Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations

A new parameterization of the DFT/CIS method with applications to core-level spectroscopy

Time-dependent density functional theory (TD-DFT) within a restricted excitation space is an efficient means to compute core-level excitation energies using only a small subset of the occupied orbitals. However, core-to-valence excitation energies are significantly underestimated when standard exchange-correlation functionals are used, which is partly traceable to systemic issues with TD-DFT's description of Rydberg and charge-transfer excited states. To mitigate this, we have implemented an empirically modified combination of configuration interaction with single substitutions (CIS) based on Kohn-Sham orbitals, which is known as "DFT/CIS." This semi-empirical approach is well-suited for simulating x-ray near-edge spectra, as it contains sufficient exact exchange to model charge-transfer excitations yet retains DFT's low-cost description of dynamical electron correlation. Empirical corrections to the matrix elements enable semi-quantitative simulation of near-edge x-ray spectra without the need for significant a posteriori shifts; this should be useful in complex molecules and materials with multiple overlapping x-ray edges. Parameter optimization for use with a specific range-separated hybrid functional makes this a black-box method intended for both core and valence spectroscopy. Results herein demonstrate that realistic K-edge absorption and emission spectra can be obtained for second- and third-row elements and 3d transition metals, with promising results for L-edge spectra as well. DFT/CIS calculations require absolute shifts that are considerably smaller than what is typical in TD-DFT.

Range Separation Method for Density Functional Theory Based on Two-Electron Infinite-Order Two-Component Hamiltonian

The range separation method for density functional theory (DFT) was extended to a two-component relativistic theory based on the unitary transformation of one- and two-electron operators and a density operator. In the framework of the spin-free infinite-order two-component Hamiltonian, we implemented several types of two-electron integrals of range-separated two-electron interactions arising from the unitary transformation. Numerical assessments were performed using long-range-corrected (LC)-DFT, which utilizes the range separation of an exchange functional. The present method successfully reproduced the reference values obtained by the four-component LC-DFT calculations when the whole unitary transformations of one-electron, full-range, and range-separated two-electron operators and a density operator were considered. An efficient scheme for the unitary transformation, which is termed the local unitary transformation (LUT), was also applied to the range-separated two-electron term and other operators. The LUT method reduced the computational costs of the LC-DFT calculations significantly without any loss of accuracy.

Basis Set Limit of CCSD(T) Energies: Explicit Correlation Versus Density-Based Basis-Set Correction

A thorough comparison is carried out for explicitly correlated and density-based basis-set correction approaches, which were primarily developed to mitigate the basis-set incompleteness error of wave function methods. An efficient implementation of the density-based scheme is also presented, utilizing the density-fitting approximation. The performance of these approaches is comprehensively tested for the second-order Møller-Plesset (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] methods with respect to the corresponding complete basis set references. It is demonstrated that the density-based correction together with complementary auxiliary basis set (CABS)-corrected Hartree-Fock energies is highly robust and effectively reduces the error of the standard approaches; however, it does not outperform the corresponding explicitly correlated methods. Nevertheless, what still makes the density-corrected CCSD and CCSD(T) methods competitive is that their computational costs are roughly half of those of the corresponding explicitly correlated variants. Additionally, an incremental approach for standard CCSD and CCSD(T) is introduced. In this simple scheme, the total energies are corrected with the CABS correction and explicitly correlated MP2 contributions. As demonstrated, the resulting methods yield surprisingly good results, below 1 kcal/mol for thermochemical properties even with a double-ζ basis, while their computational expenses are practically identical to those of the density-based basis-set correction approaches.

How Accurately Can DFT Describe Non-valence Anions?

Weakly bound non-valence anions are molecular systems where the excess electron stabilizes in a very diffuse orbital whose size, shape, and binding energy (∼1-100 meV) are governed by the long-range electrostatic potential of the molecule. Its binding energy comes mainly from charge-dipole or charge-multipole interactions or dispersion forces. While highly correlated methods, like coupled cluster methods, are considered to be the state of the art for describing anionic systems, especially when the electron lies in a very diffuse orbital, we consider here the possibility to use DFT-based calculations. In such molecular anions, the outer electron experiences long-range exchange and correlation interactions. We show that DFT can describe long-range bound states provided that a correct asymptotic exchange and correlation potential is used, namely, that from a range-separated hybrid functional. This opens an alternative to the computationally demanding highly correlated method calculations. It is also suggested that the study of weakly bound anions could help in the construction of new DFT potentials to study systems where nonlocal effects are significant.

Toward highly efficient hyperfluorescence-based emitters through excited-states alignment using novel optimally tuned range-separated models

Hyperfluorescence has recently been introduced as a promising strategy to achieve organic light-emitting diodes (OLEDs) with high color purity and enhanced stability. In this approach, fluorescent emitters (FEs) with strong and narrow band fluorescence are integrated in thin films containing sensitizers exhibiting thermally activated delayed fluorescence (TADF). Toward highly efficient hyperfluorescence-based emitters, the excited-states ordering of the FEs should be well-aligned. Given some recent endeavors in this context, the related theoretical explorations are relatively limited and have proven to be challenging. In this work, alignments of the corresponding excited-states, crucial for both the fast Förster resonance energy transfer and suppression of the Dexter energy transfer from TADF sensitizers to FEs, have theoretically been investigated using optimally tuned range-separated hybrid functionals (OT-RSHs). We have proposed and validated several variants of the models including OT-RSHs, their coupled versions with the polarizable continuum model, OT-RSHs-PCM, as well as the screened versions accounting for the screening effects by the electron correlation through the scalar dielectric constant, OT-SRSHs, for a reliable description of the excited-states ordering in the FEs of the hyperfluorescence-based materials. Particular attention is paid to the influence of the underlying density functional approximations as well as the short- and long-range Hartree-Fock (HF) exchange contributions and the range-separation parameter. Considering a series of experimentally known hyperfluorescence-based emitters as working models, it is unveiled that any combination of the ingredients in the proposed models does not render the correct order of the excited-states of the FEs, but a particular compromise among the involved parameters is needed to more accurately account for the relevant excited-states alignment. Perusing the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM with the correct asymptotic behavior and incorporating no (low) HF exchange contribution at the short-range regime. The proposed models show superior performances not only with respect to their standard counterparts with the default parameters but also as compared to other range-separated approximations. Accountability of the best-proposed model is also put into broader perspective, where it has been employed for the computational design of several molecules as promising FE candidates prone to be utilized in hyperfluorescence-based materials. Summing up, the proposed models in this study can be recommended for both the theoretical modeling and confirming the experimental observations in the field of hyperfluorescence-based OLEDs.

Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach

Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.

Density Functional Calculations Based on the Exponential Ansatz

This work explores the application of the singles-based exponential ansatz to density functional calculations. In contrast to the standard approach where Kohn-Sham (KS) orbitals are determined prior to computing molecular quantities of interest, we consider the single-reference Hartree-Fock wave function as a starting point. Applying the exponential ansatz to this single reference gives an auxiliary wave function that is employed to calculate the electronic properties of the system. This wave function is determined self-consistently through the standard KS Hamiltonian but evaluated over the Hartree-Fock molecular orbital basis. By using spin-symmetry breaking, we recover size-consistent results free of unphysical fractional charges in the dissociation limit. Our method shows consistency with standard KS density functional calculations when the system geometry is similar to the equilibrium one or in repulsive configurations. For moderately long distances between atoms, not at dissociation, because of self-interaction the exponential ansatz may give instabilities in the form of large cluster amplitudes. To avoid these, this work introduces a relatively simple regularization method that preserves size-consistency and penalizes high amplitudes of the cluster operator, whereas the results remain physically meaningful. We also present the time-dependent extension of our theory and show that it can feature quantum states where multiple electrons are excited.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput. 17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

A new form of transcorrelated Hamiltonian inspired by range-separated DFT

The present work introduces a new form of explicitly correlated factor in the context of the transcorrelated methods. The new correlation factor is obtained from the r₁₂ ≈ 0 mathematical analysis of the transcorrelated Hamiltonian, and its analytical form is obtained such that the leading order in 1/r₁₂ of the scalar part of the effective two-electron potential reproduces the long-range interaction of the range-separated density functional theory. The resulting correlation factor exactly imposes the cusp and is tuned by a unique parameter μ, which controls both the depth of the coulomb hole and its typical range in r₁₂. The transcorrelated Hamiltonian obtained with such a new correlation factor has a straightforward analytical expression depending on the same parameter μ, and its physical contents continuously change by varying μ: One can change from a non-divergent repulsive Hamiltonian at large μ to a purely attractive one at small μ. We investigate the convergence of the ground state eigenvalues and right eigenvectors of such a new transcorrelated Hamiltonian as a function of the basis set and as a function of μ on a series of two-electron systems. We found that the convergence toward the complete basis set is much faster for quite a wide range of values of μ. We also propose a specific value of μ, which essentially reproduces the results obtained with the frozen Gaussian geminal introduced by Ten-no [Chem. Phys. Lett. 330, 169 (2000)].

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

A range-separated generalized Kohn-Sham method including a long-range nonlocal random phase approximation correlation potential

Based on our recently published range-separated random phase approximation (RPA) functional [Kreppel et al., "Range-separated density-functional theory in combination with the random phase approximation: An accuracy benchmark," J. Chem. Theory Comput. 16, 2985-2994 (2020)], we introduce self-consistent minimization with respect to the one-particle density matrix. In contrast to the range-separated RPA methods presented so far, the new method includes a long-range nonlocal RPA correlation potential in the orbital optimization process, making it a full-featured variational generalized Kohn-Sham (GKS) method. The new method not only improves upon all other tested RPA schemes including the standard post-GKS range-separated RPA for the investigated test cases covering general main group thermochemistry, kinetics, and noncovalent interactions but also significantly outperforms the popular G₀W₀ method in estimating the ionization potentials and fundamental gaps considered in this work using the eigenvalue spectra obtained from the GKS Hamiltonian.

Computational Investigations of Dispersion Interactions between Small Molecules and Graphene-like Flakes

We investigate dispersion interactions in a selection of atomic, molecular, and molecule-surface systems, comparing high-level correlated methods with empirically corrected density functional theory (DFT). We assess the efficacy of functionals commonly used for surface-based calculations, with and without the D3 correction of Grimme. We find that the inclusion of the correction is essential to get meaningful results, but there is otherwise little to distinguish between the functionals. We also present coupled-cluster quality interaction curves for H₂, NO₂, H₂O, and Ar interacting with large carbon flakes, acting as models for graphene surfaces, using novel absolutely localized molecular orbital based methods. These calculations demonstrate that the problems with empirically corrected DFT when investigating dispersion appear to compound as the system size increases, with important implications for future computational studies of molecule-surface interactions.