Spin Contamination Research Articles

The fate of the tert-butyl radical in low-temperature autoignition reactions.

Alkyl combustion models depend on kinetic parameters derived from reliable experimental or theoretical energetics that are often unavailable for larger species. To this end, we have performed a comprehensive investigation of the tert-butyl radical (R• in this paper) autoignition pathways. CCSD(T)/ANO0 geometries and harmonic vibrational frequencies were obtained for key stationary points for the R• + O2 and QOOH + O2 mechanisms. Relative energies were computed to chemical accuracy (±1 kcal mol-1) via extrapolation of RCCSD(T) energies to the complete basis-set limit, or usage of RCCSD(T)-F12 methods. At 0 K, the minimum energy R• + O2 pathway involves direct elimination of HO2∙ (30.3 kcal mol-1 barrier) from the tert-butyl peroxy radical (ROO•) to give isobutene. This pathway lies well below the competing QOOH-forming intramolecular hydrogen abstraction pathway (36.2 kcal mol-1 barrier) and ROO• dissociation (35.9 kcal mol-1 barrier). The most favorable decomposition channel for QOOH radicals leads to isobutene oxide (12.0 kcal mol-1 barrier) over isobutene (18.6 kcal mol-1 barrier). For the QOOH + O2 pathways, we studied the transition states and initial products along three pathways: (1) α-hydrogen abstraction (42.0 kcal mol-1 barrier), (2) γ-hydrogen abstraction (27.0 kcal mol-1 barrier), and (3) hydrogen transfer to the peroxy moiety (24.4 kcal mol-1 barrier). The barrier is an extensive modification to the previous 18.7 kcal mol-1 value and warrants further study. However, it is still likely that the lowest energy QOOH + O2 pathway corresponds to pathway (3). We found significant spin contamination and/or multireference character in multiple stationary points, especially for transition states stemming from QOOH. Lastly, we provide evidence for an A∼-X∼ surface crossing at a Cs-symmetric, intramolecular hydrogen abstraction structure.

Performance of TD-DFT for Excited States of Open-Shell Transition Metal Compounds.

Time-dependent density functional theory (TD-DFT) has been very successful in accessing low-lying excited states of closed-shell systems. However, it is much less so for excited states of open-shell systems: unrestricted Kohn-Sham based TD-DFT (U-TD-DFT) often produces physically meaningless excited states due to heavy spin contaminations, whereas restricted Kohn-Sham based TD-DFT often misses those states of lower energies. A much better variant is the explicitly spin-adapted TD-DFT (X-TD-DFT) [J. Chem. Phys. 2011, 135, 194106] that can capture all the spin-adapted singly excited states yet without computational overhead over U-TD-DFT. While the superiority of X-TD-DFT over U-TD-DFT has been demonstrated for open-shell systems of main group elements, it remains to be seen if this is also the case for open-shell transition metal compounds. Taking as benchmark the results by MS-CASPT2 (multistate complete active space second-order perturbation theory) and ic-MRCISD (internally contracted multireference configuration interaction with singles and doubles), it is shown that X-TD-DFT is indeed superior to U-TD-DFT for the vertical excitation energies of ZnH, CdH, ScH2, YH2, YO, and NbO2. Admittedly, there exist a few cases where U-TD-DFT appears to be better than X-TD-DFT. However, this is due to a wrong reason: the underestimation (due to spin contamination) and the overestimation (due to either the exchange-correlation functional itself or the adiabatic approximation to the exchange-correlation kernel) happen to be compensated in the case of U-TD-DFT. As for [Cu(C6H6)2]2+, which goes beyond the capability of both MS-CASPT2 and ic-MRCISD, X-TD-DFT revises the U-TD-DFT assignment of the experimental spectrum.

Computational Study of Oxidation of Guanine by Singlet Oxygen (1 Δg ) and Formation of Guanine:Lysine Cross-Links.

Oxidation of guanine in the presence of lysine can lead to guanine-lysine cross-links. The ratio of the C4, C5 and C8 crosslinks depends on the manner of oxidation. Type II photosensitizers such as Rose Bengal and methylene blue can generate singlet oxygen, which leads to a different ratio of products than oxidation by type I photosensitizers or by one electron oxidants. Modeling reactions of singlet oxygen can be quite challenging. Reactions have been explored using CASSCF, NEVPT2, DFT, CCSD(T), and BD(T) calculations with SMD implicit solvation. The spin contamination in open-shell calculations were corrected by Yamaguchi's approximate spin projection method. The addition of singlet oxygen to guanine to form guanine endo- peroxide proceeds step-wise via a zwitterionic peroxyl intermediate. The subsequent barrier for ring closure is smaller than the initial barrier for singlet oxygen addition. Ring opening of the endoperoxide by protonation at C4-O is followed by loss of a proton from C8 and dehydration to produce 8-oxoGox . The addition of lysine (modelled by methylamine) or water across the C5=N7 double bond of 8-oxoGox is followed by acyl migration to form the final spiro products. The barrier for methylamine addition is significantly lower than for water addition and should be the dominant reaction channel. These results are in good agreement with the experimental results for the formation of guanine-lysine cross-links by oxidation by type II photosensitizers.

Addressing first derivative discontinuities in orbital-optimised opposite-spin scaled second-order perturbation theory with regularisation

ABSTRACTOrbital-optimised opposite-spin scaled second-order perturbation theory (O2) generates a single-reference wave function composed of approximate Brueckner orbitals with fourth-order computational scaling. While O2 provides significantly improved treatment of radicals by reducing spin contamination, it has been shown to suffer from first derivative discontinuities for bond stretching near the unrestriction point. That qualitative failure is resolved in this work by the implementation of regularised O2, which includes a regularisation parameter in the denominator of its second-order term. The value of the regularisation parameter is semi-empirically chosen to qualitatively describe bond stretching energetics of hydrogen, ethane and ethene, while also considering the effect of the regularisation parameter on thermochemical errors for the well-known Gaussian-2 (G2) test set. The generality of the empirical scaling and semi-empirical regularisation parameter is studied by application to the 3dMLBE20, DBH24, RSE43 and W4-11 test sets. We demonstrate that accuracy of O2 is roughly maintained and sometimes even improved by regularisation, with root mean squares of regularised O2 between factors of 1.6 and 0.8 from corresponding root mean squares of O2.

Computation of the Isotropic Hyperfine Coupling Constant: Efficiency and Insights from a New Approach Based on Wave Function Theory.

The present paper reports an original computational strategy for the computation of the isotropic hyperfine coupling constants (hcc). The algorithm proposed here is based on an approach recently introduced by some of the authors, namely, the first-order breathing orbital self-consistent field (FOBO-SCF). The approach is an almost parameter-free wave function method capable to accurately treat the spin delocalization together with the spin polarization effects while staying in a restricted formalism and avoiding spin contamination. The efficiency of the method is tested on a series of small radicals, among which four nitroxide radicals and the comparison with high-level ab initio methods show very encouraging results. On the basis of these results, the method is then applied to compute the hcc of a challenging system, namely, the DEPMPO-OOH radical in various conformations. The reference values obtained on such a large system allows us to validate a cheap computational method based on density functional theory (DFT). Another interesting feature of the model applied here is that it allows for the rationalization of the results according to a relatively simple scheme based on a two-step mechanism. More precisely, the results are analyzed in terms of two separated contributions: first the spin delocalization and then the spin polarization.

Hidden complexities in the reaction of H2O2 and HNO revealed by ab initio quantum chemical investigations.

Nitroxyl (HNO) and hydrogen peroxide have both been implicated in a variety of reactions relevant to environmental and physiological processes and may contribute to a unique, unexplored, pathway for the production of nitrous acid (HONO) in soil. To investigate the potential for this reaction, we report an in-depth investigation of the reaction pathway of H2O2 and HNO forming HONO and water. We find the breaking of the peroxide bond and a coupled proton transfer in the first step leads to hydrogen nitryl (HNO2) and an endogenous water, with an extrapolated NEVPT2 (multireference perturbation theory) barrier of 29.3 kcal mol-1. The first transition state is shown to possess diradical character linking the far peroxide oxygen to the bridging, reacting, peroxide oxygen. The energy of this first step, when calculated using hybrid density functional theory, is shown to depend heavily on the amount of Hartree-Fock exchange in the functional, with higher amounts leading to a higher barrier and more diradical character. Additionally, high amounts of spin contamination cause CCSD(T) to significantly overestimate the TS1 barrier with a value of 36.2 kcal mol-1 when using the stable UHF wavefunction as the reference wavefunction. However, when using the restricted Hartree-Fock reference wavefunction, the TS1 CCSD(T) energy is lowered to yield a barrier of 31.2 kcal mol-1, in much better agreement with the NEVPT2 result. The second step in the reaction is the isomerization of HNO2 to trans-HONO through a Grotthuss-like mechanism accepting a proton from and donating a proton to the endogenous water. This new mechanism for the isomerization of HNO2 is shown to have an NEVPT2 barrier of 23.3 kcal mol-1, much lower than previous unimolecular estimates not including an explicit water. Finally, inclusion of an additional explicit water is shown to lower the HNO2 isomerization barrier even further.

Complete spin contamination-free MP2 method

To improve the unrestricted second-order Møller-Plesset (UMP2) method, we propose a method in which spin contamination is eliminated due to spin adaptation of the double excitation space based on the unitary group approach (UGA), because the UMP2 calculations intrinsically involve spin contamination from the double excitation space. Numerical results for the activation energies of several radical reactions show that this UGA-UMP2 method offers substantial improvement over the UMP2 method. Furthermore, the UGA-SUMP2 method, which completely eliminates the spin contamination from both the reference and excitation space present in UMP2 calculations, is also formulated.

Quasi-Restricted Orbital Treatment for the Density Functional Theory Calculations of the Spin-Orbit Term of Zero-Field Splitting Tensors.

A quasi-restricted orbital (QRO) approach for the calculation of the spin-orbit term of zero-field splitting tensors (DSO tensors) by means of density functional theory (DFT) importantly features in the fact that it is free from spin contamination problems because it uses spin eigenfunctions for the zeroth order wave functions. In 2011, however, Schmitt and co-workers pointed out that in the originally proposed QRO working equation some possible excitations were not included in their sum-over-states procedure, which causes spurious DSO contributions from closed-shell subsystems located far from the magnetic molecule under study. We have revisited the derivation of the QRO working equation and modified it, making it include all possible types of excitations in the sum-over-states procedure. We have found that the spurious DSO contribution can be eliminated by taking into account contributions from all possible types of singly excited configuration state functions. We have also found that only the SOMO(α) → SOMO(β) excited configurations have nonzero contributions to the DSO tensors as long as α and β spin orbitals have the same spatial distributions and orbital energies. For the DSO tensor calculations, by using a ground state wave function free from spin contamination, we propose a natural orbital-based Pederson-Khanna (NOB-PK) method, which utilizes the single determinant wave function consisting of natural orbitals in conjunction with the Pederson-Khanna (PK) type perturbation treatment. Some relevant calculations revealed that the NOB-PK method can afford more accurate DSO tensors than the conventional PK method as well as the QRO approach in MnII complexes and ReIV-based single molecule magnets.

New quantum number for the many-electron Dirac-Coulomb Hamiltonian

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator $\mathcal{K}_+$, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator $\mathcal{K}$, the $\mathcal{K}^2_+$ has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that $\mathcal{K}_+$ is connected to $\mathcal{K}$ through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call $\mathcal{K}_+$ the generator of the many-electron TR symmetry. By diagonalizing the operator $\mathcal{K}^2_+$ in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with $\mathcal{K}^2_+$ has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree--Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

Reparameterization of PM6 Applied to Organic Diradical Molecules.

We have performed a reparameterization of PM6 (called rPM6) to compute open-shell species, specifically organic diradical molecules, within a framework of the spin-unrestricted semiempirical molecular orbital (SE-UMO) method. The parameters for the basic elements (hydrogen, carbon, nitrogen, and oxygen) have been optimized simultaneously using the training set consisting of 740 reference data. On the basis of the GMTKN30 database, the mean absolute error of rPM6 is decreased from 16.1 to 14.1 kcal/mol, which reassures its accuracy for ground-state properties. Applications of the spin-unrestricted rPM6 (UrPM6) method to small diradicals and relatively large polycyclic aromatic hydrocarbons have provided substantial improvement over the standard SE-UMO methods like UAM1, UPM3, and the original UPM6. The UrPM6 calculation is much less susceptible to spin contamination and, therefore, reproduces geometric parameters and adiabatic singlet-triplet energy gaps obtained by UDFT (UB3LYP and/or UBHandHLYP) at much lower computational cost.

DFT and ab initio composite methods: Investigation of oxygen fluoride species

The capability of ccCA, G3, and G3B3 for the prediction of the enthalpies of formation of oxygen fluoride species was evaluated. In addition to these composite methods, the performance of M06 and M06-2X in conjunction with the correlation consistent basis sets (aug-cc-pVnZ), where n=D, T, Q, was also examined for predicting the structures and enthalpies of formation of oxygen fluoride species. A set of various oxygen fluorides were considered, including FOx radicals, FOxH, and FOxF, where x=1–3. The effects of basis set size and spin contamination were also considered.

Spin contamination-free N-electron wave functions in the excitation-based configuration interaction treatment.

This work deals with the spin contamination in N-electron wave functions provided by the excitation-based configuration interaction methods. We propose a procedure to ensure a suitable selection of excited N-electron Slater determinants with respect to a given reference determinant, required in these schemes. The procedure guarantees the construction of N-electron wave functions which are eigenfunctions of the spin-squared operator Sˆ(2), avoiding any spin contamination. Our treatment is based on the evaluation of the excitation level of the determinants by means of the expectation value of an excitation operator formulated in terms of spin-free replacement operators. We report numerical determinations of energies and 〈Sˆ(2)〉 expectation values, arising from our proposal as well as from traditional configuration interaction methods, in selected open-shell systems, in order to compare the behavior of these procedures and their computational costs.

Approximate Spin-Projected Density-Based Romberg Differentiation Procedure to Evaluate the Second-Hyperpolarizability of p-Quinodimethane and Twisted Ethylene and Their Diradical Character Dependence.

The evaluation of the static second hyperpolarizability (γ) of diradical species is a challenging task due to the use of spin-unrestricted methods, which may suffer from spin contamination. Here, we present the methodological aspect of a density-based differentiation procedure to evaluate static polarizability and hyperpolarizabilities. The finite-field calculations are done on the spin-projected electron density to remove the spin contamination, and the automatized Romberg's differentiation procedure is used to improve the numerical accuracy in the finite-field method. This implementation is tested in the present report for the challenging case of the evaluation of the second hyperpolarizability of the singlet ground state of p-quinodimethane (PQM) for the equilibrium geometry as well as for a stretched geometry where the diradical character of PQM is increased, and for twisted ethylene models where the diradical character changes with the dihedral angle. The application of the approximate spin-projected (ASP) scheme leads to a major improvement of the density functional theory calculations. In particular, for PQM models, BHandHLYP functional reproduces the UCCSD(T) values when the diradical character is below 0.5. The visualization of the γ-densities shows that (i) when increasing the diradical character, the amount of γ-density increases on the -CH2(•) extremities, and (ii) the ASP scheme decreases the amount of "p-like" γ-density for diradical character below 0.4, and increases it for larger diradical character. For twisted ethylene model, we show that the UCCSD(T) reference values can be reproduced by the ASP-UB3LYP method for y < 0.4 and by the ASP-UBHandHLYP method for y > 0.6. To best reproduce the UCCSD(T) reference calculations, the amount of exact exchange in hybrid functionals needs to be tuned along the range of diradical characters.

Beyond Time-Dependent Density Functional Theory Using Only Single Excitations: Methods for Computational Studies of Excited States in Complex Systems.

Single-excitation methods, namely, configuration interaction singles and time-dependent density functional theory (TDDFT), along with semiempirical versions thereof, represent the most computationally affordable electronic structure methods for describing electronically excited states, scaling as [Formula: see text] absent further approximations. This relatively low cost, combined with a treatment of electron correlation, has made TDDFT the most widely used excited-state quantum chemistry method over the past 20+ years. Nevertheless, certain inherent problems (beyond just the accuracy of this or that exchange-correlation functional) limit the utility of traditional TDDFT. For one, it affords potential energy surfaces whose topology is incorrect in the vicinity of any conical intersection (CI) that involves the ground state. Since CIs are the conduits for transitions between electronic states, the TDDFT description of photochemistry (internal conversion and intersystem crossing) is therefore suspect. Second, the [Formula: see text] cost can become prohibitive in large systems, especially those that involve multiple electronically coupled chromophores, for example, the antennae structures of light-harvesting complexes or the conjugated polymers used in organic photovoltaics. In such cases, the smallest realistic mimics might already be quite large from the standpoint of ab initio quantum chemistry. This Account describes several new computational methods that address these problems. Topology around a CI can be rigorously corrected using a "spin-flip" version of TDDFT, which involves an α → β spin-flipping transition in addition to occupied → virtual excitation of one electron. Within this formalism, singlet states are generated via excitation from a high-spin triplet reference state, doublets from a quartet, etc. This provides a more balanced treatment of electron correlation between ground and excited states. Spin contamination is problematic away from the Franck-Condon region, but we describe a "spin-complete" version of the theory in which proper spin eigenstates are obtained by construction. For systems of coupled chromophores, we have developed an ab initio version of the Frenkel-Davydov exciton model in which collective excitations of the system are expanded in a basis of excited states computed for individual chromophores. The monomer calculations are trivially parallelizable, as is computation of the coupling matrix elements needed to construct the exciton Hamiltonian, and systems containing hundreds of chromophores can be tackled on commodity hardware. This enables calculations on organic semiconductors, where even small model systems exhibit a semicontinuum of excited states that renders traditional TDDFT computationally challenging. Despite including only single excitations on each monomer, the exciton model can describe entangled spins on two or more monomers, an effect that is responsible for excitation energy transfer between chromophores, for example, in singlet fission. Excitonic approximations can also be applied to the TDDFT equations themselves, and a particularly promising application is to describe the effects of environment on an excitation that is localized on a single chromophore. This "local excitation approximation" to TDDFT allows an essentially arbitrary number of solvent molecules to be included in the calculation in a highly parallelizable way such that the time-to-solution increases only very slowly as additional solvent molecules are added. It is therefore possible to converge the calculation with respect to describing an ever-larger portion of the environment at a quantum-mechanical level.

Spin density and orbital optimization in open shell systems: A rational and computationally efficient proposal.

The present work describes a new method to compute accurate spin densities for open shell systems. The proposed approach follows two steps: first, it provides molecular orbitals which correctly take into account the spin delocalization; second, a proper CI treatment allows to account for the spin polarization effect while keeping a restricted formalism and avoiding spin contamination. The main idea of the optimization procedure is based on the orbital relaxation of the various charge transfer determinants responsible for the spin delocalization. The algorithm is tested and compared to other existing methods on a series of organic and inorganic open shell systems. The results reported here show that the new approach (almost black-box) provides accurate spin densities at a reasonable computational cost making it suitable for a systematic study of open shell systems.

Bond breaking in stretched molecules: multi-reference methods versus density functional theory

Several quantum chemistry methods were compared for modeling the breaking of bonds in small molecules subjected to extreme strain. This provides a rigorous test of quantum mechanical methods because a high degree of dynamical and non-dynamical correlation is required to accurately model bond breaking in a strained molecule. The methods tested included multi-reference methods, unrestricted Kohn–Sham density functional theory (DFT) using several functionals, and unrestricted coupled-cluster singles and doubles. It is challenging to employ the multi-reference method in a balanced way for the molecules considered due to the computational cost. While the DFT methods are less costly and provide balanced correlation, they do not have enough static correlation to properly model the bond-breaking curve to dissociation. Despite this, for the N12 DFT method the artifacts due to spin contamination of the unrestricted Kohn–Sham method were the least severe and tolerable. Given this, and the low computational cost, the N12 method was chosen for subsequent dynamical simulations for modeling fracture inception in polymers under extreme strain. The physical characteristics of the bond-breaking process are discussed as well as the influence of secondary conjugation on the process.

Challenging compounds for calculating molecular second hyperpolarizabilities: the triplet state of the trimethylenemethane diradical and two derivatives.

The second hyperpolarizability γ of trimethylenemethane (TMM) and two 1,3-dipole derivatives (NXA and OXA) in their triplet ground state has been evaluated at the UCCSD(T) level with the d-aug-cc-pVDZ extended basis set, highlighting that γ decreases from TMM to NXA and OXA, following the opposite order of their permanent dipole moments. These results are then used to benchmark a broad range of levels of approximation. So, the UMP2, UMP4, and UCCSD methods can be used to characterize γ of TMM and NXA but not of OXA. In that case, the large field-induced charge transfer contribution is difficult to handle using the MPn methods and only the UCCSD method provides values close to the UCCSD(T) reference. Turning to the performance of DFT with typical exchange-correlation functionals, the UM06-2X functional, which contains 54% of HF exchange, performs very well with a maximum of 4.5% of difference with respect to the reference values. On the other hand, employing less HF exchange leads to an overestimation of the responses whereas range-separated hybrids generally underestimate the second hyperpolarizabilities. Finally, the use of spin-projected methods for these 1,3-dipole triplet molecules has a little impact since the spin contamination is almost negligible.

Spin-state energies of heme-related models from spin-flip TDDFT calculations.

Spin-state energies of heme-related models are of vital importance in biochemistry. To compute the energies of different spin states, the traditional ΔSCF method based on the density functional theory (DFT) is usually employed. In this work, the spin-flip TDDFT (SF-TDDFT) approach is investigated to compute the spin-state energies, with six different exchange-correlation (XC) functionals. With the present protocol, the spin contamination is fully avoided by choosing appropriate reference states. Additionally, multiple excited states can be obtained with SF-TDDFT. Compared with the CCSD(T) results, it is shown that the SF-TDDFT calculations with the BHandHLYP functional provide better accuracy than ΔSCF for D-Q (doublet-quartet) and Q-S (quartet-sextet) gaps and agree well with the experimental results. A possible solution for the precise calculation of spin-state energies is proposed to improve the performance of SF-TDDFT, on account of that the excitation energies show highly linear dependence on the amount of Hartree-Fock (HF) exchange in the XC functionals.

Critical Assessment of TD-DFT for Excited States of Open-Shell Systems: I. Doublet-Doublet Transitions.

A benchmark set of 11 small radicals is set up to assess the performance of time-dependent density functional theory (TD-DFT) for the excited states of open-shell systems. Both the unrestricted (U-TD-DFT) and spin-adapted (X-TD-DFT) formulations of TD-DFT are considered. For comparison, the well-established EOM-CCSD (equation-of-motion coupled-cluster with singles and doubles) is also used. In total, 111 low-lying singly excited doublet states are accessed by all the three approaches. Taking the MRCISD+Q (multireference configuration interaction with singles and doubles plus the Davidson correction) results as the benchmark, it is found that both U-TD-DFT and EOM-CCSD perform well for those states dominated by singlet-coupled single excitations (SCSE) from closed-shell to open-shell, open-shell to vacant-shell, or closed-shell to vacant-shell orbitals. However, for those states dominated by triplet-coupled single excitations (TCSE) from closed-shell to vacant-shell orbitals, both U-TD-DFT and EOM-CCSD fail miserably due to severe spin contaminations. In contrast, X-TD-DFT provides balanced descriptions of both SCSE and TCSE. As far as the functional dependence is concerned, it is found that, when the Hartree-Fock ground state does not suffer from the instability problem, both global hybrid (GH) and range-separated hybrid (RSH) functionals perform grossly better than pure density functionals, especially for Rydberg and charge-transfer excitations. However, if the Hartree-Fock ground state is instable or nearly instable, GH and RSH tend to underestimate severely the excitation energies. The SAOP (statistically averaging of model orbital potentials) performs more uniformly than any other density functionals, although it generally overestimates the excitation energies of valence excitations. Not surprisingly, both EOM-CCSD and adiabatic TD-DFT are incapable of describing excited states with substantial double excitation characters.

Spin-flip, tensor equation-of-motion configuration interaction with a density-functional correction: A spin-complete method for exploring excited-state potential energy surfaces.

We revisit the formalism of the spin-adapted, spin-flip (SA-SF) configuration-interaction singles (CIS) method based on a tensor equation-of-motion formalism that affords proper spin eigenstates without sacrificing single-reference simplicity. Matrix elements for SA-SF-CIS are then modified in a manner similar to collinear spin-flip time-dependent density functional theory (SF-TDDFT), to include a DFT exchange-correlation correction. The performance of this method, which we call SA-SF-DFT, is evaluated numerically and we find that it systematically improves the energies of electronic states that exhibit significant spin contamination within the conventional SF-TDDFT approach. The new method cures the state assignment problem that plagues geometry optimizations and ab initio molecular dynamics simulations using traditional SF-TDDFT, without sacrificing computational efficiency, and furthermore provides correct topology at conical intersections, including those that involve the ground state, unlike conventional TDDFT. As such, SA-SF-DFT appears to be a promising method for generating excited-state potential energy surfaces at DFT cost.