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Density functional theory is an efficient computational tool to investigate photophysical and photochemical processes in transition metal complexes, giving invaluable assistance in the interpretation of spectroscopic and catalytic experiments. Optimally-tuned range-separated functionals are particularly promising, as they were created to cure some of the fundamental deficiencies present in approximate exchange-correlation functionals. In this paper, we scrutinize the selection of optimally tuned parameters and its influence on the excited state dynamics, using the example of the iron complex [Fe(cpmp)_2 ]^{2+} with push-pull ligands. Various tuning strategies are contemplated, based on pure self-consistent DFT protocols, as well as on the comparison with experimental spectra and multireference CASPT2 results. The two most promising sets of optimal parameters are then employed to carry out nonadiabatic surface-hopping dynamical simulations. Intriguingly, we find that the two sets lead to very different relaxation pathways and timescales, showcasing the complexity of iron-complexes excited state landscapes and the difficulty of obtaining an unambiguous parametrization of long-range corrected functionals without experimental input.

The electronic excited states of the iron(II) complex [FeII(tpy)(pyz-NHC)]2+ [tpy = 2,2′:6′,2″-terpyridine; pyz-NHC = 1,1′-bis(2,6-diisopropylphenyl)pyrazinyldiimidazolium-2,2′-diylidene] and their relaxation pathways have been theoretically investigated. To this purpose, trajectory surface-hopping simulations within a linear vibronic coupling model including a 244-dimensional potential energy surface (PES) with 20 singlet and 20 triplet coupled states have been used. The simulations show that, after excitation to the lowest-energy absorption band of predominant metal-to-ligand charge-transfer character involving the tpy ligand, almost 80% of the population undergoes intersystem crossing to the triplet manifold in about 50 fs, while the remaining 20% decays through internal conversion to the electronic ground state in about 300 fs. The population transferred to the triplet states is found to deactivate into two different regions of the PESs, one where the static dipole moment is small and shows increased metal-centered character and another with a large static dipole moment, where the electron density is transferred from the tpy to pyz-NHC ligand. Coherent oscillations of 400 fs are observed between these two sets of triplet populations, until the mixture equilibrates to a ratio of 60:40. Finally, the importance of selecting suitable normal modes is highlighted—a choice that can be far from straightforward in transition-metal complexes with hundreds of degrees of freedom., Trajectory surface-hopping simulations with a linear vibronic coupling model reveal the competition of major intersystem crossing versus minor internal conversion dynamics in an iron(II) N-heterocyclic carbene dye. The triplet population bifurcates into two regions of the potential energy surfaces, characterized by small and large static dipole moments due to different electronic character and showing coherent oscillations of 400 fs until both triplet populations coexist in a mixture of 60:40.

Previous time‐resolved spectroscopic experiments and static quantum‐chemical calculations attributed nitronaphthalene derivatives one of the fastest time scales for intersystem crossing within organic molecules, reaching the 100 fs mark. Nonadiabatic dynamics simulations on three nitronaphthalene derivatives challenge this view, showing that the experimentally observed ∼100 fs process corresponds to internal conversion in the singlet manifolds. Intersystem crossing, instead, takes place on a longer time scale of ∼1 ps. The dynamics simulations further reveal that the spin transitions occur via two distinct pathways with different contribution for the three systems, which are determined by electronic factors and the torsion of the nitro group. This study, therefore, indicates that the existence of sub‐picosecond intersystem crossing in other nitroaromatic molecules should be questioned., SHARC Bites Again: Nonadiabatic dynamics simulations reveal the photodeactivation mechanism of three nitronaphthalene derivatives. A subpicosecond process previously attributed to intersystem crossing is identified as internal conversion within the singlet states. An easy prey for the SHARC.

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we lay particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality, Comment: 81 pages, 10 figures, submitted to JACS Au

Conspectus The simulation of photoinduced non-adiabatic dynamics is of great relevance in many scientific disciplines, ranging from physics and materials science to chemistry and biology. Upon light irradiation, different relaxation processes take place in which electronic and nuclear motion are intimately coupled. These are best described by the time-dependent molecular Schrödinger equation, but its solution poses fundamental practical challenges to contemporary theoretical chemistry. Two widely used and complementary approaches to this problem are multiconfigurational time-dependent Hartree (MCTDH) and trajectory surface hopping (SH). MCTDH is an accurate fully quantum-mechanical technique but often is feasible only in reduced dimensionality, in combination with approximate vibronic coupling (VC) Hamiltonians, or both (i.e., reduced-dimensional VC potentials). In contrast, SH is a quantum–classical technique that neglects most nuclear quantum effects but allows nuclear dynamics in full dimensionality by calculating potential energy surfaces on the fly. If nuclear quantum effects do not play a central role and a linear VC (LVC) Hamiltonian is appropriate—e.g., for stiff molecules that generally keep their conformation in the excited state—then it seems advantageous to combine the efficient LVC and SH techniques. In this Account, we describe how surface hopping based on an LVC Hamiltonian (SH/LVC)—as recently implemented in the SHARC surface hopping package—can provide an economical and automated approach to simulate non-adiabatic dynamics. First, we illustrate the potential of SH/LVC in a number of showcases, including intersystem crossing in SO2, intra-Rydberg dynamics in acetone, and several photophysical studies on large transition-metal complexes, which would be much more demanding or impossible to perform with other methods. While all of the applications provide very useful insights into light-induced phenomena, they also hint at difficulties faced by the SH/LVC methodology that need to be addressed in the future. Second, we contend that the SH/LVC approach can be useful to benchmark SH itself. By the use of the same (LVC) potentials as MCTDH calculations have employed for decades and by relying on the efficiency of SH/LVC, it is possible to directly compare multiple SH test calculations with a MCTDH reference and ponder the accuracy of various correction algorithms behind the SH methodology, such as decoherence corrections or momentum rescaling schemes. Third, we demonstrate how the efficiency of SH/LVC can also be exploited to identify essential nuclear and electronic degrees of freedom to be employed in more accurate MCTDH calculations. Lastly, we show that SH/LVC is able to advance the development of SH protocols that can describe nuclear dynamics including explicit laser fields—a very challenging endeavor for trajectory-based schemes. To end, this Account compiles the typical costs of contemporary SH simulations, evidencing the great advantages of using parametrized potentials. The LVC model is a sleeping beauty that, kissed by SH, is fueling the field of excited-state molecular dynamics. We hope that this Account will stimulate future research in this direction, leveraging the advantages of the SH/VC schemes to larger extents and extending their applicability to uncharted territories.

In this work, the new ANO-R basis set for all elements of the first six periods is introduced. The ANO-R basis set is an all-electron basis set that was constructed including scalar-relativistic effects of the exact-two component (X2C) Hamiltonian and modeling the atomic nucleus by a Gaussian charge distribution, which makes the basis set suitable for calculations of both light and heavy elements. For high accuracy, it takes advantage of the general contraction scheme and was developed at the CASSCF/CASPT2 level of theory. The distinguishing feature of the ANO-R basis set is its compactness in terms of both primitive and contracted basis functions, thus containing no superfluous functions for a given quality. An optimum number of primitive basis functions was selected based on studying the convergence toward the complete basis set limit for each element individually. The primitive basis sets were then contracted using the density-averaged atomic-natural-orbital (ANO) scheme, and suitable contraction levels were determined solely based on the natural orbital occupation numbers that describe the contribution of each natural orbital to the one-particle density matrix. Rather than following the common "split-valence n-tuple zeta plus polarization functions" structure, the resulting basis sets ANO-R0 to ANO-R3 possess a unique composition for each element, ensuring that no unnecessary functions are included while the basis sets are still balanced across the first six periods (H-Rn).

The influence of vibrational motion on electronic excited state properties is investigated for the organic chromophore 2-nitronaphtalene in methanol. Specifically, the performance of two vibrational sampling techniques - Wigner sampling and sampling from an ab initio molecular dynamics trajectory- is assessed, in combination with implicit and explicit solvent models. The effects of the different sampling/solvent combinations on the energy and electronic character of the absorption bands are analyzed in terms of charge transfer and exciton size, computed from the electronic transition density. The absorption spectra obtained using sampling techniques and its underlying properties are compared to those of the electronic excited states calculated at the Franck-Condon equilibrium geometry. It is found that the absorption bands of the vibrational ensembles are red-shifted compared to the Franck-Condon bright states, and this red-shift scales with the displacement from the equilibrium geometry. Such displacements are found larger and better described when using ensembles from the harmonic Wigner distribution than snapshots from the molecular dynamics trajectory. Particularly relevant is the torsional motion of the nitro group that quenches the charge transfer character of some of the absorption bands. This motion, however, is better described in the molecular dynamics trajectory. Thus, none of the vibrational sampling approaches can satisfactorily capture all important aspects of the nuclear motion. The inclusion of solvent also red-shifts the absorption bands with respect to the gas phase. This red-shift scales with the charge-transfer character of the bands and is found larger for the implicit than for the explicit solvent model. The advantages and drawbacks of the different sampling and solvent models are discussed to guide future research on the calculation of UV-vis spectra of nitroaromatic compounds.

Nitronaphthalene derivatives efficiently populate their electronically excited triplet states upon photoexcitation through ultrafast intersystem crossing (ISC). Despite having been studied extensively by time‐resolved spectroscopy, the reasons behind their ultrafast ISC remain unknown. Herein, we present the first ab initio nonadiabatic molecular dynamics study of a nitronaphthalene derivative, 2‐nitronaphthalene, including singlet and triplet states. We find that there are two distinct ISC reaction pathways involving different electronic states at distinct nuclear configurations. The high ISC efficiency is explained by the very small electronic and nuclear alterations that the chromophore needs to undergo during the singlet–triplet transition in the dominating ISC pathway after initial dynamics in the singlet manifold. The insights gained in this work are expected to shed new light on the photochemistry of other nitro polycyclic aromatic hydrocarbons that exhibit ultrafast intersystem crossing.

In the publication of the ANO-R basis set, inconsistencies occurred in the contraction levels for a small number of.(Table Presented) elements. We have now corrected the contraction levels of the erroneous basis set contractions, and in Table 1, we provide a list with the inconsistent and corrected contraction levels. The inconsistent contraction levels were furthermore used in the basis set file that was supplied as Supporting Information in our publication. In this correction, we therefore supply an updated version of the basis set files including the complete ANO-R basis sets for all elements H−Rn. In addition, in Table 2 in the original publication of the ANO-R basis set, the contraction levels of several basis sets were erroneously reported−although they were given correctly in the Supporting Information. In Table 2, we provide a list with correct contraction levels that were also used in the basis set files provided with the original publication. In addition, we provide an updated version of Table 2 of the original ANO-R publication in Table 3 in this correction. (Table Presented). (Less)

In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with post calculation analysis and visualization, and new electronic and muonic basis sets.

In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

Although nitrobenzene is the smallest nitro-aromatic molecule, the nature of its electronic structure is still unclear. Most notably, the lowest-energy absorption band was assessed in numerous studies providing conflicting results regarding its charge-transfer character. In this study, we employ a combination of molecular dynamics and quantum chemical methods to disentangle the nature of the lowest-energy absorption band of nitrobenzene. Surprisingly, the charge-transfer transition from the benzene moiety to the nitro group is found to be quenched by a flow of charge into the opposite direction induced by vibrational motion. Beyond clarifying the charge-transfer character of nitrobenzene, we show that the widely used approach of analyzing the ground-state minimum-energy geometry provides completely wrong conclusions.

Multi-configurational second order perturbation theory (CASPT2) has become a very popular method for describing excited-state properties since its development in 1990. To account for systematic errors found in the calculation of dissociation energies, an empirical correction applied to the zeroth-order Hamiltonian, called the IPEA shift, was introduced in 2004. The errors were attributed to an unbalanced description of open-shell versus closed-shell electronic states and is believed to also lead to an underestimation of excitation energies. Here we show that the use of the IPEA shift is not justified and the IPEA should not be used to calculate excited states, at least for organic chromophores. This conclusion is the result of three extensive analyses. Firstly, we survey the literature for excitation energies of organic molecules that have been calculated with the unmodified CASPT2 method. We find that the excitation energies of 356 reference values are negligibly underestimated by 0.02 eV. This value is an order of magnitude smaller than the expected error based on the calculation of dissociation energies. Secondly, we perform benchmark full configuration interaction calculations on 137 states of 13 di- and triatomic molecules and compare the results with CASPT2. Also in this case, the excited states are underestimated by only 0.05 eV. Finally, we perform CASPT2 calculations with different IPEA shift values on 309 excited states of 28 organic small and medium-sized organic chromophores. We demonstrate that the size of the IPEA correction scales with the amount of dynamical correlation energy (and thus with the size of the system), and gets immoderate already for the molecules considered here, leading to an overestimation of the excitation energies. It is also found that the IPEA correction strongly depends on the size of the basis set. The dependency on both the size of the system and of the basis set, contradicts the idea of a universal IPEA shift which is able to compensate for systematic CASPT2 errors in the calculation of excited states.

When including relativistic effects in quantum chemical calculations, basis sets optimized for relativistic Hamiltonians such as the atomic natural orbital-relativistic core-correlated (ANO-RCC) basis set have to be used to avoid large errors that appear upon contraction of the basis set. While the large size of the ANO-RCC basis set in terms of primitive basis functions allows for highly accurate calculations, it also hinders its applicability to large sized systems due to the computational costs. To tackle this problem, a new compact relativistic ANO basis set, the ANO-eXtra Small (XS) basis set, is introduced for elements H-Ca. The number of primitive basis functions in ANO-XS is about half that of the ANO-RCC basis set. This greatly reduces the computational costs in the integral calculations especially when used in combination with Cholesky decomposition. At the same time, the ANO-XS basis set is able to predict molecular properties such as bond lengths and excitation energies with reasonable errors compared to the larger ANO-RCC basis set. The main intention for the ANO-XS basis set is to be used in conjunction with the ANO-RCC basis set for large systems that can be divided with regions demanding different qualities of basis sets. This is exemplified in CASPT2 calculations for an Ir(C3H4N)3 complex, where substituting the larger ANO-RCC for the compact ANO-XS basis set at the ligand atoms yields only minor differences for a large number of excited states compared to calculations employing the ANO-RCC basis set on all atoms. Thus, accurate calculations including relativistic effects for large systems become more affordable with the new ANO-XS basis set.

In this work we discuss the theoretical photo-double ionization spectrum of iodomethane which was obtained by the newly developed relativistic two-particle propagator and compare it to experimental data. For a correct interpretation of the spectral features in the outer valence region, spin-orbit effects play a major role and induce new features to the spectra. Additionally, wide-energy range single and double ionization spectra of iodomethane were calculated revealing possible electronic decay reactions after high-energy primary ionization. In the low energy region of the single ionization spectrum pronounced breakdown was observed resulting in a highly correlated manifold which was characterized in detail via population analysis. (C) 2012 Elsevier B. V. All rights reserved.

In this work, the four-component two-particle propagator technique is employed for the calculation of double ionization spectra of the noble gas atoms Ne through Rn. For a correct assignment of the individual final states, inclusion of spin-orbit coupling and electron correlation is mandatory and is accounted for in the framework of the relativistic propagator. It was observed that the $n{s}^{2}n{p}^{4}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{D}_{2}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$) manifolds of all investigated noble gas dications exhibit a clear main-state character with only small admixture from other configurations. This also refers to the $2{s}^{1}2\phantom{\rule{-0.16em}{0ex}}{p}^{5}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}^{o}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) states of Ne${}^{2+}$. In the argon, krypton, and xenon dications, the $n{s}^{1}n{p}^{5}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}^{o}$) states, and especially the $n{s}^{1}\phantom{\rule{-0.16em}{0ex}}n{p}^{5}$(${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) ones, lose intensity due to pronounced configuration interaction. These states experience strong mixings with ground-state shake-up satellites, which occupy the same energy region. The composition of the $5{s}^{1}5{p}^{5}$(${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) singlet state of Xe${}^{2+}$ is studied in detail by analyzing the corresponding eigenvector. As long as a $LS$ coupling picture can be approximately maintained, the amount of singlet-triplet splitting decreases in the sequence from neon to xenon. In the $6{s}^{1}6{p}^{5}$ manifold of Rn${}^{2+}$, a complete disappearance of well-defined main states takes place leading to a dense and complicated spectrum governed by very strong multiconfiguration effects. Relativistic corrections to the Coulomb interaction are accounted for by inclusion of the Gaunt (magnetic) term.

In this work we study the influence of relativistic effects, in particular spin-orbit coupling, on electronic decay processes in KrXe2 clusters of various geometries. For the first time it is shown that inclusion of spin-orbit coupling has decisive influence on the accessibility of a specific decay pathway in these clusters. The radiationless relaxation process is initiated by a Kr 4s ionization followed by an electron transfer from xenon to krypton and a final second ionization of the system. We demonstrate the existence of competing electronic decay pathways depending in a subtle way on the geometry and level of theory. For our calculations a fully relativistic framework was employed where omission of spin-orbit coupling leads to closing of two decay pathways. These findings stress the relevance of an adequate relativistic description for clusters with heavy elements and their fragmentation dynamics.