Description of excited states in [Re(Imidazole)(CO)3(Phen)]+ including solvent and spin‐orbit coupling effects: Density functional theory versus multiconfigurational wavefunction approach

The low‐lying electronic excited states of [Re(imidazole)(CO)₃(phen)]⁺ (phen = 1,10‐phenanthroline) ranging between 420 nm and 330 nm have been calculated by means of relativistic spin‐orbit time‐dependent density functional theory (TD‐DFT) and wavefunction approaches (state‐average‐CASSCF/CASPT2). A direct comparison between the theoretical absorption spectra obtained with different methods including SOC and solvent corrections for water points to the difficulties at describing on the same footing the bands generated by metal‐to‐ligand charge transfer (MLCT), intraligand (IL) transition, and ligand‐to‐Ligand‐ charge transfer (LLCT). While TD‐DFT and three‐roots‐state‐average CASSCF (10,10) reproduce rather well the lowest broad MLCT band observed in the experimental spectrum between 420 nm and 330 nm, more flexible wavefunctions enlarged either by the number of roots or by the number of active orbitals and electrons destabilize the MLCT states by introducing IL and LLCT character in the lowest part of the absorption spectrum. © 2016 Wiley Periodicals, Inc.     

Ionic bonding of lanthanides,as influenced by d‐ and f‐atomic orbitals,by core–shells and by relativity

Lanthanide trihalide molecules LnX₃ (X = F, Cl, Br, I) were quantum chemically investigated, in particular detail for Ln = Lu (lutetium). We applied density functional theory (DFT) at the nonrelativistic and scalar and SO‐coupled relativistic levels, and also the ab initio coupled cluster approach. The chemically active electron shells of the lanthanide atoms comprise the 5d and 6s (and 6p) valence atomic orbitals (AO) and also the filled inner 4f semivalence and outer 5p semicore shells. Four different frozen‐core approximations for Lu were compared: the (1s²–4d¹⁰) [Pd] medium core, the [Pd+5s²5p⁶ = Xe] and [Pd+4f¹⁴] large cores, and the [Pd+4f¹⁴+5s²5p⁶] very large core. The errors of Lu? X bonding are more serious on freezing the 5p⁶ shell than the 4f¹⁴ shell, more serious upon core‐freezing than on the effective‐core‐potential approximation. The Ln? X distances correlate linearly with the AO radii of the ionic outer shells, Ln³⁺‐5p⁶ and X^?‐np⁶, characteristic for dominantly ionic Ln³⁺‐X^? binding. The heavier halogen atoms also bind covalently with the Ln‐5d shell. Scalar relativistic effects contract and destabilize the Lu? X bonds, spin orbit coupling hardly affects the geometries but the bond energies, owing to SO effects in the free atoms. The relativistic changes of bond energy BE, bond length R_e, bond force k, and bond stretching frequency v_s do not follow the simple rules of Badger and Gordy (R_e～BE～k～v_s). The so‐called degeneracy‐driven covalence, meaning strong mixing of accidentally near‐degenerate, nearly nonoverlapping AOs without BE contribution is critically discussed. © 2015 Wiley Periodicals, Inc.     

Spin–Orbit Contributions in High‐Spin Nitrenes/Carbenes: A Hybrid CASSCF/MRMP2 Study of Zero‐Field Splitting Tensors

Zero‐field splitting (ZFS) tensors ( D tensors) of organic high‐spin oligonitrenes/oligocarbenes up to spin‐septet are quantitatively determined on the basis of quantum chemical calculations. The spin–orbit contributions, D ^SO tensors are calculated in terms of a hybrid CASSCF/MRMP2 approach, which was recently proposed by us. The spin–spin counterparts, D ^SS tensors are computed based on McWeeny–Mizuno’s equation in conjunction with the RODFT spin densities. The present calculations show that more than 10 % of ZFS arises from spin–orbit interactions in the high‐spin nitrenes under study. Contributions of spin‐bearing site–site interactions are estimated with the aid of a semi‐empirical model for the D tensors and found to be ca. 5 % of the D ^SO tensor. The analysis of intermediate states reveal that the largest contributions to the calculated D ^SO tensors are attributed to intra‐site spin flip excitations and delocalized π and π* orbitals play an important role in the inter‐site spin–orbit interactions.     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Zur Elektronenstruktur metallorganischer Komplexe der f‐Elemente. 67 Erstmalige parametrische Analyse des Absorptionsspektrums einer Molekülverbindung des CeIIIμ: Tris(η5‐tetramethylcyclopentadienyl)cer

Electronic Structures of Organometallic Complexes of f Elements. 67 First Parametric Analysis of the Absorption Spectrum of a Molecular Compound of Ce^IIIμ: Tris(η⁵‐tetramethylcyclopentadienyl)cerium(III) The absorption spectra (in the IR/NIR/Vis/UV range) of Ce(C₅Me₄H)₃ ( 1 ) and La(C₅Me₄H)₃ ( 2 ) were recorded at room and low temperatures. From the spectra obtained, two alternative closely related crystal field (CF) splitting patterns of 1 could be derived, and simulated by fitting the free parameters of a phenomenological Hamiltonian. The fact that the difference of the experimental energies of the barycenters of CF levels of the multiplets ²F_7/2 and ²F_5/2 is larger than in the gaseous free Ce³⁺ ion (“anti”‐relativistic nephelauxetic effect) could be explained by coupling effects of these multiplets via the CF, resulting in lower spin‐orbit coupling parameters than in the case of the gaseous free Ce³⁺ ion. The experimentally derived CF splitting pattern of 1 is compared with the predictions of previous non‐relativistic SW‐Xα and relativistic DV‐Xα calculations.     

A CAS study on S‐loss and O‐loss dissociation mechanisms of the SO2+ ion in the C,D, and E states

In the present work, we mainly study dissociation of the C ²B₁, D²A₁, and E²B₂ states of the SO₂⁺ ion using the complete active‐space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods. We first performed CASPT2 potential energy curve (PEC) calculations for S‐ and O‐loss dissociation from the X, A, B, C, D, and E primarily ionization states and many quartet states. For studying S‐loss predissociation of the C, D, and E states by the quartet states to the first, second, and third S‐loss dissociation limits, the CASSCF minimum energy crossing point (MECP) calculations for the doublet/quartet state pairs were performed, and then the CASPT2 energies and CASSCF spin‐orbit couplings were calculated at the MECPs. Our calculations predict eight S‐loss predissociation processes (via MECPs and transition states) for the C, D, and E states and the energetics for these processes are reported. This study indicates that the C and D states can adiabatically dissociate to the first O‐loss dissociation limit. Our calculations (PEC and MECP) predict a predissociation process for the E state to the first O‐loss limit. Our calculations also predict that the E²B₂ state could dissociate to the first S‐ and O‐loss limits via the A²B₂ ← E²B₂ transition. On the basis of the 13 predicted processes, we discussed the S‐ and O‐loss dissociation mechanisms of the C, D, and E states proposed in the previous experimental studies. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Quantum chemical topology at the spin–orbit configuration interaction level: Application to astatine compounds

We report a methodology that allows the investigation of the consequences of the spin–orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the “state-specific” natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin–orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = At F) and trihalide anions (IAtI⁻ , BrAtBr⁻ , and IAtBr⁻ ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin–orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin–orbit couplings.     

Ab initio quasirelativistic calculations on electronic transitions in ICl by the multireference many‐body perturbation theory

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state‐selective many‐electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second‐order many‐body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model‐space functions. One‐electron transition properties are evaluated via the perturbative construction of spin‐free transition density matrices. Illustrative calculations on the X0⁺ ? A1, B0⁺, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

State‐specific multireference perturbation theory with improved virtual orbitals: Taming the ground state of F2, Be2, and N2

Adaptation of improved virtual orbitals (IVOs) in state‐specific multireference perturbation theory using Møller–Plesset multipartitioning of the Hamiltonian (IVO‐SSMRPT) is examined in which the IVO‐complete active space configuration interaction (CASCI) is used as an inexpensive alternative to the more involved CAS‐self‐consistent field (CASSCF) orbitals. Unlike the CASSCF approach, IVO‐CASCI does not bear tedious and costly iterations beyond those in the initial SCF calculation. The IVO‐SSMRPT is intruder‐free, and explicitly size‐extensive. In the present preliminary study, the IVO‐SSMRPT method which relies on a small reference space is applied to study potential energy surfaces (PES) of the ground state of challenging, multiconfigurational F₂, Be₂, and N₂ molecules. These systems provide a serious challenge to any ab initio methodology due to the presence of an intricate interplay of nondynamical and dynamical correlations to the entire PES. The quality of the computed PES has been judged by extracting spectroscopic parameters and vibrational levels. The reported results illustrate that the IVO‐SSMRPT method has a potential to yield accuracies as good as the CASSCF‐SSMRPT one with reduced computational labor. Even with small reference spaces, our estimates demonstrate a good agreement with the available experimental values, and some benchmark computations. The blend of accuracy and low computational cost of IVO‐SSMRPT should deserve future attention for the accurate treatment of electronic states of small to large molecular systems for which the wavefunction is characterized by various configurations. © 2015 Wiley Periodicals, Inc.     

The effect of temperature on the stability of compounds used as UV‐MALDI‐MS matrix: 2,5‐dihydroxybenzoic acid, 2,4,6‐trihydroxyacetophenone, α‐cyano‐4‐hydroxycinnamic acid, 3,5‐dimethoxy‐4‐hydroxycinnamic acid,nor‐harmane and harmane

The thermal stability of several commonly used crystalline matrix‐assisted ultraviolet laser desorption/ionization mass spectrometry (UV‐MALDI‐MS) matrices, 2,5‐dihydroxybenzoic acid (gentisic acid; GA), 2,4,6‐trihydroxyacetophenone (THA), α‐cyano‐4‐hydroxycinnamic acid (CHC), 3,5‐dimethoxy‐4‐hydroxycinnamic acid (sinapinic acid; SA), 9H‐pirido[3,4‐b]indole (nor‐harmane; nor‐Ho), 1‐methyl‐9H‐pirido[3,4‐b]indole (harmane; Ho), perchlorate of nor‐harmanonium ([nor‐Ho + H]⁺) and perchlorate of harmanonium ([Ho + H]⁺) was studied by heating them at their melting point and characterizing the remaining material by using different MS techniques [electron ionization mass spectrometry (EI‐MS), ultraviolet laserdesorption/ionization‐time‐of‐flight‐mass spectrometry (UV‐LDI‐TOF‐MS) and electrospray ionization‐time‐of‐flight‐mass spectrometry (ESI‐TOF‐MS)] as well as by thin layer chromatography analysis (TLC), electronic spectroscopy (UV‐absorption, fluorescence emission and excitation spectroscopy) and ¹H nuclear magnetic resonance spectroscopy (¹H‐NMR). In general, all compounds, except for CHC and SA, remained unchanged after fusion. CHC showed loss of CO₂, yielding the trans‐/cis‐4‐hydroxyphenylacrilonitrile mixture. This mixture was unambiguously characterized by MS and ¹H‐NMR spectroscopy, and its sublimation capability was demonstrated. These results explain the well‐known cluster formation, fading (vanishing) and further recovering of CHC when used as a matrix in UV‐MALDI‐MS. Commercial SA (SA 98%; trans‐SA/cis‐SA 5 : 1) showed mainly cis‐ to‐trans thermal isomerization and, with very poor yield, loss of CO₂, yielding (3′,5′‐dimethoxy‐4′‐hydroxyphenyl)‐1‐ethene as the decarboxilated product. These thermal conversions would not drastically affect its behavior as a UV‐MALDI matrix as happens in the case of CHC. Complementary studies of the photochemical stability of these matrices in solid state were also conducted. Copyright © 2008 John Wiley & Sons, Ltd.     

One‐bond 29Si‐1H spin‐spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations,relativistic effects,and vibrational corrections

A number of most representative second order polarization propagator approach (SOPPA) based wavefunction methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), and density functional theory (DFT) based methods, B3LYP, PBE0, KT2, and KT3, have been benchmarked in the calculation of the one‐bond ²⁹Si‐¹H spin‐spin coupling constants in the series of halosilanes SiH_nX_4?n (X = F, Cl, Br, I), both at the non‐relativistic and full four‐parameter Dirac's relativistic levels taking into account vibrational corrections. At the non‐relativistic level, the wavefunction methods showed much better results as compared with those of DFT. At the DFT level, out of four tested functionals, the Perdew, Burke, and Ernzerhof's PBE0 showed best performance. Taking into account, relativistic effects and vibrational corrections noticeably improves wavefunction methods results, but generally worsens DFT results. Copyright © 2013 John Wiley & Sons, Ltd.     

Density functional and multiconfigurational ab initio study of the ground and excited states of Os2

Multiconfigurational ab initio methods predict that the ⁵Π_u state as the ground state instead of the ⁷Δ_u state. Although multiconfigurational perturbation theory correctly predicts the ground state, they overestimate the bond dissociation energy (BDE). Only multireference configuration interaction method can reasonably calculate the BDE. The spin‐orbit effect on the spectroscopic constants is not significant. The results calculated by density functional theory (DFT) vary significantly depending on the selection of a DFT functional. No DFT functional gives the same energy ordering as calculated by the second‐order multiconfigurational perturbation theory (CASPT2). The old generalized gradient approximations functionals are well suited for predicting the ground state and calculating the bond length and the vibrational frequency of Os₂. According to the CASPT2 calculation, the ground state of Os₂ has a quadruple bond. © 2014 Wiley Periodicals, Inc.     

The Role of Ligand‐Field States in the Ultrafast Photophysical Cycle of the Prototypical Iron(II) Spin‐Crossover Compound [Fe(ptz)6](BF4)2

Light‐induced excited spin‐state trapping (LIESST) in iron(II) spin‐crossover compounds, that is, the light‐induced population of the high‐spin (S=2) state below the thermal transition temperature, was discovered thirty years ago. For irradiation into metal–ligand charge transfer (MLCT) bands of the low‐spin (S=0) species the acknowledged sequence takes the system from the initially excited ¹MLCT to the high‐spin state via the ³MLCT state within ca. 150 fs, thereby bypassing low‐lying ligand‐field (LF) states. Nevertheless, these play a role, as borne out by the observation of LIESST and reverse‐LIESST on irradiation directly into the LF bands for systems with only high‐energy MLCT states. Herein we elucidate the ultrafast reverse‐LIESST pathway by identifying the lowest energy S=1 LF state as an intermediate state with a lifetime of 39 ps for the light‐induced high‐spin to low‐spin conversion on irradiation into the spin‐allowed LF transition of the high‐spin species in the NIR.     

Relativistic and electron‐correlation effects on magnetizabilities investigated by the Douglas‐Kroll‐Hess method and the second‐order Møller‐Plesset perturbation theory

Isotropic and anisotropic magnetizabilities for noble gas atoms and a series of singlet and triplet molecules were calculated using the second‐order Douglas‐Kroll‐Hess (DKH2) Hamiltonian containing the vector potential A and in part using second‐order generalized unrestricted Møller‐Plesset (GUMP2) theory. The DKH2 Hamiltonian was resolved into three parts (spin‐free terms, spin‐dependent terms, and magnetic perturbation terms), and the magnetizabilities were decomposed into diamagnetic and paramagnetic terms to investigate the relativistic and electron‐correlation effects in detail. For Ne, Kr, and Xe, the calculated magnetizabilities approached the experimental values, once relativistic and electron‐correlation effects were included. For the IF molecule, the magnetizability was strongly affected by the spin‐orbit interaction, and the total relativistic contribution amounted to 22%. For group 17, 16, 15, and 14 hydrides, the calculated relativistic effects were small (less than 3%), and trends were observed in relativistic and electron‐correlation effects across groups and periods. The magnetizability anisotropies of triplet molecules were generally larger than those of similar singlet molecules. The so‐called relativistic‐correlation interference for the magnetizabilities computed using the relativistic GUMP2 method can be neglected for the molecules evaluated, with exception of triplet SbH. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

GRECP/MRD‐CI calculations of spin‐orbit splitting in ground state of Tl and of spectroscopic properties of TlH

The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single‐ and double‐excitation configuration interaction (MRD‐CI) method to calculate the spin‐orbit splitting in the ²P^o ground state of the Tl atom and spectroscopic constants for the 0⁺ ground state of TlH. The 21‐electron GRECP for Tl is used, and the outer core 5s and 5p pseudospinors are frozen with the help of the level shift technique. The spin‐orbit selection scheme with respect to relativistic multireference states and the corresponding code are developed and applied in the calculations. In this procedure both correlation and spin‐orbit interactions are taken into account. A [4,4,4,3,2] basis set is optimized for the Tl atom and employed in the TlH calculations. Very good agreement is found for the equilibrium distance, vibrational frequency, and dissociation energy of the TlH ground state (R_e=1.870 Å, ω_e=1420 cm⁻¹, D_e=2.049 eV) as compared with the experimental data (R_e=1.872 Å, ω_e=1391 cm⁻¹, D_e=2.06 eV). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 409–421, 2001     

Relativistic effects in the one‐bond spin–spin coupling constants involving selenium

One‐bond spin–spin coupling constants involving selenium of seven different types, ¹ J(Se,X), X = ¹H, ¹³C, ¹⁵ N, ¹⁹ F, ²⁹Si, ³¹P, and ⁷⁷Se, were calculated in the series of 14 representative compounds at the SOPPA(CCSD) level taking into account relativistic corrections evaluated both at the RPA and DFT levels of theory in comparison with experiment. Relativistic corrections were found to play a major role in the calculation of ¹ J(Se,X) reaching as much as almost 170% of the total value of ¹ J(Se,Se) and up to 60–70% for the rest of ¹ J(Se,X). Scalar relativistic effects (Darwin and mass‐velocity corrections) by far dominate over spin–orbit coupling in the total relativistic effects for all ¹ J(Se,X). Taking into account relativistic corrections at both random phase approximation and density functional theory levels essentially improves the agreement of theoretical results with experiment. The most ‘relativistic’ ¹ J(Se,Se) demonstrates a marked Karplus‐type dihedral angle dependence with respect to the mutual orientation of the selenium lone pairs providing a powerful tool for stereochemical analysis of selenoorganic compounds. Copyright © 2014 John Wiley & Sons, Ltd.     

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin‐orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree–Fock (CAHF) algorithm for the determination of 4f quasi‐atomic active orbitals common to all multi‐electron spin manifolds contributing to the ground spin‐orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi‐Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem‐specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state–of–the–art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres , represents a more time‐efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non‐perturbative spin‐orbit coupling effects. © 2017 Wiley Periodicals, Inc.     

Thermo‐ and Acid‐Responsive Photochromic Spironaphthoxazine‐Containing Organogelators

A series of photochromic spironaphthoxazine derivatives has been designed, synthesized, and characterized by using ¹H NMR spectroscopy, FAB mass spectrometry, and elemental analysis. Their photophysical and photochromic behavior have been investigated. Two of the compounds (G¹²‐en‐SA‐SO and G¹⁶‐en‐SA‐SO) have been shown to be capable of forming stable thermoreversible organogels in organic solvents, tested by the “stable‐to‐inversion of a test tube” method. Addition of p‐toluenesulfonic acid was found to induce the formation of stable organogels at concentrations below that of the critical gelation concentration (c.g.c.), with a concomitant change in color from colorless to purple. Transmission electron microscopy and scanning electron microscopy of the xerogels showed typical fibrous structures in the micrometer scale. The activation parameters for the bleaching reaction of G⁸‐en‐SA‐SO in the solution state and G¹⁶‐en‐SA‐SO in the gel state have been determined in ethanol through kinetic studies at various temperatures. The results showed that the rate of the bleaching reaction in the gel state was much slower than that in the solution state.