static Correlation

Bannwarth

Hohenstein

et al. 2020

Preprint

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<div> <div> <div> <p>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 (CASSCF) methods are deficient in their ability to describe dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we describe the hole-hole Tamm- Dancoff approximated (<i>hh</i>-TDA) density functional theory method, which is closely related to the previously established particle-particle random phase approximation (<i>pp</i>-RPA) and its TDA variant (<i>pp</i>-TDA). In <i>hh</i>-TDA, the <i>N</i>-electron electronic states are obtained through double annihilations starting from a doubly anionic (<i>N</i>+2 electron) reference state. In this way, <i>hh</i>-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly-employed density functional approximations to the exchange-correlation potential. <i>hh</i>-TDA appears to be 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 pipi* and npi* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on <i>pp</i>-TDA, we employ a functional- dependent choice for the response kernel in <i>pp</i>- and <i>hh</i>-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT. </p> </div> </div> </div>

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Conical Intersections from Particle–Particle Random Phase and Tamm–Dancoff Approximations

Cited by 29 publications

References 27 publications

Beyond Kohn–Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory

Beyond Kohn–Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory

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

Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory: A Highly Efficient Electronic Structure Method Incorporating Dynamic and Static Correlation

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