Is the choice of a standard zeroth‐order hamiltonian in CASPT2 ansatz optimal in calculations of excitation energies in protonated and unprotonated schiff bases of retinal?

To account for systematic error of CASPT2 method empirical modification of the zeroth‐order Hamiltonian with Ionization Potential‐Electron Affinity (IPEA) shift was introduced. The optimized IPEA value (0.25 a.u.), called standard IPEA (S‐IPEA), was recommended but due to its unsatisfactory performance in multiple metallic and organic compounds it has been questioned lately as a general parameter working properly for all molecules under CASPT2 study. As we are interested in Schiff bases of retinal, an important question emerging from this conflict of choice, to use or not to use S‐IPEA, is whether the introduction of the modified zeroth‐order Hamiltonian into CASPT2 ansatz does really improve their energetics. To achieve this goal, we assessed an impact of the IPEA shift value, in a range of 0–0.35 a.u., on vertical excitation energies to low‐lying singlet states of two protonated (RPSBs) and two unprotonated (RSBs) Schiff bases of retinal for which experimental data in gas phase are available. In addition, an effect of geometry, basis set, and active space on computed VEEs is also reported. We find, that for these systems, the choice of S‐IPEA significantly overestimates both S₀→S₁ and S₀→S₂ energies and the best theoretical estimate, in reference to the experimental data, is provided with either unmodified zeroth‐order Hamiltonian or small value of the IPEA shift in a range of 0.05–0.15 a.u., depending on active space and basis set size, equilibrium geometry, and character of the excited state. © 2018 Wiley Periodicals, Inc.     

Molecular parameters of tetraatomic carbonyls X2CO and XYCO (X,Y = H,F, Cl) in the ground and lowest excited electronic states,part 1: A test of ab initio methods

Geometrical parameters of tetraatomic carbonyl molecules X₂CO and XYCO (X, Y = H, F, Cl) in the ground (S₀) and lowest excited singlet (S₁) and triplet (T₁) electronic states as well as values of barriers to inversion in S₁ and T₁ states and S₁ ← S₀ and T₁ ← S₀ adiabatic transition energies were systematically investigated by means of various quantum‐chemical techniques. The following methods were tested: HF, MP2, CIS, CISD, CCSD, EOM‐CCSD, CCSD(T), CR‐EOM‐CCSD(T), CASSCF, MR‐MP2, CASPT2, CASPT3, NEVPT2, MR‐CISD, and MR‐AQCC within cc‐pVTZ and cc‐pVQZ basis sets. The accuracy of quantum‐chemical methods was estimated in comparison with experimental data and rather accurate structures of excited electronic states were obtained. MP2 and CASPT2 methods appeared to be the most efficient and CCSD(T), CR‐EOM‐CCSD(T), and MR‐AQCC the most accurate. It was found that at equilibrium all the molecules under study are nonplanar in S₁ and T₁ electronic states with CO out‐of‐plane angle ranging from 34° (H₂CO, S₁) to 52° (F₂CO, T₁), and height of barrier to inversion varying from 300 (H₂CO, S₁) to 11,000 (F₂CO, T₁) cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The Low‐Lying Excited States of 2,2′‐Bithiophene: A Theoretical Analysis

The low‐energy regions of the singlet→singlet, singlet→triplet, and triplet→triplet electronic spectra of 2,2′‐bithiophene are studied using multiconfigurational second‐order perturbation theory (CASPT2) and extended atomic natural orbitals (ANO) basis sets. The computed vertical, adiabatic, and emission transition energies are in agreement with the available experimental data. The two lowest singlet excited states, 1¹B_u and 2¹B_u, are computed to be degenerate, a novel feature of the system to be borne in mind during the rationalization of its photophysics. As regards the observed high triplet quantum yield of the molecule, it is concluded that the triplet states 2³A_g and 2³B_u, separated about 0.4 eV from the two lowest singlet excited states, can be populated by intersystem crossing from nonplanar singlet states.     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

Phenyloxenium ions: more like phenylnitrenium ions than isoelectronic phenylnitrenes?

The geometries and energies of the electronic states of phenyloxenium ion 1 (Ph-O(+)) were computed at the multireference CASPT2/pVTZ level of theory. Despite being isoelectronic to phenylnitrene 4, the phenyloxenium ion 1 has remarkably different energetic orderings of its electronic states. The closed-shell singlet configuration ((1)A(1)) is the ground state of the phenyloxenium ion 1, with a computed adiabatic energy gap of 22.1 kcal/mol to the lowest-energy triplet state ((3)A(2)). Open-shell singlet configurations ((1)A(2), (1)B(1), (1)B(2), 2(1)A(1)) are significantly higher in energy (>30 kcal/mol) than the closed-shell singlet configuration. These values suggest a revision to the current assignments of the ultraviolet photoelectron spectroscopy bands for the phenoxy radical to generate the phenyloxenium ion 1. For para-substituted phenyloxenium ions, the adiabatic singlet-triplet energy gap (ΔE(ST)) is found to have a positive linear free energy relationship with the Hammett-like σ(+)(R)/σ(+) substituent parameters; for meta substituents, the relationship is nonlinear and negatively correlated. CASPT2 analyses of the excited states of p-aminophenyloxenium ion 5 and p-cyanophenyloxenium ion 10 indicate that the relative orderings of the electronic states remain largely unperturbed for these para substitutions. In contrast, meta-donor-substituted phenyloxenium ions have low-energy open-shell states (open-shell singlet, triplet) due to stabilization of a π,π* diradical state by the donor substituent. However, all of the other phenyloxenium ions and larger aryloxenium ions (naphthyl, anthryl) included in this study have closed-shell singlet ground states. Consequently, ground-state reactions of phenyloxenium ions are anticipated to be more closely related to closed-shell singlet arylnitrenium ions (Ar-NH(+)) than their isoelectronic arylnitrene (Ar-N) counterparts.     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

An application of second-order n-electron valence state perturbation theory to the calculation of excited states

n–electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory where all the zero-order wave functions are of multireference nature, being generated as eigenfunctions of a two–electron model Hamiltonian. The absence of intruder states makes NEVPT an interesting choice for the calculation of electronically excited states. Test calculations have been performed on several valence and Rydberg transitions for the formaldehyde and acetone molecules; the results are in good accordance with the best calculations and with the existing experimental data.Contribution to the Jacopo Tomasi Honorary Issue     

Photodeactivation paths in norbornadiene

The first high level ab initio quantum‐chemical calculations of potential energy surfaces (PESs) for low‐lying singlet excited states of norbornadiene in the gas phase are presented. The optimization of the stationary points (minima and conical intersections) and the recalculation of the energies were performed using the multireference configuration interaction with singles (MR‐CIS) and the multiconfigurational second‐order perturbation (CASPT2) methods, respectively. It was shown that the crossing between valence V₂ and Rydberg R₁ states close to the Franck–Condon (FC) point permits an easy population switch between these states. Also, a new deactivation path in which the doubly excited state with (π₃)² configuration (DE) has a prominent role in photodeactivation from the R₁ state due to the R₁/DE and the DE/V₁ conical intersections very close to the R₁ and DE minima, respectively, was proposed. Subsequent deactivation from the V₁ to the ground state goes through an Olivucci–Robb‐type conical intersection that adopts a rhombic distorted geometry. The deactivation path has negligible barriers, thereby making ultrafast radiationless decay to the ground state possible. © 2013 Wiley Periodicals, Inc.     

Ab initio calculations on urea

Multiconfiguration wave functions constructed from contracted Gaussian-lobe functions have been found for the ground and valence-excited states of urea. ICSCF molecular orbitals of the excited states were used as the parent configurations for the CI calculations except for the ¹A₁(π → π*) state. The ¹A₁(π → π*) state used as its parent configuration an orthogonal linear combination of natural orbitals obtained from the second root of a three-configuration SCF calculation. The lowest excited states are predicted to be the n π → π* and π → π* triplet states. The lowest singlet state is predicted to be the n π → π* state with an energy in good agreement with the one known UV band at 7.2 eV. The π → π* singlet state is predicted to be about 1.9 eV higher, contrary to several previous assignments which assumed the lowest band was a π → π* amide resonance band. The predicted ionization energy of 9.0 eV makes this and higher states autoionizing.     

A multireference perturbation theory study on the vertical electronic spectrum of thiophene

The vertical electronic spectrum of the thiophene molecule is investigated by means of second and third order multireference perturbation theory (NEVPT). Single-state and quasi-degenerate NEVPT calculations of more than 25 singlet excited states have been performed. The study is addressed to the theoretical characterization of the four lowest-energy valence states, as well as the 3s, 3p and 3d Rydberg states. In addition, the excitation energies of two and valence states are also reported. For almost all the excited states, coupled cluster calculations (CCSD and CCSDR(3)) have been also carried out, using the same geometry and basis set used for the NEVPT ones, in order to make the comparison between the results of the two methods meaningful. A remarkable accordance between the NEVPT and CC excitation energies is found. The present results, over all, confirm the experimental assignments but, above all, represent an important contribution to the assignments of some low-energy states, valence and Rydberg, for which a firm interpretation is not available in the literature.     

Exploring the Photodeactivation Pathways of Pt[O^N^C^N] Complexes: A Theoretical Perspective

In this article, the influence of the tert‐butyl unit on the photodeactivation pathways of Pt[O^N^C^N] (O^N^C^N=2‐(4‐(3,5‐di‐tert‐butylphenyl)‐6‐(3‐(pyridin‐2‐l)phenyl) pyridin‐2‐yl)phenolate) is investigated by DFT/TDDFT calculations. To further explore the factors that determine the radiative processes, the transition dipole moments of the singlet excited states, spin–orbit coupling (SOC) matrix elements, and energy gaps between the lowest triplet excited states and singlet excited states are calculated. As demonstrated by the results, compared with Pt‐3 , Pt‐1 and Pt‐2 have larger SOC matrix elements between the lowest triplet excited states and singlet excited states, an indicator that they have faster radiative decay processes. In addition, the SOC matrix elements between the lowest triplet excited states and ground states are also computed to elucidate the temperature‐independent non‐radiative decay processes. Moreover, the temperature‐dependent non‐radiative decay mechanisms are also explored via the potential energy profiles.     

Electronic structure of benzaldehyde: A comparative study of the lowest excited singlet π* ← π and π* ← n states

VE-PPP, CNDO/2, and CNDO/s-CI methods have been used to investigate the electronic spectrum and structure of benzaldehyde. Electronic charge distributions and bond orders in the ground and lowest excited singlet π* ← π and π* ← n states of the molecule have been studied. The molecule has been shown to be nonplanar in the lowest π* ← n excited singlet state, in agreement with the conclusions drawn from the study of vibrational spectra. Dipole moments in both excited states have been shown to be larger than the ground-state value. Thus, the ambiguity in the experimental result for the π* ← π n excited singlet state dipole moment has been resolved. It has been shown that the n orbital is mainly localized on the CHO group. Furthermore, charge distributions, dipole moments, and molecular geometries are shown to be very different in the excited singlet π* ← π and π* ← n states.     

Multiconfigurational perturbation theory (CASPT2) applied to the study of the low-lying singlet and triplet excited states of cyclopropene

The electronic spectrum of cyclopropene has been studied using multiconfigurational second-order perturbation theory (CASPT2) with extended ANO-type basis sets. The calculation comprises two valence states and the 3s, 3p, 3d members of the Rydberg series converging to the π and σ ionization limits. A total of twenty singlet and twenty triplet excited states have been analyzed. The results confirm the valence nature of the lowest energy singlet-singlet band and yield a conclusive assignment: the first dipole-allowed transition in cyclcopropene is due to absorption to a (σ → π*) state. The (π → π*) (V) state is interleaved among a number of Rydberg states in the most intense band of the system. The remaining spectral bands are due to Rydberg transitions of higher energy. The two lowest singlet-triplet transitions involve the same valence states. The results are in agreement with available experimental data and provide a number of new assignments of the experimental spectra.     

Electronic spectra of nitroethylene

A systematic study of the electronic excited states of nitroethylene (C₂H₃NO₂) was carried out using the approximate coupled‐cluster singles‐and‐doubles approach with the resolution of the identity (RI‐CC2), the time dependent density functional theory with the CAMB3LYP functional (TDDFT/CAMB3LYP) and the DFT multireference configuration interaction (DFT/MRCI) method. Vertical transition energies and optical oscillator strengths were computed for a maximum of 20 singlet transitions. Semiclassical simulations of the ultraviolet (UV) spectra were performed at the RI‐CC2 and DFT/MRCI levels. The main features in the UV spectrum were assigned to a weak n‐π* transition, and two higher energy π_CC+O‐π* bands. These characteristics are common to molecules containing NO₂ groups. Simulated spectra are in good agreement with the experimental spectrum. The energy of the bands in the DFT/MRCI simulation agrees quite well with the experiment, although it overestimates the band intensities. RI‐CC2 produced intensities comparable to the experiment, but the bands were blue shifted. A strong π_CC+O‐π* band, not previously measured, was found in the 8–9 eV range. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin–orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the 2|H_so|S₁>, 1|H_so|S₁>, and 1|H_so|S₀> spin–orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S₁→T₁ population transfer is found to proceed at a rate of ≈10⁷ s⁻¹ in the isolated molecule.     

On the zeroth‐order hamiltonian for CASPT2 calculations of spin crossover compounds

Complete active space self‐consistent field theory (CASSCF) calculations and subsequent second‐order perturbation theory treatment (CASPT2) are discussed in the evaluation of the spin‐states energy difference (ΔH_elec) of a series of seven spin crossover (SCO) compounds. The reference values have been extracted from a combination of experimental measurements and DFT + U calculations, as discussed in a recent article (Vela et al., Phys Chem Chem Phys 2015, 17, 16306). It is definitely proven that the critical IPEA parameter used in CASPT2 calculations of ΔH_elec, a key parameter in the design of SCO compounds, should be modified with respect to its default value of 0.25 a.u. and increased up to 0.50 a.u. The satisfactory agreement observed previously in the literature might result from an error cancellation originated in the default IPEA, which overestimates the stability of the HS state, and the erroneous atomic orbital basis set contraction of carbon atoms, which stabilizes the LS states. © 2015 Wiley Periodicals, Inc.     

Initial excited‐state relaxation of locked retinal protonated schiff base chromophore. An insight from coupled cluster and multireference perturbation theory calculations

The initial S₁ excited‐state relaxation of retinal protonated Schiff base (RPSB) analog with central C11C12 double bond locked by eight‐membered ring (locked‐11.8) was investigated by means of multireference perturbation theory methods (XMCQDPT2, XMS‐CASPT2, MS‐CASPT2) as well as single‐reference coupled‐cluster CC2 method. The analysis of XMCQDPT2‐based geometries reveals rather weak coupling between in‐plane and out‐of‐plane structural evolution and minor energetical relaxation of three locked‐11.8 conformers. Therefore, a strong coupling between bonds length inversion and backbone out‐of‐plane deformation resulting in a very steep S₁ energy profile predicted by CASSCF/CASPT2 calculations is in clear contradiction with the reference XMCQDPT2 results. Even though CC2 method predicts good quality ground‐state structures, the excited‐state structures display more advanced torsional deformation leading to ca. 0.2 eV exaggerated energy relaxation and significantly red shifted (0.4–0.7 eV) emission maxima. According to our findings, the initial photoisomerization process in locked‐11.8, and possibly in other RPSB analogs, studied fully (both geometries and energies) by multireference perturbation theory may be somewhat slower than predicted by CASSCF/CASPT2 or CC2 methods. © 2018 Wiley Periodicals, Inc.     

Ab initio n-electron valence state perturbation theory study of the adiabatic transitions in carbonyl molecules: formaldehyde, acetaldehyde, and acetone

The application of the recently developed second-order n-electron valence state perturbation theory (NEVPT2) to small carbonyl molecules (formaldehyde, acetaldehyde, and acetone) is presented. The adiabatic transition energies are computed for the singlet and triplet n-->pi(*), pi-->pi(*), and sigma-->pi(*) states performing a full geometry optimization of the relevant states at the single state CASSCF level and taking into account the zero point energy correction in the harmonic approximation. The agreement with the known experimental values and with previously published high level calculations confirms that NEVPT2 is an efficient tool to be used for the interpretation of molecular electronic spectra. Moreover, different insight into the nature of the excited states has been obtained. Some of the transitions presented here have never been theoretically computed previously [(3)(pi-->pi(*)) and (3)(sigma-->pi(*)) adiabatic transitions in acetaldehyde and acetone] or have been studied only using moderate level (single reference based) ab initio methods (all adiabatic transitions in acetaldehyde). In the present work a consistent disagreement between NEVPT2 and experiment has been found for the (3)(pi-->pi(*)) adiabatic transition in all molecules: this result is attributed to the low intensity of the transition to the first vibrational levels of the excited state. The n-->pi(*) singlet and triplet vertical transition energies are also reported for all the molecules.     

N‐Alkoxyheterocycles As Irreversible Photooxidants

Irreversible photooxidation based on N–O bond fragmentation is demonstrated for N‐methoxyheterocycles in both the singlet and triplet excited state manifolds. The energetic requirements for bond fragmentation are studied in detail. Bond fragmentation in the excited singlet manifold is possible for ππ* singlet states with energies significantly larger than the N–O bond dissociation energy of ca 55 kcal mol^?1. For the nπ* triplet states, N–O bond fragmentation does not occur in the excited state for orbital overlap and energetic reasons. Irreversible photooxidation occurs in the singlet states by bond fragmentation followed by electron transfer. Irreversible photooxidation occurs in the triplet states via bimolecular electron transfer to the donor followed by bond fragmentation. Using these two sensitization schemes, donors can be irreversibly oxidized with oxidation potentials ranging from ca 1.6–2.2 V vs SCE. The corresponding N‐ethylheterocycles are characterized as conventional reversible photooxidants in their triplet states. The utility of these sensitizers is demonstrated by irreversibly generating the guanosine radical cation in buffered aqueous solution.