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.     

Density functional theory study of 1,2‐dioxetanone decomposition in condensed phase

The decomposition of 1,2‐dioxetanone into a CO₂ molecule and into an excited state formaldehyde molecule was studied in condensed phase, using a density functional theory approach. Singlet and triplet ground and excited states were all included in the calculations. The calculations revealed a novel mechanism for the chemiluminescence of this compound. The triplet excitation can be explained by two intersystem crossings (ISCs) with the ground state, while the singlet excitation can be accounted by an ISC with the triplet state. The experimentally verified small excitation yield can then be explained by the presence of an energy barrier present in the potential energy surface of the triplet excited state, which will govern both triplet and singlet excitation. It was also found that the triplet ground state interacts with both the triplet excited and singlet ground states. A MPWB1K/mPWKCIS approach provided results in agreement with the existent literature. © 2012 Wiley Periodicals, Inc.     

Is tetramethyleneethane a ground state triplet?

We have examined a number of possible ways by which tetramethyleneethane (TME) can be a ground state triplet, as claimed by experimental studies, in violation of Ovchinnikov’s theorem for alternant hydrocarbons of equal bond lengths. Model exact π calculations of the low-lying states of TME, 3,4-dimethylenefuran and 3,4-dimethylenepyrrole were carried out using a diagrammatic valence bond approach. The calculations failed to yield a triplet ground state even after (a) tuning of electron correlation, (b) breaking alternancy symmetry, and (c) allowing for geometric distortions. In contrast to earlier studies of fine structure constants in other conjugated systems, the computedD andE values of all the low-lying triplet states of TME for various geometries are at least an order of magnitude different from the experimentally reported values. Incorporation of σ-π mixing by means of UHF MNDO calculations is found to favour a singlet ground state even further. A reinterpretation of the experimental results of TME is therefore suggested to resolve the conflict.     

Photophysical Properties of Benzoylgermane and para‐Substituted Derivatives: Substituent Effects on Electronic Transitions

In the present study, a selection of basic substitution patterns on benzoyl(trimethyl)germane was investigated using time‐dependent density‐functional theory (TDDFT) to explore the influence on the stability and on the relative order of the lowest excited electronic states. The theoretical results are in agreement with absorption and fluorescence measurements. We show that electron‐withdrawing groups decrease the energetic level of the lowest singlet and triplet state relative to the electron‐pushing systems resulting in red‐shifted radiative transitions (fluorescence). In the first triplet state electron‐withdrawing groups lead to an increased dissociation barrier and a close approach with the singlet ground state before the transition state in the triplet state is reached, favoring radiationless ground‐state recovery. The results are also in good agreement with empirical concepts of organic chemistry, therefore providing simple rules for synthetic strategies towards tuning the excited‐state properties of benzoylgermanes.     

Multireference perturbation theory with improved virtual orbitals for radicals: More degeneracies,more problems

IVO-SSMRPT is an affordable and accurate type of state-specific multireference perturbation (SSMRPT) theory that adds dynamic correlation energy to improved virtual orbital (IVO) complete active space configuration interaction (CASCI) wave functions using a single-root parametrization of multi-root Hilbert-space ansatz. We applied it to many chemically important di- and tri-radicals to analyze the geometries and electronic properties of spectroscopic interest for both closed- and open-shell singlet- and nonsinglet ground as well as excited states. We observed that IVO-SSMRPT identifies optimized geometries, splitting between multiplets and frequencies for several radicals that are similar to those displayed by current generation state-of-the-art methods but with admiringly decreased computational effort. This study illustrates the importance of having an accurate treatment of both nondynamical and dynamical correlation effects when examining multiradical species. Chemically and spectroscopically relevant answers can be obtained using our computationally tractable method. Our method will be a serviceable avenue for portraying open-shell interactions in other radicals.     

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.     

In Search of Singlet Phosphinidenes

We have examined singlet-triplet energy separations in different phosphinidenes (RP) substituted by first- and second-row elements, making use of ab initio molecular orbital theory. Our main purpose is to find out the substituents that particularly favor the singlet electronic state. The QCISD(T)/6-311++G(3df,2p) + ZPE level has been applied to small molecules and the CISD(Q) and QCISD(T) with the 6-311G(d,p) basis set for all species considered. We have identified few factors that come into play rendering the singlet phosphinidene more stable than the triplet. The parent phosphinidene, PH, has a triplet ground state lying 28 kcal/mol below the closed-shell singlet excited state. The triplet ground state is mainly favored when negative hyperconjugation is involved. In the boryl-, alkyl-, and silyl-substituted phosphinidenes, the triplet state remains by far the ground state. When the substituents have pi-type lone pair electrons (i.e., -NX(2), -PX(2), -OX, -SX), the singlet state becomes stabilized by such an amount that both states have similar energies or even a change in ground state occurs. The most stabilized singlet ground states are attributed to PSF and PSCl. P and S have similar p-orbital sizes, making pi-delocalization easier. Implantation of alkyl and/or amino groups in the beta-position of amino- and phosphinophosphinidenes also contributes to a singlet stabilization. Bulky beta-groups also destabilize the triplet state by a steric effect. From a practical viewpoint, amino (P-NR(2)) and phosphino (P-PR(2)) derivatives bearing large alkyl groups (R) are the most plausible and feasible targets for preparing phosphinidenes possessing a closed-shell singlet ground state.     

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.     

Stabilization Studies on Divalent Five‐Membered Rings C4H4C,C4H4Si,C4H4Ge,C4H4Sn,and C4H4Pb

Energy differences, ΔX_S‐t (X = E, H and G) (ΔX_S‐t = X_(singlet)‐X_(triplet)) between singlet (s) and triplet (t) states are calculated at B3LYP/6‐311++G (3df,2p). The DFT calculations show that the triplet state of C₄H₄C is a ground state with planar conformer respect to its corresponding nonplanar singlet state. Both singlet and triplet states of C₄H₄M (M = Si, Ge, Sn and Pb) have a planar conformer with the singlet ground state. Four isodesmic reactions are presented for determining the stability energies, SE. NICS calculations are carried out for C₄H₄M to determine the aromatic character.     

Theoretical investigation of excited states of C(3)

In this work, we present ab initio calculations for the potential energy surfaces of C(3) in different electronic configurations, including the singlet ground state [X (1)Sigma(g) (+),((1)A(1))], the triplet ground state [a (3)Pi(u),((3)B(1), (3)A(1))], and some higher excited states. The geometries studied include triangular shapes with two identical bond lengths, but different bond angles between them. For the singlet and triplet ground states in the linear geometry, the total energies resulting from the mixed density functional--Hartree-Fock and quadratic configuration interaction methods reproduce the experimental values, i.e., the triplet occurs 2.1 eV above the singlet. In the geometry of an equilateral triangle, we find a low-lying triplet state with an energy of only 0.8 eV above the energy of the singlet in the linear configuration, so that the triangular geometry yields the lowest excited state of C(3). For the higher excited states up to about 8 eV above the ground state, we apply time-dependent density functional theory. Even though the systematic error produced by this approach is of the order of 0.4 eV, the results give different prospective to insight into the potential energy landscape for higher excitation energies.     

Theoretical Studies on Reaction Mechanism of CH3SO with NO

The potential energy surface （PES） of CH3SO radical with NO reaction has been studied at MP2/6-311G（2df, p） and QCISD/6-311G（2df, p） levels. Geometries of the reactants, transition states （TS） and products were optimized at B3LYP/6-311G （d,p） level. The geometries of the transition states were found for the first time. The calculated results show that the reaction can proceed via singlet-state or triplet-state PES. Because of the high energy barrier of triplet surface, the singlet surface reactions are dominant. The topological analysis of electron density shows that there are two kinds of structaral transition states （the bifurcation-type ring structure transition state and the T-shaped conflict structure transition state） in the titled reaction. The total electronic density of the reactants, TS and products and the spin electronic density on the triplet surface were also discussed in this paper.     

Singlet excitation energies of thiophene derivatives of fluorene: TD‐DFT study

Fluorene‐thiophene (FT)‐based oligomers and polymers and their derivatives are good candidates for organic blue light‐emitting diodes. In this work, the intrinsic properties of the ground and excited states of FT monomer and its derivatives are studied. The ground‐state optimized structures and energies are obtained using molecular orbital theory and density functional theory (DFT). The ground‐state potential energy curves or surfaces of FT and its derivatives are also obtained. All derivatives are nonplanar in their electronic ground states. The character and energy of the first 20 singlet–singlet electronic transitions are investigated by applying the time‐dependent density functional theory (TD‐DFT) approximations to the correspondingly optimized ground‐state geometries. The lowest singlet state is studied with the configuration interaction (singles) approach (CIS). Excitation energies are red shifted when the FT unit or its derivatives are extended longitudinally. CIS results suggest geometry relaxation in the first singlet excited state. When available, a comparison is made with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Quinoidal Oligothiophenes: Towards Biradical Ground‐State Species

A family of quinoidal oligothiophenes, from the dimer to the hexamer, with fused bis(butoxymethyl)cyclopentane groups has been extensively investigated by means of electronic and vibrational spectroscopy, electrochemical measurements, and density functional calculations. The latter predict that the electronic ground state always corresponds to a singlet state and that, for the longest oligomers, this state has biradical character that increases with increasing oligomer length. The shortest oligomers display closed‐shell quinoidal structures. Calculations also predict the existence of very low energy excited triplet states that can be populated at room temperature. Aromatization of the conjugated carbon backbone is the driving force that determines the increasing biradical character of the ground state and the appearance of low‐lying triplet states. UV/Vis, Raman, IR, and electrochemical experiments support the aromatic biradical structures predicted for the ground state of the longest oligomers and reveal that population of the low‐lying triplet state accounts for the magnetic activity displayed by these compounds.     

Ab initio calculation of the lowest singlet and triplet states in CH2, CHF,CF2, and CHCH3

The lowest singlet and triplet states of the radicals CH₂, CHF, CF₂, and CHCH₃ have been investigated both in SCF and IEPA approximation (“independent electron pair approach” to account for electron correlation). The SCF calculations yield triplet ground states for CH₂, CHF, and CHCH₃, and a singlet ground state for CF₂. Electron correlation stabilizes the singlet state by about 14 kcal/mole with respect to the triplet for all four radicals leading to a singlet ground state also for CHF. The final triplet-singlet energy separations are 10, 6, ?11, ?47 kcal/mole for CH₂, CHCH₃, CHF, CF₂, respectively. Values for equilibrium bond angles, ionization potentials and bond energies are also given.     

Involvement of excited triplet state in the photodissociation of cyclobutane

The potential energy curves (PECs) of the ground state and the low‐lying excited states for the photodissociation of cyclobutane have been calculated at the multi‐reference configuration interaction with singlet and doublet excitation (MRCISD) and the multi‐reference second order perturbation theory (MRPT2). Firstly, the PECs are constructed following a reaction path determined by semiclassical dynamics simulation, which suggests that the lowest triplet state of tetramethylene is involved in the photodissociation of cyclobutane. Then, the adiabatic PECs are calculated for the breaking processes of C1? C3 and C2? C4 bond respectively. The singlet‐triplet PECs' intersections have been found in the two breaking C? C bond processes. During the breaking process of the second C2? C4 bond, a local minimum has been found on the PEC of the lowest triplet state, which gives us some insight to reinterpret the experimental observed diradical intermediate as being trapped in its triplet state. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The electronic structure of oxo-Mn(salen): single-reference and multireference approaches

Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.     

Geometries,vibrational frequencies,and excitation energies of a series of fluorine‐substituted carbenes,FCX (X = H,F, Cl,Br, and I): A high‐level multireference configuration interaction study

High‐level calculations using internally contracted multireference configuration interaction including Davidson correction (icMRCI+Q) method have been carried out for the ground singlet states, the first excited states, and the lowest triplet states of a series of fluorine‐substituted carbenes FCX (X = H, F, Cl, Br, and I). Equilibrium geometries and vibrational frequencies of the three electronic states, adiabatic transition energy of the first excited singlet state, as well as the ground singlet—lowest triplet energy gap (S‐T gap) of each of FCX carbenes have been obtained. Effects of the basis set of icMRCI+Q calculation on the geometries and energies have been investigated. In addition, various corrections, including the scalar relativistic effect, spin‐orbit coupling, and core‐valence correlation, have been studied in calculating the transition energies and the S‐T gaps, especially for heavy‐atom carbenes. This results have been compared with previous calculations using a variety of methods. Our icMRCI+Q results are in very good agreement with the high‐resolution laser‐based spectroscopic results where available. Some structure and spectroscopic constants of the fluorine‐substituted carbenes which are void in the literature have been provided with consistent high‐level calculations. © 2013 Wiley Periodicals, Inc.     

The Antiferromagnetic Spin Coupling in Non‐Kekulé Acenes—Impressive Polyradical Character Revealed by High‐Level Multireference Methods

Complete active space (CASSCF) and multireference (MR‐CISD(Q) and MR‐AQCC) calculations were performed for non‐Kekulé analogues of acenes, dimethylenepolycyclobutadienes, with lengths of up to eight cyclobutadiene (CBD) units. Multireference calculations predict that the most stable energy state of the system is either triplet (if there is an odd number of CBD units) or singlet (if there is an even number of CBD units) due to antiferromagnetic spin coupling, which thus violates Hund's rule in larger molecules. We also show an impressive polyradical character in the system that increases with the size of the molecule, as witnessed by more than eleven unpaired electrons in the singlet state of the molecule with eight CBD units. Together with the small energy gap between singlet and higher multiplicity energy states even above the triplet state, this demonstrates the exceptional polyradical properties of these π‐conjugated oligomeric chains.     

Intramolecular photoexcitation dynamics and magnetic field effects in an intermediate-case molecule

Molecular vibration and rotation play a significant role in the intramolecular photoexcitation dynamics of the so-called intermediate-case molecule, and the fluorescence intensity, decay and polarization of s-triazine vapor are shown to depend on the excited rovibronic level of the S₁ state. Fluorescence characteristics are interpreted by assuming three zero-order states: (1) a zero-order singlet state that carries the absorption intensity and emits fluorescence with sharp structure; (2) zero-order singlet states that do not carry the absorption intensity but emit broad fluorescence; and (3) zero-order triplet states. The interaction among these states depends not only on the vibrational level but also on the rotational level excited. It is suggested that the number of triplet states coupled to the singlet state increases with increasing excess vibrational energy. It is also suggested that K-scrambling occurs both in the triplet manifold following intersystem crossing (ISC) and in the singlet manifold following intramolecular vibrational energy redistribution (IVR). The fluorescence intensity and decay of s-triazine vapor are significantly influenced by a magnetic field, and the field effects are interpreted in terms of the spin decoupling in the triplet manifold following ISC; the role of external magnetic fields is to mix the spin sublevels of different rovibronic levels coupled to the excited singlet state. Magnetic depolarization of fluorescence also occurs because of the efficient interaction between the excited singlet state and the triplet state.