CASPT2 Level Research Articles

Probing the Photodynamics of Rhodopsins with Reduced Retinal Chromophores.

While the light-induced population dynamics of different photoresponsive proteins has been investigated spectroscopically, systematic computational studies have not yet been possible due to the phenomenally high cost of suitable high level quantum chemical methods and the need of propagating hundreds, if not thousands, of nonadiabatic trajectories. Here we explore the possibility of studying the photodynamics of rhodopsins by constructing and investigating quantum mechanics/molecular mechanics (QM/MM) models featuring reduced retinal chromophores. In order to do so we use the sensory rhodopsin found in the cyanobacterium Anabaena PCC7120 (ASR) as a benchmark system. We find that the basic mechanistic features associated with the excited state dynamics of ASR QM/MM models are reproduced using models incorporating a minimal (i.e., three double-bond) chromophore. Furthermore, we show that ensembles of nonadiabatic ASR trajectories computed using the same abridged models replicate, at both the CASPT2 and CASSCF levels of theory, the trends in spectroscopy and lifetimes estimated using unabridged models and observed experimentally at room temperature. We conclude that a further expansion of these studies may lead to low-cost QM/MM rhodopsin models that may be used as effective tools in high-throughput in silico mutant screening.

Mechanisms and kinetics of reaction CHClBr•+NO2

The reaction CHClBr•+NO2 was investigated via quantum chemical methods and kinetic calculations. The reaction mechanism on the singlet potential energy surface(PES) was considered by B3LYP method, and the energies were calculated at the CCSD(T) and CASPT2 levels of theory. The rate constants and the ratios of products were obtained by utilizing VTST and RRKM methods over wide temperature and pressure ranges. Our results indicate that carbon-to-nitrogen approach via a barrierless process is preferred in the initial association of CHClBr• and NO2. The dominant product is BrNO+CHClO(P1), which agrees well with the experimental observation. P2(ClNO+CHBrO) and P3(HNO+CBrClO) may also have minor contributions to the reaction. The calculated overall rate constants are independent of pressure and consistent with the experimental data, which can be fitted with the following equation over the temperature range of 200—1500 K: k(T)=2.31×10–15 T 0.99exp(771/T). Compared with reaction CH2Br•+NO2, reaction CHClBr•+NO2

Electronic excitation energies in dimers between radical ions presenting long, multicenter bonding.

The formation of long, multicenter dimers between radical ions is usually monitored through UV-vis spectroscopy given the characteristic low-energy absorption band that they exhibit, not observed for the parent monomers. In this work, the performance of CASPT2, RASPT2, and TD-DFT methods for obtaining excitation energies of the long, multicenter bonded π-[TCNE]2(2-) and π-[TTF]2(2+) dimers has been addressed (TCNE = tetracyanoethylene; TTF = tetrathiafulvalene). The impact of the active space on the vertical electronic transitions computed at the RASPT2 and CASPT2 levels has been tested against experimentally observed absorption bands. Analogous tests have been carried out for a wide variety of density functionals within the TD-DFT formalism. Our calculations show that whereas CASPT2 predicts very accurate excitation energies for the π-[TCNE]2(2-), the mean absolute error for π-[TTF]2(2+) is higher for CASPT2 than for TD-DFT calculations, whenever pure density functionals or low % HF exchange hybrid functionals are used. Hybrid functionals with high % HF exchange (and thus RSH functionals) conduct to large errors on the excitation energies in both dimers. Furthermore, vertical electronic transitions are also obtained for 100 configurations extracted from a 45 ps molecular dynamics (CPMD) simulation aimed at providing an accurate description of the thermal fluctuation effects of a π-[TCNE]2(2-) dimer in dichloromethane. These thermal effects explain the shape of the experimental UV-vis spectrum, where the lowest HOMO → LUMO absorption presents a broad band and the following HOMO-1 → LUMO absorption exhibits a narrower band.

Erratum to "Geometries and Vertical Excitation Energies in Retinal Analogues Resolved at the CASPT2 Level of Theory: Critical Assessment of the Performance of CASSCF, CC2, and DFT Methods".

A systematic investigation of structural properties and vertical excitation energies of a series of structurally modified 11-cis-retinal chromophores in vacuo was performed by means of multiconfigurational second-order perturbation theory (CASPT2). CASPT2-based geometries agree reasonably well with Moller–Plesset second-order perturbation theory (MP2), local second-order approximate coupled cluster singles and doubles (LCC2), and density functional theory (DFT) geometries, while the complete active space self-consistent field (CASSCF) method exaggerates dramatically the bond length pattern in the polyene chain. The quality of the resulting vertical excitation energies obtained by employing CASSCF, second-order approximate coupled cluster singles and doubles (CC2), LCC2, and time-dependent density functional theory (TD-DFT) approaches is assessed with respect to the CASPT2 data. We show that the commonly used CASSCF/CASPT2 approach works reasonably well in the case of vertical excitation energies of planar...

A two-scale approach to electron correlation in multiconfigurational perturbation theory.

We present a new approach for the calculation of dynamic electron correlation effects in large molecular systems using multiconfigurational second-order perturbation theory (CASPT2). The method is restricted to cases where partitioning of the molecular system into an active site and an environment is meaningful. Only dynamic correlation effects derived from orbitals extending over the active site are included at the CASPT2 level of theory, whereas the correlation effects of the environment are retrieved at lower computational costs. For sufficiently large systems, the small errors introduced by this approximation are contrasted by the substantial savings in both storage and computational demands compared to the full CASPT2 calculation. Provided that static correlation effects are correctly taken into account for the whole system, the proposed scheme represent a hierarchical approach to the electron correlation problem, where two molecular scales are treated each by means of the most suitable level of theory.

Molecular and electronic structures of the NbC2−/0 clusters through the assignment of the anion photoelectron spectra by quantum chemical calculations

CASPT2 and RCCSD(T) methods were used to investigate the low-lying states of NbC2−/0. The ground states of the anionic and neutral clusters are consistently calculated as the 3B1 and 4B1 states of the cyclic isomer, respectively. Franck–Condon simulations at the BP86 level for the 3B1→4B1 ionization shows that the predicted vibrational progression is in good agreement with the experimental X band of the 532nm spectrum of NbC2−. At the CASPT2 level, all bands in the 355nm photoelectron spectrum could be interpreted as originating from the 3B1 state.

Ab initio reaction pathways for photodissociation and isomerization of nitromethane on four singlet potential energy surfaces with three roaming paths.

Photodissociation pathways of nitromethane following π → π(*) electronic excitation are reported. The potential energy surfaces for four lowest singlet states are explored, and structures of many intermediates, dissociation limits, transition states, and minimum energy conical intersections were determined using the automated searching algorism called the global reaction route mapping strategy. Geometries are finally optimized at CASSCF(14e,11o) level and energies are computed at CAS(14o,11e)PT2 level. The calculated preferable pathways and important products qualitatively explain experimental observations. The major photodissociation product CH3 and NO2 ((2)B2) is formed by direct dissociation from the S1 state. Important pathways involving S1 and S0 states for production of various dissociation products CH3NO + O ((1)D), CH3O(X(2)E) + NO (X(2)Π), CH2NO + OH, and CH2O + HNO, as well as various isomerization pathways have been identified. Three roaming processes also have been identified: the O atom roaming in O dissociation from CH3NO2, the OH radical roaming in OH dissociation from CH2N(O)(OH), and the NO roaming in NO dissociation from CH3ONO.

Heavy‐Atom Tunneling in the Ring Opening of a Strained Cyclopropene at Very Low Temperatures

The highly strained 1H-bicyclo[3.1.0]-hexa-3,5-dien-2-one 1 is metastable, and rearranges to 4-oxacyclohexa-2,5-dienylidene 2 in inert gas matrices (neon, argon, krypton, xenon, and nitrogen) at temperatures as low as 3 K. The kinetics for this rearrangement show pronounced matrix effects, but in a given matrix, the reaction rate is independent of temperature between 3 and 20 K. This temperature independence means that the activation energy is zero in this temperature range, indicating that the reaction proceeds through quantum mechanical tunneling from the lowest vibrational level of the reactant. At temperatures above 20 K, the rate increases, resulting in curved Arrhenius plots that are also indicative of thermally activated tunneling. These experimental findings are supported by calculations performed at the CASSCF and CASPT2 levels by using the small-curvature tunneling (SCT) approximation.

Multireference ab initio study on the low-lying excited states of isoselenocyanic acid, HNCSe

The electronic spectra of HNCSe were studied by performing multireference ab initio calculations at CASPT2 level of theory taking into account spin-orbit (SO) coupling. Our highly accurate calculation indicated that theoretically determined geometric parameters and harmonic vibrational frequencies for the ground state X 1 A ′ are consistent with observed experimental data. We present the oscillator strengths, electronic and structural changes accompanying the excitation process. The bonding characteristics in the low-lying excited states were analyzed on the basis of the valence molecular orbitals (MOs). And the excited states of HNCSe exist in the complex of Se and HNC radical pair. According to our calculations, the ground-state of HNCSe + is linear, and the value of the ionization potential of HNCSe has been found. The existence of bound excited anion states has been found for the first time in HNCSe -.

First-Principles Study on Site Preference and 4f → 5d Transitions of Ce3+ in Sr3AlO4F

The local structures and 4f → 5d transition energies of Ce(3+) located on the two crystallographic strontium sites of Sr3AlO4F, with charge compensation by means of nearby sodium substitutions for strontium (NaSr') or oxygen substitutions for coordinating fluorine (OF'), have been studied using the density functional theory (DFT) within the supercell model and the wave function-based embedded cluster calculations, respectively. The DFT total energy calculations show that Ce(3+) prefers strongly to occupy the eight-coordinated (Sr2) site over the ten-coordinate (Sr1) site. On the basis of the results from embedded cluster calculations at the CASPT2 level with the spin-orbit effect, the experimentally observed excitation bands are identified in association with the charge-compensated cerium centers. Especially, the two bands observed at ∼404 and ∼440 nm have been both assigned to the Ce(3+) located at the Sr2 sites but with compensation by one and two nearest-neighbor OF' substitutions, respectively, rather than to the Ce(3+) on the Sr1 and the Sr2 sites, respectively, as proposed earlier. Furthermore, the structural and electronic reasons for the red shift of the lowest 4f → 5d transition caused by coordinating OF' substitutions are analyzed in terms of the variations in centroid energy and crystal-field splitting of the 5d(1) configuration with the local environment. Finally, the thermal quenching of 5d luminescence at relatively high Ce(3+) concentrations is discussed on the basis of the electronic properties calculated with the hybrid DFT method.

Geometries and Vertical Excitation Energies in Retinal Analogues Resolved at the CASPT2 Level of Theory: Critical Assessment of the Performance of CASSCF, CC2, and DFT Methods.

A systematic investigation of structural properties and vertical excitation energies of a series of structurally modified 11-cis-retinal chromophores in vacuo was performed by means of multiconfigurational second-order perturbation theory (CASPT2). CASPT2-based geometries agree reasonably well with Møller-Plesset second-order perturbation theory (MP2), local second-order approximate coupled cluster singles and doubles (LCC2), and density functional theory (DFT) geometries, while the complete active space self-consistent field (CASSCF) method exaggerates dramatically the bond length pattern in the polyene chain. The quality of the resulting vertical excitation energies obtained by employing CASSCF, second-order approximate coupled cluster singles and doubles (CC2), LCC2, and time-dependent density functional theory (TD-DFT) approaches is assessed with respect to the CASPT2 data. We show that the commonly used CASSCF/CASPT2 approach works reasonably well in the case of vertical excitation energies of planar structures, but lack of dynamic correlation leads to large errors in energetics for strongly strained structures. For example, the highly twisted conformers of 9,10-dimethyl and 9,10,13-trimethyl species are found as global minima at the CASSCF level, whereas they turn almost planar at the CASPT2, MP2, LCC2, and DFT levels of theory. The CC2 method has shown a remarkable performance, manifested by a maximum deviation of 0.05 eV from the reference CASPT2 results, whereas the local version of CC2 seems to fail to describe the charge-transfer character of the S0 → S1 transitions correctly. We believe that our CASPT2 benchmark set will provide a reference that can be utilized for validation and development studies on 11-cis-retinal protonated Schiff base chromophore analogues.

Structure and Other Molecular Properties of Actinide Trichlorides AnCl3 (An = Th–Cm)

The ground-state molecular properties of the trichlorides of light actinides (An = Th-Cm) have been predicted by state-of-the-art quantum chemical calculations. The ground electronic states have been determined by multireference calculations at the CASPT2 level including both scalar and spin-orbit relativistic effects. These studies supported the expected single-configuration character of ThCl3 and CmCl3 with their well-defined 6dσ/7s hybrid and 5f(7) configurations, respectively. In contrast, the intermediate actinides (PaCl3-AmCl3) with partly filled 5f shells have numerous very low-lying excited states and consequently a mixed character of the spin-orbit ground states. Apart from the planar ThCl3 the ground-state molecular geometries proved to be pyramidal with C(3v) symmetry. The gradually decreasing An-Cl bond distances reveal the actinide contraction known for the atomic and ionic radii of these actinide atoms. Other ground-state molecular properties as vibrational frequencies and natural charges have been obtained by density functional theory calculations using the B3LYP exchange-correlation functional in conjunction with small-core relativistic energy-consistent pseudopotentials for the actinides.

Multireference Ab Initio Density Matrix Renormalization Group (DMRG)-CASSCF and DMRG-CASPT2 Study on the Photochromic Ring Opening of Spiropyran.

The photochromic ring-opening reaction of spiropyran has been revisited at the multireference CASSCF and CASPT2 level with a CAS(22e,20o) active space, in combination with density matrix renormalization group (DMRG) methods. The accuracy of the DMRG-CASSCF and DMRG-CASPT2 calculations, with respect to the number of renormalized states, the number of roots in state-averaged wave functions, and the number basis functions, was examined. For the current system, chemically accurate results can be obtained with a relatively small number of renormalized states. The nature and vertical excitation energies of the excited (S1 and S2) states are consistent with conventional CAS(or RAS)PT2 with medium active spaces. The capability of the DMRG-CASSCF method in the optimization of molecular geometry is demonstrated for the first time. The computation costs (several hours per optimization cycle) are comparable with that of the conventional CASSCF geometry optimization with small active space. Finally, the DMRG-PT2 computed S1-MEP for the C-O and C-N bond-cleavage processes show good agreement with our previous calculations with a CAS(12e,10o) active space [Liu, F.; Morokuma, K. J. Am. Chem. Soc. 2013, 135, 10693-10702]. Especially, the role of the HOOP valleys in the S1 → S0 nonadiabatic decay has been confirmed.

Mapping the Excited State Potential Energy Surface of a Retinal Chromophore Model with Multireference and Equation-of-Motion Coupled-Cluster Methods.

The photoisomerization of the retinal chromophore of visual pigments proceeds along a complex reaction coordinate on a multidimensional surface that comprises a hydrogen-out-of-plane (HOOP) coordinate, a bond length alternation (BLA) coordinate, a single bond torsion and, finally, the reactive double bond torsion. These degrees of freedom are coupled with changes in the electronic structure of the chromophore and, therefore, the computational investigation of the photochemistry of such systems requires the use of a methodology capable of describing electronic structure changes along all those coordinates. Here, we employ the penta-2,4-dieniminium (PSB3) cation as a minimal model of the retinal chromophore of visual pigments and compare its excited state isomerization paths at the CASSCF and CASPT2 levels of theory. These paths connect the cis isomer and the trans isomer of PSB3 with two structurally and energetically distinct conical intersections (CIs) that belong to the same intersection space. MRCISD+Q energy profiles along these paths provide benchmark values against which other ab initio methods are validated. Accordingly, we compare the energy profiles of MRPT2 methods (CASPT2, QD-NEVPT2, and XMCQDPT2) and EOM-SF-CC methods (EOM-SF-CCSD and EOM-SF-CCSD(dT)) to the MRCISD+Q reference profiles. We find that the paths produced with CASSCF and CASPT2 are topologically and energetically different, partially due to the existence of a "locally excited" region on the CASPT2 excited state near the Franck-Condon point that is absent in CASSCF and that involves a single bond, rather than double bond, torsion. We also find that MRPT2 methods as well as EOM-SF-CCSD(dT) are capable of quantitatively describing the processes involved in the photoisomerization of systems like PSB3.

Multiple Pathways for the Primary Step of the Spiropyran Photochromic Reaction: A CASPT2//CASSCF Study

CASSCF and CASPT2 studies on the reaction mechanism of the photochromic ring-opening process of a spiropyran (SP) (1',3',3'-trimethylspiro-[2H-1-benzopyran-2,2'-indoline], also known as BIPS) have been performed and possible excited-state C-O (and C-N) bond cleavage pathways and S1-to-S0 nonadiabatic transition channels have been explored. (1) The C-O bond dissociation in SP does not follow a conical-intersection mechanism that has been proposed in a model study with a simplified benzopyran. The CASSCF-optimized crossing points are actually avoided crossings with a large S1-S0 energy gap at the CASPT2 level; thus, they could not act as efficient S1-to-S0 funnels. (2) C-O bond cleavage paths on S1 leading to both the CCC (cis-cis-cis with respect to the configuration around α, β, γ) and TCC (trans-cis-cis) intermediates of merocyanine (MC) are barrierless, in line with the experimentally observed ultrafast formation of MC. (3) An unexpected low-energy hydrogen-out-of-plane (HOOP) valley on the (π→σ*) surface was located not far from the C-O bond cleavage path and was suggested to be an efficient S1-to-S0 nonadiabatic decay channel. Triggered by the active HOOP mode, the molecule can easily access the S1-HOOP valley and then make a transition to the S0 surface through the narrow S1-S0 gap that exists in an extended region. Nonadiabatic decay through a conical intersection on C-N dissociation path as well as the HOOP funnel is responsible for high internal conversion yields of SP. These findings shedding light on the complex mechanism of SP-MC interconversion provide fundamental information for design spiropyran-based photochromic devices.

Ab initio study of many-body decomposition of the interaction energy in small beryllium clusters [formula omitted

We present the decomposition of interaction energies in beryllium clusters, Bem=3-6, into a series of nonidentical m-body nonadditivities up to m=6. We analyse the role of the electron correlation and compare nonadditivities at HF, CASSCF, MP2, CASPT2 and CCSD levels of theory with the reference aug-cc-pVTZ CCSD(T) results. The dominant nonadditivity terms are the three- and four-body. Five and six-body terms are relatively large in Be5-6 clusters, but the total interaction energy of Be6 is affected only marginally, due to their mutual cancellation.

Molecular Structures for FeS4–/0 As Determined from an ab Initio Study of the Anion Photoelectron Spectra

For the purpose of assigning the photoelectron spectra of the FeS4(-) molecular entity, geometric and electronic structures of low-lying FeS4(-/0) isomers were investigated at the B3LYP, CASPT2, and RCCSD(T) computational quantum chemical levels. The anionic ground state is predicted to be the (4)B1g state of the D2h (η(2)-(S2))2Fe(-) isomer with two S2(2-) molecular ligands side-on bond in a D2h fashion to iron, which has an oxidation state of +3. The experimental photoelectron spectra of FeS4(-) were successfully assigned as originating from this isomer. The composed lowest energy X band is the result of ionizations to the (3)B3g, (5)B1u, and (5)B1g states. Analyses of the CASSCF orbitals indicated an almost degeneracy of the nonbonding 3d orbitals of iron and the π* orbitals of S2(2-). All the experimental observed higher ionization energy bands could also be theoretically assigned as originating from the proposed anion ground state by detachment of an electron from either of these iron or ligand orbitals.

Spin-Crossing in an Organometallic Pt-Benzene Complex.

The interaction between the Pt atom and the benzene (Bz) molecule was investigated theoretically, using a symmetric Pt-Bz half-sandwich complex. Various levels of wave function theory (HF, MP2, CCSD(T), CASPT2, multistate (MS) MS-CASPT2) together with several functionals (PBE, PBE+D3, PBE+vdW, PBE/EE+vdW) of the density functional theory (DFT) were complemented by quantum Monte Carlo (QMC) calculations. Spin-orbit coupling (SOC) effects were also taken into account at the CASPT2 and DFT levels of theory. The inclusion of dynamic correlation energy was found to be essential to maintaining the stability of the complex. The dative type of bonding was identified to be responsible for the Pt-Bz binding in the ground state. Single-reference CCSD(T) and MP2 as well as multireference CASPT2 and MS-CASPT2 methods reveal that the interaction curve has a single energy minimum (corresponding to the (1)S0 state) and a shoulder (arising from the crossing between the (1)S0 and (3)D3 states) at longer distances. The inclusion of SOC at the CASPT2 level leads to the appearance of another well-separated minimum, which corresponds to the triplet state (3)F4. The PBE/EE+vdW functional, which includes a fraction of exact-exchange (EE) and nonlocal electron correlation, shows the best qualitative agreement with respect to the CCSD(T) data among all DFT functionals used. Large-scale QMC calculations, based on DFT wave functions constructed using TPSSh and M11 functionals, were confronted with the CCSD(T) results. The QMC-TPSSh protocol favorably agrees with the CCSD(T) data, suggesting its possible use in other Pt-containing organometallic systems. All of the methods used (except for HF) show that the Pt-benzene binding leads to the quenching of the Pt high-spin triplet ground state, and the low-spin closed-shell singlet state is found to be preferred in the ground-state of the complex.

Combined Theoretical and Experimental Study of the Photophysics of Asulam

The photophysics of the neutral molecular form of the herbicide asulam has been described in a joint experimental and theoretical, at the CASPT2 level, study. The unique π → π* aromatic electronic transition (f, ca. 0.5) shows a weak red-shift as the polarity of the solvent is increased, whereas the fluorescence band undergoes larger red-shifts. Solvatochromic data point to higher dipole moment in the excited state than in the ground state (μ(g) < μ(e)). The observed increase in pKa in the excited state (pKa* - pKa, ca. 3) is consistent with the results of the Kamlet-Abboud-Taft and Catalán et al. multiparametric approaches. Fluorescence quantum yield varies with the solvent, higher in water (ϕ(f) = 0.16) and lower in methanol and 1-propanol (approx. 0.02). Room temperature fluorescence lifetime in aqueous solution is (1.0 ± 0.2) ns, whereas the phosphorescence lifetime in glassy EtOH at 77 K and the corresponding quantum yield are (1.1 ± 0.1) s and 0.36, respectively. The lack of mirror image symmetry between modified absorption and fluorescence spectra reflects different nuclear configurations in the absorbing and emitting states. The low value measured for the fluorescence quantum yield is justified by an efficient nonradiative decay channel, related with the presence of an easily accessible conical intersection between the initially populated singlet bright (1)(L(a) ππ*) state and the ground state (gs/ππ*)(CI). Along the main decay path of the (1)(L(a) ππ*) state the system undergoes an internal conversion process that switches part of the population from the bright (1)(L(a) ππ*) to the dark (1)(L(b) ππ*) state, which is responsible for the fluorescence. Additionally, singlet-triplet crossing regions have been found, a fact that can explain the phosphorescent emission detected. An intersystem crossing region between the phosphorescent state (3)(L(a) ππ*) and the ground state has been characterized, which contributes to the nonradiative deactivation of the excitation energy.

Theoretical Investigation of the Electronic Structure of Fe(II) Complexes at Spin-State Transitions.

The electronic structure relevant to low spin (LS)↔high spin (HS) transitions in Fe(II) coordination compounds with a FeN6 core are studied. The selected [Fe(tz)6]2+ (1) (tz = 1H-tetrazole), [Fe(bipy)3]2+ (2) (bipy = 2,2′-bipyridine), and [Fe(terpy)2]2+ (3) (terpy = 2,2′:6′,2″-terpyridine) complexes have been actively studied experimentally, and with their respective mono-, bi-, and tridentate ligands, they constitute a comprehensive set for theoretical case studies. The methods in this work include density functional theory (DFT), time-dependent DFT (TD-DFT), and multiconfigurational second order perturbation theory (CASPT2). We determine the structural parameters as well as the energy splitting of the LS–HS states (ΔEHL) applying the above methods and comparing their performance. We also determine the potential energy curves representing the ground and low-energy excited singlet, triplet, and quintet d6 states along the mode(s) that connect the LS and HS states. The results indicate that while DFT is well suited for the prediction of structural parameters, an accurate multiconfigurational approach is essential for the quantitative determination of ΔEHL. In addition, a good qualitative agreement is found between the TD-DFT and CASPT2 potential energy curves. Although the TD-DFT results might differ in some respect (in our case, we found a discrepancy at the triplet states), our results suggest that this approach, with due care, is very promising as an alternative for the very expensive CASPT2 method. Finally, the two-dimensional (2D) potential energy surfaces above the plane spanned by the two relevant configuration coordinates in [Fe(terpy)2]2+ were computed at both the DFT and CASPT2 levels. These 2D surfaces indicate that the singlet–triplet and triplet–quintet states are separated along different coordinates, i.e., different vibration modes. Our results confirm that in contrast to the case of complexes with mono- and bidentate ligands, the singlet–quintet transitions in [Fe(terpy)2]2+ cannot be described using a single configuration coordinate.