Probing the rhodopsin cavity with reduced retinal models at the CASPT2//CASSCF/AMBER level of theory

We show that the ab initio CASPT2//CASSCF strategy previously used to investigate the ground and excited states of the chromophore of the vision receptor rhodopsin (Rh) in vacuo can be successfully implemented in a QM/MM scheme allowing for CASPT2//CASSCF/AMBER geometry optimization and excited state property evaluation in proteins. Two receptor models (Rh-1 and Rh-2) incorporating different reduced chromophores are investigated. It is shown that Rh-2 features a chromophore equilibrium structure with the correct helicity and a lambdamax that is only 52 nm blue-shifted from the observed value. This result should open the way to a qualitatively correct ab initio QM/MM modeling of the early excited state transient species involved in the vision process.     

Properties of the emitting state of the green fluorescent protein resolved at the CASPT2//CASSCF/CHARMM level

A "brute-force" ab initio CASPT2//CASSCF/CHARMM computational approach is employed to investigate the properties of the emitting state of the wild-type green fluorescence protein. The results indicate that the emitting moiety corresponds to a slightly perturbed H2O- - -chromophore complex. Thus, the protein matrix seems to be designed in such a way to mimic an environment that is more similar to gas-phase than water solution.     

A CASSCF and CASPT2 study on the excited states of s-trans-formaldazine

The low-lying excited states of s-trans-formaldazine (H2CN-NCH2) have been investigated using the complete active space self-consistent field (CASSCF) and the multiconfigurational second-order perturbation (CASPT2) methods. The vertical excitation energies have been calculated at the state-average CASSCF and multistate CASPT2 levels employing the cc-pVTZ basis set. The photodissociation mechanisms starting from the S1 state have been determined. The lowest energy points along the seams of surface intersections have been located in both the Franck-Condon region and the N-N dissociation pathway in the S1 state. Once the system populates the S1 state, in the viewpoint of energy, the radiationless decay via S1/S0(3) conical intersection followed by the N-N bond fission in the ground-state is more favorable in comparison with the N-N dissociation process in the S1 state. A three-surface crossing region (S1/T1/T2), where the S1, T1, and T2 states intersect, was also found. However, the intersystem crossing process via S1/T1/T2 is not energetically competitive with the internal conversion via S1/S0(3).     

Low-lying electronic states of HNCS and its ions: a CASSCF/CASPT2 study

Complete active space self-consistent-field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) calculations in conjunction with the ANO-L basis set were performed to investigate systematically the low-lying electronic states of HNCS and its ions in C _s symmetry. Our highly accurate calculation indicated that theoretically determined geometric parameters and harmonic vibrational frequencies for the ground-state X ¹A′ are in good agreement with observed experimental data. The geometry of triplet HNCS is clearly favored C ₁ symmetry, and the relative energy is predicted to be 3.000 eV (69.2 kcal/mol). The vertical transition energies for the selected excited states of HNCS were calculated at CASSCF/CASPT2/ANO-L level of theory based on CASSCF optimized geometry. Except for a few linear states of X ²Π (1²A′, 1²A″), 1⁴Σ⁻ (1⁴A″), and 1²Σ⁺ (3²A′) states of HNCS⁺, our results confirmed that the majority of excited states are twisted trans-bend structures. The existence of bound excited anion states has been found for the first time in HNCS⁻. A more elaborate examination of ionization potential of HNCS (AIP, VIP) than previous reports has been presented.     

Origin, nature, and fate of the fluorescent state of the green fluorescent protein chromophore at the CASPT2//CASSCF resolution

Ab initio CASPT2//CASSCF relaxation path computations are employed to determine the intrinsic (e.g., in vacuo) mechanism underlying the rise and decay of the luminescence of the anionic form of the green fluorescent protein (GFP) fluorophore. Production and decay of the fluorescent state occur via a two-mode reaction coordinate. Relaxation along the first (totally symmetric) mode leads to production of the fluorescent state that corresponds to a planar species. The second (out-of-plane) mode controls the fluorescent state decay and mainly corresponds to a barrierless twisting of the fluorophore phenyl moiety. While a "space-saving" hula-twist conical intersection decay channel is found to lie only 5 kcal mol(-1) above the fluorescent state, the direct involvement of a hula-twist deformation in the decay is not supported by our data. The above results indicate that the ultrafast fluorescence decay observed for the GFP chromophore in solution is likely to have an intrinsic origin. The possible effects of the GFP protein cavity on the fluorescence lifetime of the investigated chromophore model are discussed.     

A CASSCF/CASPT2 study on the low-lying excited states of HSiCN, HSiNC and their ions

Equilibrium geometries of low-lying electronic states of cyanosilylene (HSiCN), isocyanosilylene (HSiNC), and their ions have been investigated using the complete active space self-consistent field (CASSCF) approach. The harmonic vibrational frequencies on the optimized geometries were calculated using the multiconfiguration linear response (MCLR) method. Taking the further correlation effects into account, the complete active space perturbation theory of second-order (CASPT2) was carried out for the energetic correction. The CASPT2 calculations have been performed to obtain the vertical excitation energies of selected low-lying excited states of HSiCN and HSiNC. Computed results show that the singlet-triplet splittings are calculated to be 0.99 and 1.30 eV for HSiCN and HSiNC, respectively. The vertical excitation energies of the lowest singlet and triplet excited states in HSiCN are lower than those in HSiNC. The first vertical ionization energy of HSiCN (10.04 eV) is higher than that of HSiNC (9.97 eV). The ground-state adiabatic electron affinities are found to be rather high, and the value of HSiCN (1.85 eV) higher than that of HSiNC (1.52 eV). The existences of dipole-bound excited negative ion states have been discovered within HSiCN and HSiNC.     

Probing highly efficient photoisomerization of a bridged azobenzene by a combination of CASPT2//CASSCF calculation with semiclassical dynamics simulation

Mechanism of phototriggered isomerization of azobenzene and its derivatives is of broad interest. In this paper, the S(0) and S(1) potential energy surfaces of the ethylene-bridged azobenzene (1) that was recently reported to have highly efficient photoisomerization were determined by ab initio electronic structure calculations at different levels and further investigated by a semiclassical dynamics simulation. Unlike azobenzene, the cis isomer of 1 was found to be more stable than the trans isomer, consistent with the experimental observation. The thermal isomerization between cis and trans isomers proceeds via an inversion mechanism with a high barrier. Interestingly, only one minimum-energy conical intersection was determined between the S(0) and S(1) states (CI) for both cis → trans and trans → cis photoisomerization processes and confirmed to act as the S(1) → S(0) decay funnel. The S(1) state lifetime is ～30 fs for the trans isomer, while that for the cis isomer is much longer, due to a redistribution of the initial excitation energies. The S(1) relaxation dynamics investigated here provides a good account for the higher efficiency observed experimentally for the trans → cis photoisomerization than the reverse process. Once the system decays to the S(0) state via CI, formation of the trans product occurs as the downhill motion on the S(0) surface, while formation of the cis isomer needs to overcome small barriers on the pathways of the azo-moiety isomerization and rotation of the phenyl ring. These features support the larger experimental quantum yield for the cis → trans photoisomerization than the trans → cis process.     

Electronic spectra of uranyl chloride complexes in acetone: a CASSCF/CASPT2 investigation

A theoretical study is presented of the electronic spectra of the complexes UO(2)Cl(2)ac(4), UO(2)Cl(2)ac(3), [UO(2)Cl(3)ac(2)](-) and [UO(2)Cl(3)ac](-) (ac = acetone) using perturbation theory based on a complete-active-space type wavefunction (CASSCF/CASPT2). Both scalar relativistic effects and spin-orbit coupling were included in the calculations. The calculated excitation energies and oscillator strength values have been compared to the experimental absorption spectrum for uranyl chloride complexes in acetone solution, for chloride-to-uranyl ratios between two and three. The main purpose of this work was to investigate the origin of the remarkable intensity increase observed in the lower part of the experimental absorption spectra, upon addition of chloride to uranyl complexes in acetone. The calculated excitation energies for the different complexes are similar and closely correspond to the experimental data. However, in none of the theoretical spectra, the high intensities observed in the lower part of the experimental spectrum are reproduced.     

CASPT2 and CASSCF studies on the low-lying electronic states of the HCCO radical and its anion

The complete active space self-consistent field and multiconfigurational second-order perturbation theory methods have been used to investigate the low-lying electronic states of the HCCO radical and its anion. The calculated geometrical structure and harmonic vibrational frequencies for the X ²A″ state of HCCO are in good agreement with experimental values. The barrier to 1²П (1²A′) is estimated to be 0.069 eV (554 cm^?1), which is also close to experimental result (540 cm^?1). Moreover, we find that the 2²A′ state is bent, while 2²П (2²A″) is linear. By comparing the oscillator strengths and adiabatic excitation energies, we show that the 2²П (2²A″) ← X ²A″ transition is the most intense among these transitions. The unpaired electrons mainly locate on the C atoms in the 2²A′ and 2²П (2²A″) states according to the Mulliken spin populations. On the other hand, for HCCO^?, the first adiabatic and vertical detachment energies are 2.210 and 2.362 eV, respectively, which reasonably agree with experimental value of 2.338 ± 0.008 eV. Remarkably, we explore several higher excited states of the HCCO radical (1⁴A′, 2⁴A″ and cis-1⁴A′) and its anion (1³A″, 1¹A″ and 1³A′), which have not been reported in previous studies.     

Ground- and triplet excited-state properties correlation: a computational CASSCF/CASPT2 approach based on the photodissociation of allylsilanes

Excited-state properties, although extremely useful, are hardly accessible. One indirect way would be to derive them from relationships to ground-state properties which are usually more readily available. Herewith, we present quantitative correlations between triplet excited-state (T?) properties (bond dissociation energy, D?(T?), homolytic activation energy, E(a)(T?), and rate constant, k(r)) and the ground-state bond dissociation energy (D?), taking as an example the photodissociation of the C-Si bond of simple substituted allylsilanes CH?=CHC(R1R2)-SiH? (R1 and R2 = H, Me, and Et). By applying the complete-active-space self-consistent field CASSCF(6,6) and CASPT2(6,6) quantum chemical methodologies, we have found that the consecutive introduction of Me/Et groups has little effect on the geometry and energy of the T? state; however, it reduces the magnitudes of D?, D?(T?) and E(a)(T?). Moreover, these energetic parameters have been plotted giving good linear correlations: D?(T?) = α? + β? · D?, E(a)(T?) = α? + β? · D?(T?), and E(a)(T?) = α? + β? · D? (α and β being constants), while k(r) correlates very well to E(a)(T?). The key factor behind these useful correlations is the validity of the Evans-Polanyi-Semenov relation (second equation) and its extended form (third equation) applied for excited systems. Additionally, the unexpectedly high values obtained for E(a)(T?) demonstrate a new application of the principle of nonperfect synchronization (PNS) in excited-state chemistry issues.     

Energetics of cytosine singlet excited-state decay paths--a difficult case for CASSCF and CASPT2

Three deactivation paths for singlet excited cytosine are calculated at the CASPT2//CASSCF (complete active space second-order perturbation//complete active space self-consistent field) level of theory, using extended active spaces that allow for a reliable characterization of the paths and their energies. The lowest energy path, with a barrier of approximately 0.1 eV, corresponds to torsion of the C5-C6 bond, and the decay takes place at a conical intersection analogous to the one found for ethylene and its derivatives. There is a further path with a low energy barrier of approximately 0.2 eV associated with the (n(N),pi*) state which could also be populated with a low energy excitation. The path associated with a conical intersection between the ground and (n(O),pi*) states is significantly higher in energy (> 1 eV). The presence of minima on the potential energy surface for the (n,pi*) states that could contribute to the biexponential decay found in the gas phase was investigated, but could not be established unequivocally.     

A CASSCF/CASPT2 study on the low‐lying electronic states of the CH3SS and its cation

Complete active space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) calculations with contracted ANO‐RCC basis set were performed for low‐lying electronic states of CH₃SS and its cation in C_s symmetry. For the ground state X²A″ of CH₃SS, the calculated S‐S stretching mode is in good agreement with experimental reports. The electron transitions of CH₃SS⁺, X¹A′ → 1¹A″, X¹A′ → 2¹A′, and X¹A′ → 2¹A″, are predicted at 1.055, 3.247, and 3.841 eV. Moreover, the calculated adiabatic and vertical ionization potential and adiabatic affinity are in reasonable agreement with the experimental data. The CASSCF/CASPT2 potential energy curves (PECs) were calculated for S₂‐loss dissociation from the X²A″, 1²A′, and 2²A″ states. The electronic states of the CH₃ radical and S₂ molecule as the dissociation products were carefully determined by checking energies and geometries of the asymptote products. The S₂‐loss PEC for CH₃SS indicate that S₂‐loss dissociation occurs from the X²A″ state leading to CH₃ (1²A″) + S₂ (X³Σ), the 1²A′ and 2²A″ leading to CH₃ (1²A″) + S₂ (¹Δ_g). © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012.     

A CASSCF/CASPT2 insight into excited‐state intramolecular proton transfer of four imidazole derivatives

Excited‐state intramolecular proton transfer (ESIPT) of four imidazole derivatives, 2‐(2′‐hydroxyphenyl)imidazole (HPI), 2‐(2′‐hydroxyphenyl)benzimidazole (HPBI), 2‐(2′‐hydroxyphenyl)‐1H‐phenanthro[9,10‐d]imidazole (HPPI) and 2‐(2′‐hydroxyphenyl)‐1‐phenyl‐1H‐phenanthro[9,10‐d]imidazole (HPPPI), were studied by the sophisticated CASSCF/CASPT2 methodology. The state‐averaged SA‐CASSCF method was used to optimize their geometry structures of S₀ and S₁ electronic states, and the CASPT2 calculations were used for the calibration of all the single‐point energies, including the absorption and emission spectra. A reasonable agreement is found between the theoretical predictions and the available experimental spectral data. The forward ESIPT barriers of four target compounds gradually decrease with the increase of molecular size. On the basis of the present calculations, it is a plausible speculation that the larger the size, the faster is the ESIPT rate, and eventually, HPPPI molecule can undergo a completely barrierless ESIPT to the more stable S₁ keto form. Additionally, taking HPI as a representative example, the radiationless decays connecting the S₀ and S₁/S₀ conical intersection structures were also studied by constructing a linearly interpolated internal coordinate (LIIC) reaction path. The qualitative analysis shows that the LIIC barrier of HPI in the keto form is remarkably lower than that of its enol‐form, indicating that the former has a big advantage over the latter in the nonradiative process. © 2015 Wiley Periodicals, Inc.     

Dibenzo-p-dioxin. An ab initio CASSCF/CASPT2 study of the pi-pi* and n-pi* valence excited states

The pi-pi* and n-pi* valence excited states of dibenzo-p-dioxin (DD) were studied via the complete active space SCF and multiconfigurational second-order perturbation theory employing the cc-pVDZ basis set and the full pi-electron active spaces of 16 electrons in 14 active orbitals. The geometry and harmonic vibrational wavenumbers of the ground state correlate well with the experimental and other theoretical data. In particular, significant improvements over previously reported theoretical results are observed for the excitation energies. All of the pi-pi* excited states exhibit planar D(2h)minima. Thus no evidence was found for a C(2v) butterfly-like relaxation, although the wavenumbers of the b(3u) butterfly flapping mode proved exceedingly low in both the ground S(0)((1)A(g)) and the lowest dipole allowed excited S(1)((1)B(2u)) state. The calculations of oscillator strengths established the 2(1)B(2u) <-- 1(1)A(g) and 2(1)B(1u) <-- 1(1)A(g) transitions as by far the most intense, whereas the only allowed of the n-pi* transitions ((1)B(3u)) should possess only a modest intensity. Studies into dependence of the oscillator strengths on the extent of the butterfly-like folding showed that the electronic spectrum is more consistent with a folded equilibrium geometry assumed by DD in solution.     

A theoretical investigation of the excited states of OCLO radical, cation, and anion using the CASSCF/CASPT2 method

Using the complete active space self-consistent field method with a large atomic natural orbital basis set, 10, 13, and 9 electronic states of the OClO radical, OClO(+) cation, and OClO(-) anion were calculated, respectively. Taking the further correlation effects into account, the second-order perturbation (CASPT2) calculations were carried out for the energetic calibration. The photoelectron spectroscopy of the OClO radical and OClO(-) anion were extensively studied in the both case of the adiabatic and vertical ionization energies. The calculated results presented the relatively complete assignment of the photoelectron bands of the experiments for OClO and its anion. Furthermore, the Rydberg states of the OClO radical were investigated by using multiconfigurational CASPT2 (MS-CASPT2) theory under the basis set of large atomic natural orbital functions augmented with an adapted 1s1p1d Rydberg functions that have specially been built for this study. Sixteen Rydberg states were obtained and the results were consistent with the experimental results.     

CASSCF and CASPT2 study on O- and Cl-loss predissociation mechanisms of OClO (A(2)A2)

For studying O- and Cl-loss predissociation mechanisms of OClO (A(2)A(2)), we calculated O- and Cl-loss dissociation potential energy curves (adiabatic minimum-energy dissociation paths) of several low-lying doublet and quartet states at the CASPT2 level and located the MECPs (minimum energy crossing points) for many pairs of the potential energy surfaces (PESs) at the CASPT2 and CASSCF levels. On the basis of our calculation results (including the spin-orbit couplings at the MECPs), we predict three processes for O-loss predissociation of A(2)A(2) and four processes for Cl-loss predissociation of A(2)A(2). The most favorable process for O-loss predissociation is OClO (A(2)A(2)) → A(2)A(2)/1 (2)B(2) MECP → 1 (2)B(2) (1 (2)A') → O ((3)P(g)) + ClO (X(2)Π) (the first O-loss limit), and the needed energy for this process from X(2)B(1) is 2.92 eV. The most favorable process for Cl-loss predissociation is OClO (A(2)A(2)) → A(2)A(2)/1 (2)B(2) MECP → TS1 (1 (2)B(2)) → 1 (2)B(2)/1 (2)A(1) MECP → Cl ((2)P(u)) + O(2) (X(3)Σ(g)(-)) (the first limit), and the needed energy is 3.08 eV. In the previously suggested mechanisms (processes), the A(2)A(2) state was considered to go to the important 1 (2)B(2) state via 1 (2)A(1) (A(2)A(2) → 1 (2)A(1) → 1 (2)B(2)). In the present study we have found that the A(2)A(2) state can directly go to 1 (2)B(2) (at the located A(2)A(2)/1 (2)B(2) MECP the CASPT2 energy (relative to X(2)B(1)) and CASSCF spin-orbit coupling are 2.92 eV and 61.3 cm(-1), respectively). We have compared our processes (A(2)A(2) → 1 (2)B(2) → ...) with the processes (A(2)A(2) → 1 (2)A(1) → 1 (2)B(2) → ...) suggested in the previous MRCI studies and rewritten by us using our calculation results. Energetically the MRCI process for O-loss predissociation (to the first limit) is only slightly (0.13 eV) more favorable than our process, and the MRCI processes for Cl-loss predissociation (to the first and second limits) need the same energies as our processes. By considering the probabilities of radiationless transitions, the MRCI processes are less favorable than our processes since the MRCI processes proceed via more PES/PES crossings (more MECPs). The experimental facts concerning the photodissociation are explained.     

The decay from the dark npi* excited state in uracil: an integrated CASPT2/CASSCF and PCM/TD-DFT study in the gas phase and in water

By integrating the results of MS-CASPT2/CASSCF and TD-PBE0 calculations, we propose a mechanism for the decay of the excited dark state in pyrimidine, fully consistent with all the available experimental results. An effective conical intersection (CI-npi) exists between the spectroscopic pi/pi* excited state (Spi) and a dark n/pi* state (Sn), and a fraction of the population decays to the minimum of Sn (Sn-min). The conical intersection between Sn and the ground-state is not involved in the decay mechanism, because of its high energy gap with respect to Sn-min. On the other hand, especially in hydrogen bonding solvents, the energy gap between Sn-min and CI-npi is rather small. After thermalization in Sn-min, the system can thus recross CI-npi and then quickly proceed on the Spi barrierless path toward the conical intersection with the ground state.     

CASSCF/CASPT2 and TD-DFT study of valence and Rydberg electronic transitions in fluorene, carbazole, dibenzofuran, and dibenzothiophene

A combination of multireference CASSCF/CASPT2 and time-dependent DFT (TD-B3P86) theoretical treatments was employed to test their predictions against recently proposed assignments of the vacuum-UV spectra of fluorene and its three heteroanalogues-dibenzofuran, carbazole, and dibenzothiophene-up to the ionization threshold. For the low-lying transitions, the theoretically based assignments are generally not problematic because of the well-resolved bands, although, even in this region, the two methods yield some opposing predictions. Further on toward the vacuum region, the assignments prove increasingly challenging because of predicted crowding of transitions, many of which exhibit significant intensity. Some of the transitions in this region and beyond-toward the ionization thresholds-are thus necessarily assigned only tentatively. Overall, the two methods are frequently found to complement each other well, and equivalent transitions usually appear as bracketed from the high- (CASPT2) and low- (TD-B3P86) energy sides.