Spin-flip Configuration Interaction Research Articles

Charge transfer via spin flip configuration interaction: Benchmarks and application to singlet fission.

Charge transfer and multi-exciton states are among the most difficult to characterize using electronic structure theories. Previously, restricted active space-spin flip (RAS-SF) methods have been applied to describe multi-exciton states, but these have not yet been shown to be useful for charge-transfer states. Herein, a variant of RAS-SF is introduced to treat charge-transfer states and electronic couplings. This approach relies on partitioning of the full RAS-SF Hamiltonian into charge-transfer and non-charge-transfer blocks, allowing the different types of diabatic states to be resolved in a straightforward fashion. To demonstrate this approach in practice, model dimer systems, intramolecular charge-transfer dyads, and an intramolecular singlet fission system were examined. Being low-cost and relatively accurate, RAS-SF provides important insight into electron transfer pathways in conventional donor-acceptor systems, as well as characterizations of charge transfer mechanisms involving strongly correlated multi-exciton states. Studies of electron transfer from an intramolecular singlet fission chromophore to an anthraquinone acceptor demonstrate the unique capabilities of the proposed RAS-SF method.

First Principle Prediction of Intramolecular Singlet Fission and Triplet Triplet Annihilation Rates.

Intramolecular singlet fission and triplet-triplet annihilation (TTA) has been experimentally observed and reported. However, problems remain in theoretically accounting for the corresponding intramolecular electronic couplings and their rates. We used the fragment excitation difference (FED) scheme to calculate the coupling with states from restricted active-space spin-flip configuration interaction. We investigated three covalently linked pentacene dimers via a phenyl group in an ortho-, meta-, and para-arrangement. The singlet fission and TTA couplings were enhanced when two chromophores were covalently linked. With the Fermi golden rule, both the estimated singlet fission and TTA rates were in line with the experimental results. For systems with significant singlet-fission coupling, charge-transfer components were observed in the excited states involved, and charge-transfer states were also seen within 1 eV above the singlet excited states. Our approach allows for an analysis of through-bond versus through-space singlet fission in the full electronic wave functions. The FED scheme is useful for calculating intramolecular singlet-fission and TTA couplings.

A general spin-complete spin-flip configuration interaction method.

A new, general spin-correct spin-flip configuration interaction (SF-CI) method is introduced by extending the occupation restricted multiple active spaces (ORMAS) CI method in GAMESS. SF-ORMAS is a single reference CI method that utilizes a high-spin restricted open shell determinant on which an arbitrary amount of spin-flipped excitations are carried out to generate a wave function of desired multiplicity. Furthermore, the SF-ORMAS method allows for a flexible design of the active space(s) to fit the chemical problem at hand. Therefore, a variety of spin-flip schemes can be implemented within this one formalism. As SF-ORMAS mostly accounts for static correlation, dynamic correlation is included through perturbation theory. The new method is demonstrated for single and multiple bond breaking, diradical systems, vertical excitations of linear alkenes, and the singlet-triplet energy gap of silicon trimer.

Recovering dynamic correlation in spin flip configuration interaction through a difference dedicated approach.

This article introduces the restricted-active-space n-spin flip configuration interaction models, RAS(S)-SF and RAS(S,2h,2p)-SF, which provide highly correlated, yet low cost approaches for treating polyradical systems. These levels of theory add electronic degrees of freedom beyond those of previous spin flip approaches in order to achieve accurate ground and excited state energetics. The effects of additional dynamic correlation were investigated by comparing these two techniques to the prior RAS(h,p)-SF method on a variety of test systems, including multiple electronic states of methylene, tetramethyleneethane, three binuclear transition metal complexes, and a tetracene dimer. RAS(S,2h,2p)-SF significantly improves state descriptions in all cases and provides high accuracy even when using a minimal number of spin flips. Furthermore, this correlated level of theory is shown to be extensible to the large systems involved in singlet fission, where the multi-excitonic states in tetracene dimers are difficult to simulate with standard methods and therefore are still a matter of debate. Using a triple-zeta basis, the double triplet state, 1(TT), is predicted to be unbound. This result contradicts lower levels of theory and provides important insight into tetracene's ability to undergo efficient singlet fission.

Spin-flip configuration interaction singles with exact spin-projection: Theory and applications to strongly correlated systems.

Spin-flip approaches capture static correlation with the same computational scaling as the ordinary single reference methods. Here, we extend spin-flip configuration interaction singles (SFCIS) by projecting out intrinsic spin-contamination to make it spin-complete, rather than by explicitly complementing it with spin-coupled configurations. We give a general formalism of spin-projection for SFCIS, applicable to any spin states. The proposed method is viewed as a natural unification of SFCIS and spin-projected CIS to achieve a better qualitative accuracy at a low computational cost. While our wave function ansatz is more compact than previously proposed spin-complete SF approaches, it successfully offers more general static correlation beyond biradicals without sacrificing good quantum numbers. It is also shown that our method is invariant with respect to open-shell orbital rotations, due to the uniqueness of spin-projection. We will report benchmark calculations to demonstrate its qualitative performance on strongly correlated systems, including conical intersections that appear both in ground-excited and excited-excited degeneracies.

Singlet-triplet energy gaps for diradicals from particle-particle random phase approximation.

The particle-particle random phase approximation (pp-RPA) for calculating excitation energies has been applied to diradical systems. With pp-RPA, the two nonbonding electrons are treated in a subspace configuration interaction fashion while the remaining part is described by density functional theory (DFT). The vertical or adiabatic singlet-triplet energy gaps for a variety of categories of diradicals, including diatomic diradicals, carbene-like diradicals, disjoint diradicals, four-π-electron diradicals, and benzynes are calculated. Except for some excitations in four-π-electron diradicals, where four-electron correlation may play an important role, the singlet-triplet gaps are generally well predicted by pp-RPA. With a relatively low O(r(4)) scaling, the pp-RPA with DFT references outperforms spin-flip configuration interaction singles. It is similar to or better than the (variational) fractional-spin method. For small diradicals such as diatomic and carbene-like ones, the error of pp-RPA is slightly larger than noncollinear spin-flip time-dependent density functional theory (NC-SF-TDDFT) with LDA or PBE functional. However, for disjoint diradicals and benzynes, the pp-RPA performs much better and is comparable to NC-SF-TDDFT with long-range corrected ωPBEh functional and spin-flip configuration interaction singles with perturbative doubles (SF-CIS(D)). In particular, with a correct asymptotic behavior and being almost free from static correlation error, the pp-RPA with DFT references can well describe the challenging ground state and charge transfer excitations of disjoint diradicals in which almost all other DFT-based methods fail. Therefore, the pp-RPA could be a promising theoretical method for general diradical problems.

Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory.

We revisit the calculation of analytic derivative couplings for configuration interaction singles (CIS), and derive and implement these couplings for its spin-flip variant for the first time. Our algorithm is closely related to the CIS analytic energy gradient algorithm and should be straightforward to implement in any quantum chemistry code that has CIS analytic energy gradients. The additional cost of evaluating the derivative couplings is small in comparison to the cost of evaluating the gradients for the two electronic states in question. Incorporation of an exchange-correlation term provides an ad hoc extension of this formalism to time-dependent density functional theory within the Tamm-Dancoff approximation, without the need to invoke quadratic response theory or evaluate third derivatives of the exchange-correlation functional. Application to several different conical intersections in ethylene demonstrates that minimum-energy crossing points along conical seams can be located at substantially reduced cost when analytic derivative couplings are employed, as compared to use of a branching-plane updating algorithm that does not require these couplings. Application to H3 near its D(3h) geometry demonstrates that correct topology is obtained in the vicinity of a conical intersection involving a degenerate ground state.

Perturbative approximations to single and double spin flip equation of motion coupled cluster singles doubles methods

Spin flip equation of motion coupled cluster (EOM-SF-CC) can correctly treat situations involving electronic degeneracies or near degeneracies, e.g., bond breaking, di- and tri-radicals, etc. However, for large systems EOM-SF-CC (even in single and double excitations) is computationally prohibitively expensive. Therefore, earlier approximations to EOM-SF-CC methods such as spin flip configuration interaction singles with perturbative doubles (SF-CIS(D)) have been proposed. In this work, we present a new perturbative approximation to EOM-SF-CC, which has been found to be more accurate than SF-CIS(D). The capabilities, advantages, and timings of the new approach have been demonstrated considering the singlet-triplet gaps in di- and triradicals as well as bond breaking examples. The method is extended to double spin flip EOM-CC and its capabilities have been tested.

Restricted active space spin-flip configuration interaction: Theory and examples for multiple spin flips with odd numbers of electrons

The restricted active space spin flip (RAS-SF) method is extended to allow ground and excited states of molecular radicals to be described at low cost (for small numbers of spin flips). RAS-SF allows for any number of spin flips and a flexible active space while maintaining pure spin eigenfunctions for all states by maintaining a spin complete set of determinants and using spin-restricted orbitals. The implementation supports both even and odd numbers of electrons, while use of resolution of the identity integrals and a shared memory parallel implementation allow for fast computation. Examples of multiple-bond dissociation, excited states in triradicals, spin conversions in organic multi-radicals, and mixed-valence metal coordination complexes demonstrate the broad usefulness of RAS-SF.

Avoided crossings, conical intersections, and low-lying excited states with a single reference method: The restricted active space spin-flip configuration interaction approach

The restricted active space spin-flip CI (RASCI-SF) performance is tested in the electronic structure computation of the ground and the lowest electronically excited states in the presence of near-degeneracies. The feasibility of the method is demonstrated by analyzing the avoided crossing between the ionic and neutral singlet states of LiF along the molecular dissociation. The two potential energy surfaces (PESs) are explored by means of the energies of computed adiabatic and approximated diabatic states, dipole moments, and natural orbital electronic occupancies of both states. The RASCI-SF methodology is also used to study the ground and first excited singlet surface crossing involved in the double bond isomerization of ethylene, as a model case. The two-dimensional PESs of the ground (S(0)) and excited (S(1)) states are calculated for the complete configuration space of torsion and pyramidalization molecular distortions. The parameters that define the state energetics in the vicinity of the S(0)/S(1) conical intersection region are compared to complete active space self-consistent field (CASSCF) results. These examples show that it is possible to describe strongly correlated electronic states using a single reference methodology without the need to expand the wavefunction to high levels of collective excitations. Finally, RASCI is also examined in the electronic structure characterization of the ground and 2(1)A(g)(-), 1(1)B(u)(+), 1(1)B(u)(-), and 1(3)B(u)(-) states of all-trans polyenes with two to seven double bonds and beyond. Transition energies are compared to configuration interaction singles, time-dependent density functional theory (TDDFT), CASSCF, and its second-order perturbation correction calculations, and to experimental data. The capability of RASCI-SF to describe the nature and properties of each electronic state is discussed in detail. This example is also used to expose the properties of different truncations of the RASCI wavefunction and to show the possibility to use an excitation operator with any number of α-to-β electronic promotions.

Diabatic couplings for charge recombination via Boys localization and spin-flip configuration interaction singles

We describe a straightforward technique for obtaining diabatic couplings applicable to charge transfer from or charge recombination to the electronic ground state. Our method is nearly black box, requiring minimal chemical intuition from the user, and merges two well-established approaches in electronic structure theory: first, smooth and balanced adiabatic states are generated using spin-flip-configuration interaction singles (SF-CIS) based on a triplet HF state; second, Boys localization is applied to rotate all adiabatic states into charge-localized diabatic states. The method is computationally inexpensive, scaling only with the cost of CIS, and does not require a choice of active space, which is usually required for such intrinsically multiconfigurational problems. Molecular LiF in vacuum and LiF solvated by a single water molecule are examined as model systems. We find nearly smooth diabatic potential energy surfaces and couplings and we find that the Condon approximation is obeyed approximately for this model problem.

Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory

The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.

Restricted active space spin-flip configuration interaction approach: theory, implementation and examples

A new formulation of the spin-flip (SF) method is presented. The electronic wave function is specified by the definition of an active space and through alpha-to-beta excitations from a Hartree-Fock reference. The method belongs to the restricted active space (RAS) family, where the CI expansion is restricted by classifying the molecular orbitals in three subspaces. Properties such as spin completeness, variationality, size consistency, size intensivity, and orbital invariance are discussed. The implementation and applications use a particular truncation of the wave function, with the inclusion of hole and particle contributions such that for fixed active space size, the number of amplitudes is linear in molecular size. This approach is used to investigate single and double bond-breaking, the singlet-triplet gap of linear acenes, electronic transitions in three Ni(II) octahedral complexes, the low-lying states of the 2,5-didehydrometaxylylene (DDMX) tetraradical and the ground state multiplicity of 28 non-Kekulé structures. The results suggest that this approach can provide a quite well balanced description of nearly degenerate electronic states at moderate computational cost.

Finite-Field Spin-Flip Configuration Interaction Calculation of the Second Hyperpolarizabilities of Singlet Diradical Systems.

Ab initio spin-flip configuration interaction (SF-CI) methods with the finite-field (FF) scheme are applied to the calculation of static second hyperpolarizabilities (γ) of several singlet diradical systems, i.e., the model H2 molecule under dissociation, p-quinodimethane, o-quinoid five-membered ring, and 1,4-bis(imidazole-2-ylidene)cyclohexa-2,5-diene (BI2Y) models. The SF-CI method using the UHF reference wave function provides the qualitatively correct diradical character (y) dependence of γ in a wide range of a diradical character region for H2 under dissociation and p-quinodimethane as well as o-quinoid five-membered ring models. For BI2Y, which is a real diradical system, a non-negligible spin contamination is found in the spin-unrestricted Hartree-Fock (UHF) triplet state, which results in overestimations (SF-CIS) or underestimations (SF-CIS(D)) of γ. Such deficiencies are significantly reduced when using the pure spin state, i.e., the restricted open-shell HF (ROHF) triplet wave function as the reference wave function. These results indicate the applicability of the FF-SF-CI method starting with a pure or a nearly pure high-spin state to provide qualitative or semiquantitative γ for large-size diradical systems. For selected systems, these SF-CI results are also compared to the SF equation of motion coupled cluster singles and doubles (SF-EOM-CCSD) and to SF time-dependent density functional theory (SF-TDDFT) schemes. In particular, large amounts of Hartree-Fock exchange in the functional are required to obtain qualitatively correct dependence of γ on y in the case of p-quinodimethane.

Spin-flip configuration interaction: an electronic structure model that is both variational and size-consistent

A new formulation of the configuration interaction (CI) method is presented. It is based on the recently introduced spin-flip (SF) approach. SF-CI target states are described as spin-flipping excitations from the reference Hartree–Fock high-spin, e.g., M s=1 (| αα〉), determinant. The resulting model is both variational and size-consistent. Moreover, the SF-CI model can describe within a single-reference formalism some inherently multi-reference situations, such as single bond-breaking and diradicals. Initial benchmarks for the SF-CI model with single and double substitutions (SF-CISD) are presented.