Ab initio computations of spin-orbit interactions in polyatomic molecules. Splitting of sulfur LII,III states and singlet–triplet transitions in SO2

Spin-orbit interactions among the ground and the first few excited electronic states of SO₂, are computed with ab initio molecular wave functions and Gaussian atomic orbitals. All spin-other orbits contributions to the matrix elements are included. The computed intensity of the first singlet–triplet transition is found to be in broad agreement with experiment and sensitive to an extension of the configuration interaction expansion of molecular wave functions. Also, the splitting of sulfur L_{II ,III} states in SO₂ is derived as an example of large spin-orbit interactions among electronic states.     

Hartree–Fock instabilities and electronic properties

Hartree–Fock instabilities are investigated for about 80 compounds, from acetylene to mivazerol (27 atoms) and a cluster of 18 water molecules, within a double ζ basis set. For most conjugated systems, the restricted Hartree–Fock wave function of the singlet fundamental state presents an external or so‐called triplet instability. This behavior is studied in relation with the electronic correlation, the vicinity of the triplet and singlet excited states, the electronic delocalization linked with resonance, the nature of eventual heteroatoms, and the size of the systems. The case of antiaromatic systems is different, because they may present a very large internal Hartree–Fock instability. Furthermore, the violation of Hund's rule, observed for these compounds, is put in relation with the fact that the high symmetry structure in its singlet state has no feature of a diradical‐like species. It appears that the triplet Hartree–Fock instability is directly related with the spin properties of nonnull orbital angular momentum electronic systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 483–504, 2000     

The modified all-valence INDO method with the inclusion of spin–orbit coupling

The all-valence INDO method has been modified for the inclusion of spin–orbit coupling effects. In the method presented, the Hamiltonian includes spin–orbit coupling and the basis set constitutes the singlet and triplet determinental wave functions constructed from molecular orbitals resulting from nonrelativistic calculations. Eigenvectors obtained are later used for the evaluation of transition probabilities among different states. The results presented include lifetimes of different states of organic molecules and transition energies for halogen molecules and they are in a good agreement with experimental results. © 1992 John Wiley & Sons, Inc.     

Spin-state dependent radical stabilization in nitrenes: the unusually small singlet-triplet splitting in 2-furanylnitrene

Geometries and energies of the triplet and singlet states of 2-furanylnitrene and 3-furanylnitrene have been calculated by using spin-flip coupled-cluster methods. Calculations with triple-ζ basis sets predict a singlet-triplet splitting of 10.9 kcal/mol for 2-furanylnitrene, 4.5 kcal/mol smaller than that in phenylnitrene. In contrast, the singlet-triplet splitting in 3-furanylnitrene is computed to be 1.9 kcal/mol larger than that in phenylnitrene. The differences in the singlet-triplet splittings for the furanylnitrenes are attributed to the differences in the radical stabilizing abilities of the 2-furanyl- and 3-furanyl-groups compared to a phenyl ring. Comparison of the singlet-triplet splittings of more than 20 substituted aromatic nitrenes and the radical stabilizing ability of the aromatic systems reveals a high degree of correlation between the singlet-triplet splitting and the radical stabilizing ability, indicating that singlet states of aromatic nitrenes are preferentially stabilized by radical stabilizing substituents. The preferential stabilization of the singlet states is attributed to the decrease in electron pair repulsion resulting from increased delocalization of the radical electron.     

Observation of a Thermally Accessible Triplet State Resulting from Rotation around a Main‐Group π Bond

We report the first direct spectroscopic observation by electron paramagnetic resonance (EPR) spectroscopy of a triplet diradical that is formed in a thermally induced rotation around a main‐group π bond, that is, the Si?Si double bond of tetrakis(di‐tert‐butylmethylsilyl)disilene ( 1 ). The highly twisted ground‐state geometry of singlet 1 allows access to the perpendicular triplet diradical 2 at moderate temperatures of 350–410 K. DFT‐calculated zero‐field splitting (ZFS) parameters of 2 accurately reproduce the experimentally observed half‐field transition. Experiment and theory suggest a thermal equilibrium between 1 and 2 with a very low singlet–triplet energy gap of only 7.3 kcal mol^?1.     

Spin–orbit coupling in the intersystem crossing of the ring-opened oxirane biradical

The intersystem crossing (ISC ) between the lowest triplet and singlet states occurring in the reaction of atomic oxygen with ethylene was studied. The importance of spin–orbit coupling (SOC ) in oxirane biradicals (?R′R″—CRR*—?) is stressed through calculations where the spin–orbit matrix elements over the full Breit–Pauli SOC operator has been obtained in the singlet–triplet crossing region. The calculations are performed with a multiconfigurational linear response approach, in which the spin–orbit couplings are obtained from triplet response functions using differently correlated singlet-reference-state wave functions. Computational results confirm earlier semiempirical predictions of the spin–orbit coupling as an important mechanism behind the ring opening of oxiranes and addition of oxygen O(³P) atoms to alkenes. © 1995 John Wiley & Sons, Inc.     

Extension of EWMO model to particle-hole excitations

Examination of the random phase approximation in relation to the energy weighted maximum overlap model suggests a way of accounting for singlet–triplet splittings in particle–hole spectra. Calculations for the first row hydride molecules are used to illustrate applications.     

A DFT study of the ground state multiplicities of linear vs angular polyheteroacenes

Unrestricted density functional calculations in combination with the broken-symmetry approach and spin-projection methods have been employed to study a series of formally 4n pi antiaromatic linear and angular polyheteroacenes. Calculations show that the linear polyheteroacene molecules have either stable singlet zwitterionic 6-9 or singlet diradical 5 ground states because they sacrifice the aromaticity of the central arene to form two independent cyanines. The corresponding angular compounds 10-14 have robust triplet states, since they cannot create independent cyanines to escape their overall antiaromaticity. An analysis based on the SOMO-SOMO energy splittings, their spatial distributions, and the spin density populations for the triplet states is presented to clarify the factors that determine their ground state multiplicities.     

Ab initio calculation of the NH(3sigma-)-NH(3sigma-) interaction potentials in the quintet, triplet, and singlet states

We present the ab initio potential-energy surfaces of the NH-NH complex that correlate with two NH molecules in their 3sigma- electronic ground state. Three distinct potential-energy surfaces, split by exchange interactions, correspond to the coupling of the S(A) = 1 and S(B) = 1 electronic spins of the monomers to dimer states with S = 0, 1, and 2. Exploratory calculations on the quintet (S = 2), triplet (S = 1), and singlet (S = 0) states and their exchange splittings were performed with the valence bond self-consistent-field method that explicitly accounts for the nonorthogonality of the orbitals on different monomers. The potential surface of the quintet state, which can be described by a single Slater determinant reference function, was calculated at the coupled cluster level with single and double excitations and noniterative treatment of the triples. The triplet and singlet states require multiconfiguration reference wave functions and the exchange splittings between the three potential surfaces were calculated with the complete active space self-consistent-field method supplemented with perturbative configuration interaction calculations of second and third orders. Full potential-energy surfaces were computed as a function of the four intermolecular Jacobi coordinates, with an aug-cc-pVTZ basis on the N and H atoms and bond functions at the midpoint of the intermolecular vector R. An analytical representation of these potentials was given by expanding their dependence on the molecular orientations in coupled spherical harmonics, and representing the dependence of the expansion coefficients on the intermolecular distance R by the reproducing kernel Hilbert space method. The quintet surface has a van der Waals minimum of depth D(e) = 675 cm(-1) at R(e) = 6.6a0 for a linear geometry with the two NH electric dipoles aligned. The singlet and triplet surfaces show similar, slightly deeper, van der Waals wells, but when R is decreased the weakly bound NH dimer with S = 0 and S = 1 converts into the chemically bound N2H2 diimide (also called diazene) molecule with only a small energy barrier to overcome.     

Electronic structure of the metabolites of cyclophosphamide

Some physical and chemical properties of the metabolites of the cancerostat cyclophosphamide (trade name: ENDOXAN) have been calculated with an appropriately prepared CNDO/S-CI method. The ground state properties (e.g., charge densities and free valences) do not indicate a significant change, compared with the results of cyclophosphamide, and the same fact is also true for the energy levels of the two lowest excited singlet and triplet states. With respect to the dipole transition moments only the metabolite N-mustard-diamido-phosphoric acid (Friedman acid) differs drastically from cyclophosphamide and the other metabolites. The chemical reactivity has been considered under the aspect of singlet–triplet transitions between quasidegenerate singlet and triplet states. Again Friedman acid behaves quite differently from the other compounds, and only this metabolite exhibits the remarkable ability to act as an alkylating agent via splitting off chloride ions.     

Ultrafast Decay of the Excited Singlet States of Thioxanthone by Internal Conversion and Intersystem Crossing

The experimental ultrafast photophysics of thioxanthone in several aprotic organic solvents at room temperature is presented, measured using femtosecond transient absorption together with high‐level ab initio CASPT2 calculations of the singlet‐ and triplet‐state manifolds in the gas phase, including computed state minima and conical intersections, transition energies, oscillator strengths, and spin–orbit coupling terms. The initially populated singlet ππ* state is shown to decay through internal conversion and intersystem crossing processes via intermediate nπ* singlet and triplet states, respectively. Two easily accessible conical intersections explain the favorable internal conversion rates and low fluorescence quantum yields in nonpolar media. The presence of a singlet–triplet crossing near the singlet ππ* minimum and the large spin–orbit coupling terms also rationalize the high intersystem crossing rates. A phenomenological kinetic scheme is proposed that accounts for the decrease in internal conversion and intersystem crossing (i.e. the very large experimental crescendo of the fluorescence quantum yield) with the increase of solvent polarity.     

Calculated photoelectron spectra of singlet and triplet methylene

Vertical ionization potentials for singlet and triplet methylene are calculated by a CI perturbation method based on ab initio SCF molecular orbitals (6–31 G^** basis). The shape and vibrational fine structure of the first photoelectron band are investigated using the MINDO/3 method. The computed singlet-triplet splitting for methylene is 16.4 kcal/mol, in reasonable agreement with the experimental value of 19.5 kcal/mol.     

Kramers' restricted hartree—fock method for polyatomic molecules using ab initio relativistic effective core potentials with spin—orbit operators

A two-component Kramers' restricted Hartree–Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin–orbit operators at the Hartree–Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin–orbit interactions at the HF level. KRHF calculations have been performed for the HX, X₂, XY(X, Y = I, Br), and CH₃I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin–orbit interactions.     

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.     

Ground-state and some excited states of Li2 by the half-projected Hartree–Fock method

The half-projected Hartree–Fock wave function (HPHF ) is one of simplest models for introducing some electronic correlation effects. In this model, the wave function is built up with only two Slater determinants. This simple form suggests its application for the direct determination of singlet excited states. On the other hand, because the HPHF model does not mix singlet and triplet states with M_s = 0, it can be used for determining independently singlet and triplet states without any mutual contamination. In the present work, we applied this model to determine nine electronic states of the lithium molecule; one of them exhibits even the same symmetry of the fundamental one. For this purpose, the 6-311G (d) basis was used. Potential energy curves were determined and some spectroscopic constants derived. The numerical results were compared with the available experimental data, as well as with other theoretical values. © 1995 John Wiley & Sons, Inc.     

A diabatic representation including both valence nonadiabatic interactions and spin-orbit effects for reaction dynamics

A diabatic representation is convenient in the study of electronically nonadiabatic chemical reactions because the diabatic energies and couplings are smooth functions of the nuclear coordinates and the couplings are scalar quantities. A method called the fourfold way was devised in our group to generate diabatic representations for spin-free electronic states. One drawback of diabatic states computed from the spin-free Hamiltonian, called a valence diabatic representation, for systems in which spin-orbit coupling cannot be ignored is that the couplings between the states are not zero in asymptotic regions, leading to difficulties in the calculation of reaction probabilities and other properties by semiclassical dynamics methods. Here we report an extension of the fourfold way to construct diabatic representations suitable for spin-coupled systems. In this article we formulate the method for the case of even-electron systems that yield pairs of fragments with doublet spin multiplicity. For this type of system, we introduce the further simplification of calculating the triplet diabatic energies in terms of the singlet diabatic energies via Slater's rules and assuming constant ratios of Coulomb to exchange integrals. Furthermore, the valence diabatic couplings in the triplet manifold are taken equal to the singlet ones. An important feature of the method is the introduction of scaling functions, as they allow one to deal with multibond reactions without having to include high-energy diabatic states. The global transformation matrix to the new diabatic representation, called the spin-valence diabatic representation, is constructed as the product of channel-specific transformation matrices, each one taken as the product of an asymptotic transformation matrix and a scaling function that depends on ratios of the spin-orbit splitting and the valence splittings. Thus the underlying basis functions are recoupled into suitable diabatic basis functions in a manner that provides a multibond generalization of the switch between Hund's cases in diatomic spectroscopy. The spin-orbit matrix elements in this representation are taken equal to their atomic values times a scaling function that depends on the internuclear distances. The spin-valence diabatic potential energy matrix is suitable for semiclassical dynamics simulations. Diagonalization of this matrix produces the spin-coupled adiabatic energies. For the sake of illustration, diabatic potential energy matrices are constructed along bond-fission coordinates for the HBr and the BrCH(2)Cl molecules. Comparison of the spin-coupled adiabatic energies obtained from the spin-valence diabatics with those obtained by ab initio calculations with geometry-dependent spin-orbit matrix elements shows that the new method is sufficiently accurate for practical purposes. The method formulated here should be most useful for systems with a large number of atoms, especially heavy atoms, and/or a large number of spin-coupled electronic states.     

Singlet-triplet splitting of divalent five-membered fused rings C<Subscript>12</Subscript>H<Subscript>8</Subscript>M (M = C,Si, Ge,Sn, and Pb): Application in nanocomplex synthesis

Energy differences, ΔX _s−t (X = E, H, and G) (ΔX _s−t = X(singlet) − X(triplet)) between singlet (s) and triplet (t) states of C₁₂H₈M were calculated at B3LYP/6-311+G*. The DFT calculations indicated that the ΔG _s−t between singlet (s) and triplet (t) states of C₁₂H₈M were increased from M = C to M = Pb. The ΔG _s−t of C₁₂H₈M was compared with its analogue C₄H₄M through replacement of heavy atoms from M = C to M = Pb. Configurations of the electrons in orbitals (σ² or π²) for the singlet state of C₁₂H₈M were discussed.     

Relativistic molecular orbital theory of zero-field splittings in triplets

A method of calculating matrix elements of 1/r₁₂ in a basis of Dirac scattered-wave (DSW) orbitals is outlined. In the limit c → ∞, this method reduces to that described by Cook and Karplus for non-relativistic orbitals. For triplet states that can be described by a single configuration with two unpaired electrons, the relativistic exchange integrals give not only the singlet—triplet splittings (as in non-relativistic theory), but also the spin—orbit contributions to the triplet zero-field splittings. Results are reported for the ³ (n → π*) excited state of γ-thiopyrone (4H-pyran-4-thione), which has a very large value of D (calc. ?31 cm^?1, exp. ?24 to ?28 cm^?1).     

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 studies of tetrafluoroethylene and tetratrifluoromethylethylene molecules in the ground and “twisted” states

Ab initio calculations with full optimization of geometry have been carried out with the 6–31 G^* basis set on tetrafluoroethylene (with the unrestricted Hartree-Fock method—UHF and the second-order Moller-Plesset perturbation theory—MP2) and tetratrifluoromethylethylene (with UHF) molecules in the singlet ground and triplet biradical states. The symmetry of the tetrafluoroethylene molecule in the triplet biradical state was demonstrated to differ from that of ethylene (D _2d ) due to the deviation of fluorine atoms from CCFF plane. The MP2 optimized geometries of ethylene and tetrafluoroethylene were used for higher level calculations (MP3, MP4, CCSD). The energy of the ground state singlet-biradical triplet splitting decreases in the series: ethylene>tetrafluoroethylene> tetratrifluoromethylethylene. These data on energy splitting explain the increase in reactivity toward the [2+2]-cycloaddition on going from ethylene to tetrafluoroethylene. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 605–607, April, 1998.