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When using quantum chemical methods to study electronically excited states of open-shell molecules, it is often beneficial to start with wave functions that are spin eigenfunctions. For excited states of molecules containing heavy elements, spin–orbit coupling (SOC) is important and needs to be included as well. An efficient approach is to include SOC perturbatively on top of a restricted open-shell Kohn–Sham (ROKS) time-dependent density functional theory, which can be combined with the Tamm–Dancoff approximation (TDA) to suppress numerical instabilities. We implemented and assessed the potential of such a ROKS-TDA-SOC method, also featuring the possibility of calculating transition dipole moments between states to allow for full spectrum simulation. Our study shows that the ROKS-TDA-SOC formalism yields a clear and easy-to-use method to obtain electronically excited states of open-shell molecules that are of moderate size and contain heavy elements. [ABSTRACT FROM AUTHOR]

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm–Dancoff approximation, also their corresponding electronic couplings—quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained. [ABSTRACT FROM AUTHOR]

Resonance Raman spectroscopy has long been established as one of the most sensitive techniques for detection, structure characterization, and probing the excited-state dynamics of biochemical systems. However, the analysis of resonance Raman spectra is much facilitated when measurements are accompanied by Density Functional Theory (DFT) calculations that are expensive for large biomolecules. In this work, resonance Raman spectra are therefore computed with the Density Functional Tight-Binding (DFTB) method in the time-dependent excited-state gradient approximation. To test the accuracy of the tight-binding approximations, this method is first applied to typical resonance Raman benchmark molecules, such as β-carotene, and compared to results obtained with pure and range-separated exchange–correlation functionals. We then demonstrate the efficiency of the approach by considering a computationally challenging heme variation. Overall, we find that the vibrational frequencies and excited-state properties (energies and gradients) that are needed to simulate the spectra are reasonably accurate and suitable for interpretation of experiments. We can therefore recommend DFTB as a fast computational method to interpret resonance Raman spectra. [ABSTRACT FROM AUTHOR]

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree–Fock virtual orbitals by natural orbitals (NOs). In this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller–Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties—electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F–Ts), and parity-violating energy differences for H2Z2 (Z = O–Se)—we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces. [ABSTRACT FROM AUTHOR]

In the new field of quantum plasmonics, plasmonic excitations of silver and gold nanoparticles are utilized to manipulate and control light–matter interactions at the nanoscale. While quantum plasmons can be described with atomistic detail using Time-Dependent Density Functional Theory (DFT), such studies are computationally challenging due to the size of the nanoparticles. An efficient alternative is to employ DFT without approximations only for the relatively fast ground state calculations and use tight-binding approximations in the demanding linear response calculations. In this work, we use this approach to investigate the nature of plasmonic excitations under the variation of the separation distance between two nanoparticles. We thereby provide complementary characterizations of these excitations in terms of Kohn–Sham single–orbital transitions, intrinsic localized molecular fragment orbitals, scaling of the electron–electron interactions, and probability of electron tunneling between monomers. [ABSTRACT FROM AUTHOR]

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree–Fock, Kohn–Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model. [ABSTRACT FROM AUTHOR]

The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593–1604 (2019)]. Here, we study the differences between effective potentials from fully numerical density functional and optimized effective potential calculations for fixed configurations. We find that the differences are small, overall, and choose exchange-only potentials at the local density approximation level of theory computed on top of Hartree–Fock densities as a good compromise. The differences between potentials arising from different atomic configurations are also found to be small at this level of theory. Furthermore, we discuss the efficient Gaussian-basis implementation of SAP via error function fits to fully numerical atomic radial potentials. The guess obtained from the fitted potentials can be easily implemented in any Gaussian-basis quantum chemistry code in terms of two-electron integrals. Fits covering the whole periodic table from H to Og are reported for non-relativistic as well as fully relativistic four-component calculations that have been carried out with fully numerical approaches. [ABSTRACT FROM AUTHOR]

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [NL-eEDM Collaboration, Eur. Phys. J. D 72, 197 (2018)]. Knowledge of the molecular properties of BaF is thus needed to plan the measurements and, in particular, to determine the optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require the incorporation of both high-order correlation and relativistic effects in the calculations. In this work, theoretical investigations of the ground and lowest excited states of BaF and its lighter homologs, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster and multireference configuration interaction methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the A 2 Π 1 / 2 → X 2 Σ 1 / 2 + transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the B 2 Σ 1 / 2 + → X 2 Σ 1 / 2 + transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the nondiagonal nature of the FCFs in this system. Special attention is given to the properties of the A′2Δ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and excited states of the three molecules and the transition dipole moments (TDMs) between the different states. Finally, using the calculated FCFs and TDMs, we determine that the A 2 Π 1 / 2 → X 2 Σ 1 / 2 + transition is suitable for transverse cooling in BaF. [ABSTRACT FROM AUTHOR]

Correction for 'Automated assessment of redox potentials for dyes in dye-sensitized photoelectrochemical cells' by Jelena Belić et al., Phys. Chem. Chem. Phys., 2022, 24, 197–210, https://doi.org/10.1039/D1CP04218A. [ABSTRACT FROM AUTHOR]

We report in this paper an implementation of a 4-component relativistic Hamiltonian based Equation-of-Motion Coupled-Cluster with singles and doubles (EOM-CCSD) theory for the calculation of ionization potential, electron affinity, and excitation energy. In this work, we utilize the previously developed double group symmetry-based generalized tensor contraction scheme and also extend it in order to carry out tensor contractions involving non-totally symmetric and odd-ranked tensors. Several approximated spin-free and two-component Hamiltonians can also be accessed in this implementation. We have applied this method to the halogen monoxide (XO, X = Cl, Br, I, At, Ts) species, in order to assess the quality of a few other recent EOM-CCSD implementations, where spin-orbit coupling contribution has been approximated in different degrees. Besides, we have also studied various excited states of CH2IBr, CH2I2, and I 3 − (as well as single electron attachment and detachment electronic states of the same species) where comparison has been made with a closely related multi-reference coupled-cluster method, namely, Intermediate Hamiltonian Fock Space Coupled-Cluster singles and doubles theory. [ABSTRACT FROM AUTHOR]

Dye‐sensitized photoelectrochemical cells are promising devices in solar energy conversion. However, several limitations still have to be addressed, such as the major loss pathway through charge recombination at the dye‐semiconductor interface. Charge separating dyes constructed as push‐pull systems can increase the spatial separation of electron and hole, decreasing the recombination rate. Here, a family of dyes, consisting of polyphenylamine donors, fluorene bridges, and perylene monoimide acceptors, was investigated in silico using a combination of semi‐empirical nuclear dynamics and a quantum propagation of photoexcited electron and hole. To optimize the charge separation, several molecular design strategies were investigated, including modifying the donor molecule, increasing the π‐bridge length, and decoupling the molecular components through steric effects. The combination of a triphenylamine donor, using an extended 2‐fluorene π‐bridge, and decoupling the different components by steric hindrance from side groups resulted in a dye with significantly improved charge separation properties in comparison to the original supramolecular complex. [ABSTRACT FROM AUTHOR]

The gas-phase infrared spectra of discrete uranyl [U[O.sub.2+]][.sup.2+] complexes ligated with acetone and/or acetonitrile are used to evaluate systematic trends of ligation on the position of the O=U=O stretch and enable to rigorous comparison with the results of computational studies. The conclusion is confirmed by the uranyl stretching frequencies measured for mixed acetone/acetonitrile complexes, which show that substitution of one acetone for one acetonitrile produced a modest red shift of 3-6 cm.sup.-1.

We present a formulation and implementation of the calculation of (orbital-unrelaxed) expectation values at the 4-component relativistic coupled cluster level with spin-orbit coupling included from the start. The Lagrangian-based analytical energy derivative technique constitutes the basic theoretical framework of this work. The key algorithms for single reference relativistic coupled cluster have been implemented using routines for general tensor contractions of up to rank-2 tensors in which the direct product decomposition scheme is employed to benefit from double group symmetry. As a sample application, we study the electric field gradient at the bismuth nucleus in the BiX (X = N, P) series of molecules, where the effect of spin-orbit coupling is substantial. Our results clearly indicate that the current reference value for the nuclear quadrupole moment of 209Bi needs revision. We also have applied our method to the calculation of the parity violating energy shift of chiral molecules. The latter property is strictly zero in the absence of spin-orbit coupling. For the H2X2 (X = O,S,Se,Te) series of molecules the effect of correlation is found to be quite small. [ABSTRACT FROM AUTHOR]

We report a time-dependent density functional based tight-binding (TD-DFTB) scheme for the calculation of UV/Vis spectra, explicitly taking into account the excitation of nuclear vibrations via the adiabatic Hessian Franck-Condon method with a harmonic approximation for the nuclear wavefunction. The theory of vibrationally resolved UV/Vis spectroscopy is first summarized from the viewpoint of TD-DFTB. The method is benchmarked against time-dependent density functional theory (TD-DFT) calculations for strongly dipole allowed excitations in various aromatic and polar molecules. Using the recent 3ob:freq parameter set of Elstner's group, very good agreement with TD-DFT calculations using local functionals was achieved. [ABSTRACT FROM AUTHOR]

Sustainable solutions for hydrogen production, such as dye-sensitized photoelectrochemical cells (DS-PEC), rely on the fundamental properties of its components whose modularity allows for their separate investigation. In this work, we design and execute a high-throughput scheme to tune the ground state oxidation potential (GSOP) of perylene-type dyes by functionalizing them with different ligands. This allows us to identify promising candidates which can then be used to improve the cell's efficiency. First, we investigate the accuracy of different theoretical approaches by benchmarking them against experimentally determined GSOPs. We test different methods to calculate the vertical oxidation potential, including GW with different levels of self-consistency, Kohn–Sham (KS) orbital energies and total energy differences. We find that there is little difference in the performance of these methods. However, we show that it is crucial to take into account solvent effects as well as the structural relaxation of the dye after oxidation. Other thermodynamic contributions are negligible. Based on this benchmark, we decide on an optimal strategy, balancing computational cost and accuracy, to screen more than 1000 dyes and identify promising candidates which could be used to construct more robust DS-PECs. [ABSTRACT FROM AUTHOR]

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF+ and YbF− species, respectively. From these calculations we predict Ω = 1/2, 3/2 states, arising from the 4f13σ 26s , 4f145d1/6p1, and 4f135d1σ 16s configurations to be able to interact as they appear in the same energy range around the ground-state equilibrium geometry. As these states are generated from different sectors of Fock space, they are almost orthogonal and provide complementary descriptions of parts of the excited state manifold. To obtain a comprehensive picture, we introduce a simple adiabatization model to extract energies of interacting Ω = 1/2, 3/2 states that can be compared to experimental observations. [ABSTRACT FROM AUTHOR]

Photocatalytic water oxidation remains the bottleneck in many artificial photosynthesis devices. The efficiency of this challenging process is inherently linked to the thermodynamic and electronic properties of the chromophore and the water oxidation catalyst (WOC). Computational investigations can facilitate the search for favorable chromophore‐catalyst combinations. However, this remains a demanding task due to the requirements on the computational method that should be able to correctly describe different spin and oxidation states of the transition metal, the influence of solvation and the different rates of the charge transfer and water oxidation processes. To determine a suitable method with favorable cost/accuracy ratios, the full catalytic cycle of a molecular ruthenium based WOC is investigated using different computational methods, including density functional theory (DFT) with different functionals (GGA, Hybrid, Double Hybrid) as well as the semi‐empirical tight binding approach GFN‐xTB. A workflow with low computational cost is proposed that combines GFN‐xTB and DFT and provides reliable results. GFN‐xTB geometries and frequencies combined with single‐point DFT energies give free energy changes along the catalytic cycle that closely follow the full DFT results and show satisfactory agreement with experiment, while significantly decreasing the computational cost. This workflow allows for cost efficient determination of energetic, thermodynamic and dynamic properties of WOCs. [ABSTRACT FROM AUTHOR]

We present a formulation of Laplace-transformed atomic orbital-based second-order Møller-Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate the effect of separation of charge distributions on the Coulomb and exchange energy contributions, which show the same long-range decay with the inter-electronic/atomic distance as for nonrelativistic MP2. A linearly scaling implementation is possible if the proper distance behavior is introduced to the quaternion Schwarz-type estimates as for non-relativistic MP2. [ABSTRACT FROM AUTHOR]

We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB. [ABSTRACT FROM AUTHOR]

Metal nanoclusters can be synthesized in various sizes and shapes and are typically protected with ligands to stabilize them. These ligands can also be used to tune the plasmonic properties of the clusters as the absorption spectrum of a protected cluster can be significantly altered compared to the bare cluster. In this paper, we computationally investigate the influence of thiolate ligands on the plasmonic intensity for silver, gold and alloy clusters. Using time-dependent density functional theory with tight-binding approximations, TD-DFT+TB, we show that this level of theory can reproduce the broad experimental spectra of Au144(SR)60 and Ag53Au91(SR)60 (R = CH3) compounds with satisfactory agreement. As TD-DFT+TB does not depend on atom-type parameters we were able to apply this approach on large ligand-protected clusters with various compositions. With these calculations we predict that the effect of ligands on the absorption can be a quenching as well as an enhancement. We furthermore show that it is possible to unambiguously identify the plasmonic peaks by the scaled Coulomb kernel technique and explain the influence of ligands on the intensity de-)enhancement by analyzing the plasmonic excitations in terms of the dominant orbital contributions. [ABSTRACT FROM AUTHOR]

The potential energy curve for the ground-state of radium dimer (Ra2) is provided by means of atomic and molecular relativistic coupled cluster calculations. The short-range part of this curve is defined by an equilibrium bond length of 5.324 Å, a dissociation energy of 897 cm-1, and a harmonic vibrational frequency of 20.5 cm-1. The asymptotic behavior at large interatomic distances is characterized by the van der Waals coefficients C6 = 5.090 × 10³, C8 = 6.978 × 105, and C10 = 8.786 × 107 atomic units. The two regions are matched in an analytical potential to provide a convenient representation for use in further calculations, for instance, to model cold collisions between radium atoms. This might become relevant in future experiments on ultracold, optically trapped, radioactive radium atoms that are used to search for a permanent electric dipole moment. [ABSTRACT FROM AUTHOR]

7,7′-Disubstituted 2,2′-methylenedioxy-1,1′-binaphthyls are highly efficient chirality inducers in nematic liquid crystals. The absolute configuration of these compounds is, however, hard to determine as they only crystallize as racemic mixtures. In this work a Vibrational Circular Dichroism (VCD) study is reported that provides an unambiguous determination of the absolute configuration of these compounds. An in-depth General Coupled Oscillator (GCO) analysis of the source of the VCD signal reveals that the unusual structure of these binaphthyl compounds inherently leads to strong and robust VCD bands. Combined with linear transit calculations, our VCD studies allow for the determination of key structural parameters. [ABSTRACT FROM AUTHOR]

We present a study of the electronic structure of the [UO2]+, [UO2]2 +, [UO2]3+, NUO, [NUO]+, [NUO]2+, [NUN]-, NUN, and [NUN]+ molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity). [ABSTRACT FROM AUTHOR]

We present a method for a subsystem-based calculation of indirect nuclear spin-spin coupling tensors within the framework of current-spin-density-functional theory. Our approach is based on the frozen-density embedding scheme within density-functional theory and extends a previously reported subsystem-based approach for the calculation of nuclear magnetic resonance shielding tensors to magnetic fields which couple not only to orbital but also spin degrees of freedom. This leads to a formulation in which the electron density, the induced paramagnetic current, and the induced spin-magnetization density are calculated separately for the individual subsystems. This is particularly useful for the inclusion of environmental effects in the calculation of nuclear spin-spin coupling constants. Neglecting the induced paramagnetic current and spin-magnetization density in the environment due to the magnetic moments of the coupled nuclei leads to a very efficient method in which the computationally expensive response calculation has to be performed only for the subsystem of interest. We show that this approach leads to very good results for the calculation of solvent-induced shifts of nuclear spin-spin coupling constants in hydrogen-bonded systems. Also for systems with stronger interactions, frozen-density embedding performs remarkably well, given the approximate nature of currently available functionals for the non-additive kinetic energy. As an example we show results for methylmercury halides which exhibit an exceptionally large shift of the one-bond coupling constants between 199 Hg and 13C upon coordination of dimethylsulfoxide solvent molecules. [ABSTRACT FROM AUTHOR]

Frozen density embedding (FDE) theory is one of the major techniques aiming to bring modeling of extended chemical systems into the realm of high accuracy calculations. To improve its accuracy it is of interest to develop kinetic energy density functional approximations specifically for FDE applications. In the study reported here we focused on optimizing parameters of a generalized gradient approximation‐like kinetic energy functional with the purpose of better describing electron excitation energies. We found that our optimized parametrizations, named excPBE and excPBE‐3 (as these are derived from a Perdew‐Burke‐Ernzerhof‐like parametrization), could not yield improvements over available functionals when applied on a test set of systems designed to probe solvatochromic shifts. Moreover, as several different functionals yielded very similar errors to the simple local‐density approximation (LDA), it is questionable whether it is worthwhile to go beyond the LDA in this context. [ABSTRACT FROM AUTHOR]