The diatropic sigma ring currents of [pi2s + pi2s + pi2s] pericyclic transition states

Ab initio current-density maps for the (4n + 2)-electron transition states of two thermally allowed [pi2s + pi2s + pi2s] trimerisations, of ethyne to benzene (1), and of ethene to cyclohexane (2), show that both support sigma diatropic ring currents, dominated by four-electron sigma --> sigma* virtual excitation of HOMO electrons.     

Relevance of pi sigma* states in the photoinduced processes of adenine, adenine dimer, and adenine-water complexes

Ab initio calculations and time-resolved photoionization spectroscopy were carried out to characterize the role of the lowest two pi sigma* excited states for the photoinduced processes in the adenine monomer, adenine dimer, and adenine-water clusters. The calculations show--with respect to the monomer--a stabilization of 0.11-0.14 eV for the pi sigma* states in different isomers of adenine dimer and an even bigger stabilization of 0.14-0.36 eV for isomers of adenine-(H2O)1 and adenine-(H2O)3. Hence, the stabilized pi sigma* states should play an important role in the excited-state relaxation of partially or fully solvated adenine. This conclusion is supported by experimental results: In the adenine monomer, strong n pi* state signals are observed. Those signals are reduced in adenine dimer and vanish in water clusters due to the competing relaxation via the pi sigma* states.     

Separation of sigma and pi energies

This work presents an all-electron density functional theory implementation of the separation of sigma and pi energies. On the basis of the separation of the electronic density, rho, into sigma and pi parts, an ansatz for the separation of the exchange-correlation energy is proposed. The behavior of the sigma and pi energy parts in benzene is investigated under different distortions. The effect of local and nonlocal functionals on the separation of the exchange-correlation energy is studied, too.     

Noncovalent interactions between cytosine and SWCNT: curvature dependence of complexes via pi...pi stacking and cooperative CH...pi/NH...pi

Fragments of C24H12, adapted from a variety of armchair [(n,n), (n = 5, 7, and 8)] and zigzag [(m,0) (m = 8, 10, and 12)] single-walled carbon nanotube (SWCNT), are used to model corresponding SWCNTs with different diameters and electronic structures. The parallel binding mainly through pi...pi stacking interaction, as well as the perpendicular binding via cooperative NH...pi and CH...pi between cytosine and the fragments of SWCNT have been extensively investigated with a GGA type of DFT, PW91LYP/6-311++G(d,p). The eclipsed tangential (ET) conformation with respect to the six-membered ring of cytosine and the central ring of SWCNT fragments is less stable than the slipped tangential (ST) conformation for the given fragment; perpendicular conformations with NH2 and CH ends have higher negative binding energy than those with NH and CH ends. At PW91LYP/6-311++G(d,p) level, two tangential complexes are less bound than perpendicular complexes. However, as electron correlation is treated with MP2/6-311G(d,p) for PW91LYP/6-311++G(d,p) optimized complexes, it turns out there is an opposite trend that two tangential complexes become more stable than three perpendicular complexes. This result implies that electron correlation, a primary source to dispersion energy, has more significant contributions to the pi...pi stacking complexes than to the complexes via cooperative NH...pi and CH...pi interactions. In addition, it was found for the first time that binding energies for two tangential complexes become more negative with increasing nanotube diameter, while those for three perpendicular complexes have a weaker dependence on the curvature; i.e., binding energies are slightly less and less negative. The performance of a novel hybrid DFT, MPWB1K, was also discussed.     

Photophysics of aromatic molecules with low-lying pi sigma* states: fluorinated benzenes

Unlike fluorinated benzenes with four or less fluorine atoms, pentafluorobenzene (PFB) and hexafluorobenzene (HFB) exhibit very small fluorescence yields and short fluorescence lifetimes. These emission anomalies suggest that the nature of the first excited singlet (S(1)) state may be different for the two classes of fluorobenzenes. Consistent with this conjecture, the time-dependent density-functional theory calculations yield S(1) state of pi pi(*) character for fluorinated benzenes with four or less F atoms, and S(1) state of pi sigma(*) character for PFB and HFB. The pi sigma(*) character of the S(1) state of PFB and HFB has been confirmed by laser-induced fluorescence, which reveal the presence of a new electronic transition to the red of the (1)pi pi(*) (L(b))<--S(0) transition, which can be identified with the predicted low-energy (1)pi sigma(*)<--S(0) absorption. The low fluorescence yields and the short fluorescence lifetimes of PFB and HFB are consistent with the small radiative decay rate of the (1)pi sigma(*) state and efficient S(1) (pi sigma(*))-->S(0) internal conversion between two electronic states of very different geometries.     

Time-dependent quantum wave-packet description of the 1pi sigma* photochemistry of phenol

The photoinduced hydrogen elimination reaction in phenol via the conical intersections of the dissociative 1pi sigma* state with the 1pi pi* state and the electronic ground state has been investigated by time-dependent quantum wave-packet calculations. A model including three intersecting electronic potential-energy surfaces (S0, 1pi sigma*, and 1pi pi*) and two nuclear degrees of freedom (OH stretching and OH torsion) has been constructed on the basis of accurate ab initio multireference electronic-structure data. The electronic population transfer processes at the conical intersections, the branching ratio between the two dissociation channels, and their dependence on the initial vibrational levels have been investigated by photoexciting phenol from different vibrational levels of its ground electronic state. The nonadiabatic transitions between the excited states and the ground state occur on a time scale of a few tens of femtoseconds if the 1pi pi*-1pi sigma* conical intersection is directly accessible, which requires the excitation of at least one quantum of the OH stretching mode in the 1pi pi* state. It is shown that the node structure, which is imposed on the nuclear wave packet by the initial preparation as well as by the transition through the first conical intersection (1pi pi*-1pi sigma*), has a profound effect on the nonadiabatic dynamics at the second conical intersection (1pi sigma*-S0). These findings suggest that laser control of the photodissociation of phenol via IR mode-specific excitation of vibrational levels in the electronic ground state should be possible.     

Dynamics of the 1 3 pi g state of K2 on helium nanodroplets

Fluorescence following optical excitation of the 1 3 sigma u+ state of K2 prepared on helium nanodroplets to the predissociative 1 3 pi g state yields molecular emission from both the (B)1 1 pi u and (A)1 1 sigma u+ K2 states as well as atomic emission from the expected 4 2P3/2, 1/2-->4 2S1/2 dissociation channel. A approximately 12 cm-1 red shift is observed in the molecular emission excitation spectrum compared to the atomic emission excitation spectrum. Time-correlated photon counting measurements demonstrate the rise time for both atomic and molecular products to be < 80 ps, independent of vibrational level excited. This lifetime is interpreted as the total depopulation time for the optically excited 1 3 pi g state, which is dominated by intersystem crossing at low vibrational energy and by predissociation at the highest vibrational level. It is deduced that the timescale for intersystem crossing must be of the order of 10 ps. Symmetry restrictions for the isolated K2 imply that the intersystem crossing from the 1 3 pi g state to the (B)1 1 pi u and (A)1 1 sigma u+ states must be induced by interaction with the helium nanodroplet.     

A computational study on pi and sigma modes of metal ion binding to heteroaromatics (CH)(5-m)X(m) and (CH)(6-m)X(m) (X = N and P): contrasting preferences between nitrogen- and phosphorous-substituted rings

The pi and sigma complexation energy of various heteroaromatic systems which include mono-, di-, and trisubstituted azoles, phospholes, azines and phosphinines with various metal ions, viz. Li(+), Na(+), K(+), Mg(2+), and Ca(2+), was calculated at the post Hartree-Fock MP2 level, MP2(FULL)/6-311+G(2d,2p)//MP2/6-31G. The azoles and azines were found to form stronger sigma complexes than the corresponding pi complexes, whereas the phospholes and phosphinines had higher pi complexation energy with Li(+), Mg(2+), and Ca(2+) while their pi and sigma complexation energies were very comparable with Na(+) and K(+). The strongest pi complex among the five-membered heteroaromatic system was that of pyrrole with all the metals except with Mg(2+), while benzene formed the strongest pi complex among the six-membered heterocyclic systems. The nitrogen heterocyclic system 4H-[1,2,4] triazole and pyridazine formed the strongest sigma complex among the five- and six-membered heteroaromatic systems considered. The complexation energy of the pi and sigma complexes of the azoles and azines was found to decrease with the increase in the heteroatom substitution in the ring, while that of phospholes and phosphinines did not vary significantly. The azoles and azines preferred to form sigma complexes wherein the metal had bidentate linkage, while the phospholes and phosphinines did not show binding mode preference. In the sigma complexes of both azoles and phospholes, the metal binds away form the electron-deficient nitrogen or phosphorus center.     

The role of pi sigma* state in intramolecular electron-transfer dynamics of 4-dimethylaminobenzonitrile and related molecules

Evidence is presented which indicates that the photoinduced intramolecular charge transfer (ICT) in 4-dimethylaminobenzonitrile proceeds by a new mechanism in which pi sigma(C triple bond N) (*) state is the intermediate of a consecutive process that takes the initially excited pi pi(*) state to the fully charge-separated ICT state. The absence of the ICT-state formation in 4-aminobenzonitrile is attributed to the smaller electron-donor strength of the amino group relative to the dimethylamino group, which hinders the pi sigma(*)-->ICT charge-shift reaction.     

Radiative lifetimes for the B1sigma(u)+ and C1pi states of the H2 molecule

With RKR electronic potentials for the B1sigma(u)+, C1pi(u) and X1sigma(u)+ states in conjunction with Huffaker's correction and appropriate asymptotic functions, the unperturbed radiative lifetimes of rovibrational levels of the B1sigma(u)+ and C1pi(u) states of H2 are calculated. Comparison with previous calculations is presented. Better lifetimes for B1sigma(u)+ are obtained in present work.     

Photophysics of aromatic molecules with low-lying pi sigma* states: excitation-energy dependence of fluorescence in jet-cooled aromatic nitriles

Excitation-energy dependence of fluorescence intensity and fluorescence lifetime has been measured for 4-dimethylaminobenzonitrile (DMABN), 4-aminobenzonitrile (ABN), 4-diisopropylaminobenzonitrile (DIABN), and 1-naphthonitrile (NN) in a supersonic free jet. In all cases, the fluorescence yield decreases rather dramatically, whereas the fluorescence lifetime decreases only moderately for S1 (pi pi*, L(b)) excess vibrational energy exceeding about 1000 cm(-1). This is confirmed by comparison of the normalized fluorescence excitation spectrum with the absorption spectrum of the compound in the vapor phase. The result indicates that the strong decrease in the relative fluorescence yield at higher energies is due mostly to a decrease in the radiative decay rate of the emitting state. Comparison of the experimental results with the TDDFT potential energy curves for excited states strongly suggests that the decrease in the radiative decay rate of the aminobenzonitriles at higher energies is due to the crossing of the pi pi* singlet state by the lower-lying pi sigma*(C[triple bond]N) singlet state of very small radiative decay rate. The threshold energy for the fluorescence "break-off" is in good agreement with the computed energy barrier for the pi pi*/pi sigma* crossing. For NN, on the other hand, the observed decrease is in fluorescence yield at higher excitation energies can best be attributed to the crossing of the pi pi* singlet state by the pi sigma* triplet state.     

Manifestation of stereoelectronic effects on the calculated carbon-hydrogen bond lengths and one-bond 1J(C-H) NMR coupling constants. Relative acceptor ability of the carbonyl (C=O), thiocarbonyl (C=S), and methylidene (C=CH2) groups toward C-H donor bonds

Theoretical examination [B3LYP/6-31G(d,p), PP/IGLO-III//B3LYP/6-31G(d,p), and NBO methods] of six-membered cyclohexane 1 and carbonyl-, thiocarbonyl-, or methylidene-containing derivatives 2-27 afforded precise structural (in particular, C-H bond distances) and spectroscopic (specifically, one-bond (1)J(C)(-)(H) NMR coupling constants) data that show the consequences of stereoelectronic hyperconjugative effects in these systems. Major observations include the following. (1) sigma(C)(-)(H)(ax)() -->(C)(=)(Y) and pi(C)(=)(Y) --> sigma(C)(-)(H)(ax)() (Y = O, S, or CH(2)) hyperconjugation leads to a shortening (strengthening) of the equatorial C-H bonds adjacent to the pi group. This effect is reflected in smaller (1)J(C)(-)(H)(ax)() coupling constants relative to (1)J(C)(-)(H)(eq)(). (2) Comparison of the structural and spectroscopic consequences of sigma(C)(-)(H)(ax)() --> pi(C)(=)(Y) hyperconjugation in cyclohexanone 2, thiocyclohexanone 3, and methylenecyclohexane 4 suggests a relative order of acceptor orbital ability C=S > C=O > C=CH(2), which is in line with available pK(a) data. (3) Analysis of the structural and spectroscopic data gathered for heterocyclic derivatives 5-12 reveals some additivity of sigma(C)(-)(H)(ax)() --> pi(C)(=)(Y), pi(C)(=)(Y) --> sigma(C)(-)(H)(ax)(), n(X) --> sigma(C)(-)(H)(ax)(), n(beta)(O) --> sigma(C)(-)(H)(eq)(), and sigma(S)(-)(C) --> sigma(C)(-)(H)(eq)() stereoelectronic effects that is, nevertheless, attenuated by saturation effects. (4) Modulation of the C=Y acceptor character of the exocyclic pigroup by conjugation with alpha-heteroatoms O, N, and S in lactones, lactams, and methylidenic analogues 13-24 results in decreased sigma(C)(-)(H)(ax)() --> pi(C)(=)(Y) and pi(C)(=)(Y) --> sigma(C)(-)(H)(ax)() hyperconjugation. (5) Additivity of sigma(C)(-)(H)(ax)() --> pi(C)(=)(Y) and pi(C)(=)(Y) --> sigma(C)(-)(H)(ax)() hyperconjugative effects is also apparent in 1,3-dicarbonyl derivative 25 (C=Y equal to C=O), 1,3-dithiocarbonyl derivative 26 (C=Y equal to C=S), and 1,3-dimethylidenic analogue 27 (C=Y equal to C=CH(2)).     

The different photoisomerization efficiency of azobenzene in the lowest n pi* and pi pi* singlets: the role of a phantom state

Azobenzene E<==>Z photoisomerization, following excitation to the bright S(pi pi*) state, is investigated by means of ab initio CASSCF optimizations and perturbative CASPT2 corrections. Specifically, by elucidating the S(pi pi*) deactivation paths, we explain the mechanism responsible for azobenzene photoisomerization, the lower isomerization quantum yields observed for the S(pi pi*) excitation than for the S1(n pi*) excitation in the isolated molecule, and the recovery of the Kasha rule observed in sterically hindered azobenzenes. We find that a doubly excited state is a photoreaction intermediate that plays a very important role in the decay of the bright S(pi pi*). We show that this doubly excited state, which is immediately populated by molecules excited to S(pi pi*), drives the photoisomerization along the torsion path and also induces a fast internal conversion to the S1(n pi*) at a variety of geometries, thus shaping (all the most important features of) the S(pi pi*) decay pathway and photoreactivity. We reach this conclusion by determining the critical structures, the minimum energy paths originating on the bright S(pi pi*) state and on other relevant excited states including S1(n pi*), and by characterizing the conical intersection seams that are important in deciding the photochemical outcome. The model is consistent with the most recent time-resolved spectroscopic and photochemical data.     

Sigma and pi contributions to the induced magnetic field: indicators for the mobility of electrons in molecules

The authors discuss the role of the sigma and pi contributions to the induced magnetic field for simple hydrocarbons containing a double or a triple bond, as well as for benzene and cyclobutadiene. While the magnetic field induced by the sigma electrons is short-ranged, the pi system is responsible for the formation of long-range cones. These cones influence the chemical shift of atoms by additional shielding (for aromatic) or deshielding (for antiaromatic molecules) contributions. While the hydrogen atoms of benzene are found to lie within the deshielded region of the magnetic field induced by the pi electrons, they are shielded by the total induced magnetic field. The induced magnetic field of the pi electrons support Pople's model on the basis of first-principles calculations.     

pi bonding in second and third row molecules: testing the strength of Linus's blanket

The flexibility of valence bond (VB) theory provides a new method of calculating pi-bond energies in the double-bonded species H(m)A=BH(n), where A, B = C, N, O, Si, P, S. This new method circumvents the problems usually associated with obtaining pi-bond strengths by targeting only the pi bond, while all other factors remain constant. In this manner, a clean separation between sigma- and pi effects can be achieved which highlights some expected trends in bond strength upon moving from left to right and up and down the Periodic Table. Intra-row pi bonds conform to the classic statement by Pauling [L. Pauling, The Natiure of the Chemical Bond, Cornell University Press, Ithaca, 1960, 3rd edition] regarding the relationship of heteronuclear bond strengths to their homonuclear constituents whereas inter-row pi bonds do not. This variance with Pauling's statement is shown to be due to the constraining effect of the underlying sigma bonds which prevents optimal p(pi)-p(pi) overlap. While Pauling's statement was based on the assumption that the resonance energy (RE) would be large for heteronuclear and small for homonuclear bonds, we have found large REs for all bonds studied herein; this leads to the conclusion that REs are dependent not only on the electronegativity difference but also the electronegativity sum of the constituent atoms. This situation where the bond is neither covalent nor ionic but originates in the covalent-ionic mixing has been termed charge shift (CS) bonding [S. Shaik, P. Maitre, G. Sini, P. C. Hiberty, J. Am. Chem. Soc. 1992, 114, 7861]. We have shown that CS bonding extends beyond single sigma bonds in first row molecules, thus supporting the idea that CS-bonding is a ubiquitous bonding form.     

The lowest singlet (n,pi*) and (pi,pi*) excited states of the hydrogen-bonded complex between water and pyrazine

The hydrogen bonding between water and pyrazine in its ground, lowest (n,pi*), and lowest (pi,pi*) states is investigated using density-functional theory (DFT), time-dependent density function theory (TD-DFT), coupled-cluster singles and doubles (CCSD) theory and equation-of-motion coupled cluster (EOM-CCSD) theory. For all states, the minimum-energy configuration is found to be an orthodox linear hydrogen-bonded species, with the bond strength increasing by 0.4 kcal mol-1 upon formation of the (pi,pi*) state and decreasing by 1.0 kcal mol-1 upon formation of the (n,pi*) state. The calculated solvent shifts for the complexes match experimental data and provide a basis for the understanding of the aqueous solvation of pyrazine, and the excited-state complexes are predicted to be only short-lived, explaining the failure of molecular beam experiments to observe them. Quite a different scenario for hydrogen bonding to the (n,pi*) excited state is found compared to those of H2O:pyridine and H2O:pyrimidine: for pyridine linear hydrogen bonds are unstable and hydrogen bonds to the electron-enriched pi cloud are strong, whereas for pyrimidine the excitation localizes on the nonbonded nitrogen leaving the hydrogen-bonding unaffected. For H2O:pyrazine, the (n,pi*) excitation remains largely delocalized, providing a distinct intermediary scenario.     

Photoinduced processes in riboflavin: superposition of pi pi*-n pi* states by vibronic coupling, transfer of vibrational coherence, and population dynamics under solvent control

Femtosecond dynamics of riboflavin, the parent chromophore of biological blue-light receptors, was measured by broadband transient absorption and stationary optical spectroscopy in polar solution. Rich photochemistry is behind the small spectral changes observed: (i) loss of oscillator strength around time zero, (ii) sub-picosecond (ps) spectral relaxation of stimulated emission (SE), and (iii) coherent vibrational motion along a' (in-) and a' (out-of-plane) modes. Loss of oscillator strength is deduced from the differences in the time-zero spectra obtained in water and DMSO, with stationary spectroscopy and fluorescence decay measurements providing additional support. The spectral difference develops faster than the time resolution (20 fs) and is explained by formation of a superposition state between the optically active (1pi pi*) S1 and closely lying dark (1n pi*) states via vibronic coupling. Subsequent spectral relaxation involves decay of weak SE in the blue, 490 nm, together with rise and red shift of SE at 550 nm. The process is controlled by solvation (characteristic times 0.6 and 0.8 ps in water and DMSO, respectively). Coherent oscillations for a' and a' modes show up in different regions of the SE band. a' modes emerge in the blue edge of the SE and dephase faster than solvation. In turn, a' oscillations are found in the SE maximum and dephase on the solvation timescale. The spectral distribution of coherent oscillations according to mode symmetry is used to assign the blue edge of the SE band to a 1n pi*-like state (A'), whereas the optically active 1pi pi* (A') state emits around the SE maximum. The following model comes out: optical excitation occurs to the Franck-Condon pi pi* state, a pi pi*-n pi* superposition state is formed on an ultrafast timescale, vibrational coherence is transferred from a' to a' modes by pi pi*-n pi* vibronic coupling, and subsequent solvation dynamics alters the pi pi*/n pi* population ratio.     

Stabilizing the elusive ortho-quinone/copper(I) oxidation state combination through pi/pi interaction in an isolated complex

The heterodinuclear compound [(PhenQ)Cu(dppf)](BF4), PhenQ = 9,10-phenanthrenequinone and dppf = 1,1'-bis(diphenylphosphino)ferrocene, was identified structurally and spectroscopically (NMR, IR, UV-vis) as a copper(I) complex of a completely unreduced ortho-quinone. Crystallographic and DFT calculation results suggest that this stabilization of a hitherto elusive arrangement is partially owed to intramolecular pi/pi interactions phenyl/PhenQ. Intermolecular PhenQ/PhenQ pi stacking is also observed in the crystal. According to DFT calculations, the pi interactions are responsible for the considerably distorted coordination geometry at CuI with one short and one longer Cu-O and Cu-P bond, respectively, and with bond angles at copper ranging from 99 degrees to 133 degrees. Electrochemical reduction proceeds reversibly at low temperatures to yield an EPR spectroscopically characterized semiquinone-copper(I) species.     

The C(2)1pi(u) state of Na2 molecule studied by polarization labelling spectroscopy method

The C1pi(u) <-- X1sigma(g)+ system of Na2 is studied by the polarization labelling spectroscopy technique. Accurate molecular constants are derived for the observed levels nu = 0-12, J = 12-100 in the C1pi(u) state.     

Ion-pair formation observed in a pulsed-field ionization photoelectron spectroscopic study of HF

The pulsed-field ionization (PFI) photoelectron (PE) spectrum of HF has been recorded at the chemical dynamics beamline of the advanced light source over the photon energy range 15.9-16.5 eV using a time-of-flight selection scheme at a resolution of 0.6 meV. Rotationally-resolved structure in the HF+(X 2 pi 3/2, 1/2, v+ = 0, 1) band systems are assigned. The spectral appearance of these systems agrees with a previous VUV laser PFI-PE study. Importantly, extensive rotationally-resolved structure between these two vibrational band systems is also observed. This is attributed to ion-pair formation via Rydberg states converging on the v+ = 1 vibrational levels of the HF+(X 2 pi 3/2, 1/2) spin-orbit states. These Rydberg states are assigned to the 1 sigma+ part of the nd-complexes (sigma, pi, and delta). Ion-pair formation is observed in this study by the detection of F- ions. Some partially rotationally-resolved structure in a previously published threshold photoelectron spectrum is similarly attributed to ion-pair formation (F- detection) through a combination of the v+ = 17 level of the (A 2 sigma+) 3s sigma Rydberg state and the (X 2 pi 3/2, 1/2, v+ = 1) 7d Rydberg states. On the basis of the present study, an accurate experimental value for the dissociation energy of the ground state of HF has been obtained, D0(HF) = 5.8650(5) eV.