Conical intersection of the ground and first excited states of water: energies and reduced density matrices from the anti-Hermitian contracted Schrödinger equation

A conical intersection between the ground and first-excited states of water is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schr?dinger equation (ACSE). This study is an extension of a previous study in which the ACSE was used to compute the energies around a conical intersection in the triplet excited states of methylene [Snyder, J. W., Jr.; Rothman, A. E.; Foley, J. J.; Mazziotti, D. A. J. Chem. Phys. 2010, 132, 154109]. We compute absolute energies of the 1(1)A' and 2(1)A' states of water (H(2)O) and the location of the conical intersection. The ACSE energies are compared to those from ab initio wave function methods. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. Unlike the situation for methylene, the two states in the vicinity of the conical intersection of water both have the same spatial symmetry. Hence, the study demonstrates the ability of the ACSE to resolve states of the same spatial symmetry that are nearly degenerate in energy. The 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from double-ζ and augmented double-ζ basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.     

Quenching of Li (2P) by H2: potential energy surfaces, conical intersection seam, and diabatic bases

The quenching of Li (1s ²2p; ²P) to Li (1s ²2s; ²S) by H₂ is considered using coupled-cluster and multireference configuration-interaction techniques. C _{2 v} (²A₁, ²B₂) and C _{∞ v} (²Π,²Σ⁺) sections of the 1²A^′ and 2²A^′ potential energy surfaces are determined. The C _{2 v} portion of the 1²A^′−2²A^′ seam of conical intersection is studied. Perhaps the most significant finding is a surprising trifurcation of this seam into a portion with only C _s symmetry and the aforementioned C _{2 v} portion. The adiabatic-to-diabatic state transformation is considered in the vicinity of the seam of conical intersection using both perturbation theory and the dipole moment operator. The ²B₂ section of the 2²A^′ potential energy surface exhibits an exciplex in the general vicinity of the seam of conical intersection. The ²Π section of the 2²A^′ potential energy surface possesses a global minimum lying 1.86kcal/mol below the Li (²P)+H₂ asymptote. A van der Waals-like minimum with C _{∞ v} symmetry was found on the 1²A^′ potential energy surface. Received: 14 August 1998 / Accepted: 20 August 1998 / Published online: 11 November 1998     

Fe(CO)4 flexible as a two‐level system avoided conical intersection

This article reports new square‐planar Fe(CO)₄ D_4h structures that are optimized, using the Hartree–Fock (HF) approach, and multiconfiguration self‐consistent field (MCSCF) theory in active space [2b_2g2e_ga_1ga_2u]⁸, and which energy increased in sequence: ³B_2g TS < ¹A_1g TS < ¹A_1g GS. A triple ζ valence basis set supplemented with 4f for Fe and 3d for C and O polarization shells [TZV (DF)] was used. At the HF/TZV (DF) level, ¹A_1g TS and ³B_2g TS (³B_2g TS energetically more favorable), there are transition states of tetrahedral inversion (defining stereochemical flexibility of Fe(CO)₄) between known equivalent ¹A₁ and ³B₂ Jahn–Teller distorted tetrahedron C_2v structures with activation energy at ～0.96 kcal/mol according to the experimental data. ¹A_1g TS differs from ¹A_1g GS in electronic configuration by occupation of a_1g and a_2u MOs. At the MCSCF/ TZV (DF) level, ¹A_1g TS and ¹A_1g GS are optimized as near‐pure states in different potential energy surfaces (PES) avoided conical intersection with near‐equal interatomic distances, and define electronic flexibility of Fe(CO)₄. Estimation of the energy separation in a two‐level system that avoids a conical intersection from vibrational spectrum is based on the effective Hamiltonian of the perturbation theory. The energy gap between two square‐planar Fe(CO)₄ D_4h ¹A_1g TS < ¹A_1g GS is 0.27 kcal/mol. The energy gap between ¹A_1g GS and ¹A₁ is 1.28 kcal/mol. It is possible to observe ³B₂, ¹A₁ and ¹A_1g GS separately in the course of the experiment. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The intersection seam between the 11A′ and 21A′ states of ozone

The intersection seam between the two lowest ¹A^′ states of ozone has been determined. The potential energy surfaces and the seam are calculated and discussed in perimetric coordinates which exhibit the full three-dimensional symmetry. The seam is shown to form a closed curve which crosses the C _{2 v} -restricted coordinate planes at six points. Three of these correspond to the previously determined intersection, the starting point of the present search. The other three correspond to highly repulsive regions on the potential energy surface where two atoms approach each other to within two-thirds of the O₂ bond length. At the former three points both states have ¹ A ₁ symmetry, but at the latter three points one state has ¹ A ₁ symmetry whereas the other has ¹ B ₂ symmetry. Consequently, there exist three additional branches of the intersection seam between these two states. Each of these branches lies entirely in one C _{2 v} -restricted coordinate plane and connects to the previously discussed C _s -seam at one point. The existence of a further intersection seam is established. A novel method for determining intersection points is described. Received: 10 January 1996 / Accepted: 2 January 1997     

Electronic rearrangements during chemical reactions. II. Planar dissociation of ethylene

The direct dissociation of ethylene into two methylenes is studied along the least motion reaction path by means of an ab initio multiconfiguration self-consistent-field (MCSCF ) calculation. All eight configurations arising from those valence orbitals that form the CC bonds, seven of them singlet coupled and one triplet coupled, are taken into account. The HCH bond angle is optimized along the entire reaction path. Separate MCSCF optimizations are carried through for the lowest two states of ¹A_g symmetry. The (¹A_gσ²π²) ethylene ground state dissociates into two (³B₁σπ) ground-state methylenes. The (¹A_gσ²π*²) excited state of ethylene dissociates into two (¹A₁σ²) excited methylenes. It is established that both these dissociations proceed without any barrier in the energy curve. In the ground state, where orbital symmetry is conserved, the π-bond breaks before the σ-bond, and the calculated heat of reaction agrees within 6 kcal/mol with the experimental value. In the excited state, where orbital symmetry is not conserved, the nonbonded repulsion between methylene σ₂ lone pairs is found to blend into the antibonding character of the excited ethylene, yielding an energy curve that is everywhere repulsive. However, the variation of the HCH angle during the dissociation process is not simple, initially it expands and subsequently it contracts. Quantitative analytical approaches are developed which furnish conceptual interpretations of the orbital changes and configurational changes along the reaction path.     

MCSCF/MCLR Studies of potential energy surfaces,spectra, and properties of the X1A1 and a3B2 states of ozone

Potential energy surfaces, properties, and spectra of singlet (X¹A₁) and triplet (a³B₂) ozone are investigated by means of MCSCF /MCLR analytical response theory calculations. MCSCF analytical gradients and Hessians are used to locate equilibrium and transition-state structures and to obtain associated vibrational and rotational constants, infrared intensities, and dipole moments. By means of MC linear response functions, electronic excitation energies, and oscillator strengths, static and dynamic polarizabilities as well as dispersion (C₆) coefficients are obtained. Good agreement is achieved, in some cases within experimental error margins, for properties where experimental data are known. A very low IR intensity for triplet ozone is predicted.     

1 Bu–2 Ag conical intersection in trans-butadiene: ultrafast dynamics and optical spectra

The potential-energy functions of the 1 ¹B_u and 2 ¹A_g excited valence states of trans-butadiene have been characterised by the CASPT2 method. Based on these ab initio data, a vibronic-coupling model describing the conical intersection of the 1 ¹B_u and 2 ¹A_g states has been constructed. UV resonance-Raman and absorption spectra have been calculated, employing the time-dependent approach. The time-dependent wave-packet calculations reproduce the expected ultrafast (≈30 fs) radiationless decay of the optically bright 1 ¹B_u state into the dark 2 ¹A_g state.     

Mg2Ru2Cl10O·16H2O

Mg₂Ru₂Cl₁₀O·16H₂O {dimagnesium μ‐oxo‐bis­[penta­chloro­ruthenate(IV)] hexa­deca­hydrate} crystallizes in the monoclinic system (space group P2₁/c). The structure consists of layers of [Ru₂Cl₁₀O]⁴⁻ anions, [Mg(H₂O)₆]²⁺ cations and water mol­ecules stacked along the a axis. Only the O atom bonded to Ru occupies the 2a site with symmetry. All the other atoms occupy general 4e sites. The crystal structure is stabilized by O—H⋯O and O—H⋯Cl inter­actions.     

K2SrNb6Cl18, dipotassium strontium hexaniobium octadecachloride

The structure of dipotassium strontium hexaniobium octadeca­chloride is based on [Nb₆Clⁱ₁₂Cl^a₆]^4? units (i and a denote `inner' and `outer' ligands, respectively), which have crystallographically imposed symmetry, linked together by K⁺ and Sr²⁺ cations. The K⁺ cation occupies a tetrahedral site in the face‐centered cubic lattice of cluster units, and is bonded to 12 Cl ligands. The Sr atom is located in an octahedral site and is bonded to six outer Cl ligands.     

Cysteine SH and Glutamate COOH Contributions to [NiFe] Hydrogenase Proton Transfer Revealed by Highly Sensitive FTIR Spectroscopy

A [NiFe] hydrogenase (H₂ase) is a proton‐coupled electron transfer enzyme that catalyses reversible H₂ oxidation; however, its fundamental proton transfer pathway remains unknown. Herein, we observed the protonation of Cys546‐SH and Glu34‐COOH near the Ni–Fe site with high‐sensitivity infrared difference spectra by utilizing Ni‐C‐to‐Ni‐L and Ni‐C‐to‐Ni‐SI_a photoconversions. Protonated Cys546‐SH in the Ni‐L state was verified by the observed SH stretching frequency (2505 cm^?1), whereas Cys546 was deprotonated in the Ni‐C and Ni‐SI_a states. Glu34‐COOH was double H‐bonded in the Ni‐L state, as determined by the COOH stretching frequency (1700 cm^?1), and single H‐bonded in the Ni‐C and Ni‐SI_a states. Additionally, a stretching mode of an ordered water molecule was observed in the Ni‐L and Ni‐C states. These results elucidate the organized proton transfer pathway during the catalytic reaction of a [NiFe] H₂ase, which is regulated by the H‐bond network of Cys546, Glu34, and an ordered water molecule.     

Hydrogen bonding and structure of Ba2Ru2Cl10O·10H2O

Dibarium μ‐oxido‐bis[pentachloridoruthenate(IV)] decahydrate, Ba₂Ru₂Cl₁₀O·10H₂O, has been prepared from ruthenium(III) chloride and barium chloride in hydrochloric acid. It crystallizes in the monoclinic system (space group C2/c). The structure consists of alternating layers of [Ru₂Cl₁₀O]⁴⁻ and [Ba(H₂O)₇]²⁺ complex ions along the a direction. The O atom bonded to ruthenium occupies the 4e site, with symmetry, while the other atoms occupy general 8f sites. The overall structure is held together by O—H...O hydrogen bonds and O—H...Cl dipole–dipole interactions.     

A Reversible Proton Relay Process Mediated by Hydrogen‐Bonding Interactions in [FeFe]Hydrogenase Modeling

A reversible and temperature‐dependent proton‐relay process is demonstrated for a Fe₂ complex possessing a terminal thiolate in the presence of nitrogen‐based acids. The terminal sulfur site (S^t) of the complex forms a hydrogen‐bond interaction with N,N‐dimethylanilinium acid at 183 K. The Fe₂ core, instead, is protonated to generate a bridging hydride at 298 K. Reversibility is observed for the tautomerization between the hydrogen‐bonded pair and the Fe–hydride species. X‐ray structural analysis of the hydrogen‐bonded species at 193 K reveals a short N(H)???S^t contact. Employment of pyridinium acid also results in similar behavior, with reversible proton–hydride interconversion. DFT investigation of the proton‐transfer pathways indicates that the pK_a value of the hydrogen‐bonded species is enhanced by 3.2 pK_a units when the temperature is decreased from 298 K to 183 K.     

Two polymorphs of 5‐cyclohexyl‐5‐ethylbarbituric acid and their packing relationships with other barbiturates

Polymorph (Ia) (m.p. 474 K) of the title compound, C₁₂H₁₈N₂O₃, displays an N—H...O=C hydrogen‐bonded layer structure which contains R₆⁶(28) rings connecting six molecules, as well as R₂²(8) rings linking two molecules. The 3‐connected hydrogen‐bonded net resulting from these interactions has the hcb topology. Form (Ib) (m.p. 471 K) displays N—H...O=C hydrogen‐bonded looped chains in which neighbouring molecules are linked to one another by two different R₂²(8) rings. Polymorph (Ia) is isostructural with the previously reported form II of 5‐(2‐bromoallyl)‐5‐isopropylbarbituric acid (noctal) and polymorph (Ib) is isostructural with the known crystal structures of four other barbiturates.     

catena‐Poly­[[di­aqua­lithium(I)]‐μ‐[9H‐purine‐2,6(1H,3H)‐dionato‐O2:N7]]

In the title compound, [Li(C₅H₃N₄O₂)(H₂O)₂]_n, the coordinate geometry about the Li⁺ ion is distorted tetrahedral and the Li⁺ ion is bonded to N and O atoms of adjacent ligand mol­ecules forming an infinite polymeric chain with Li—O and Li—N bond lengths of 1.901 (5) and 2.043 (6) Å, respectively. Tetrahedral coordination at the Li⁺ ion is completed by two cis water mol­ecules [Li—O 1.985 (6) and 1.946 (6) Å]. The crystal structure is stabilized both by the polymeric structure and by a hydrogen‐bond network involving N—H?O, O—H?O and O—H?N hydrogen bonds.     

Thioacetanilide at 120 K

The title compound, C₈H₉NS, has four symmetry‐independent molecules in the asymmetric unit. These molecules link into two independent infinite N—H...S hydrogen‐bonded chains in the a‐axis direction with graph‐set notation C₂²(8). The NH—CS group adopts a trans conformation and forms a dihedral angle of about 50° with the phenyl ring. The intermolecular hydrogen‐bond energy calculated by the density functional theory (DFT) method is −14.95 kJ mol⁻¹. The correlation between the IR spectrum of this compound and the hydrogen‐bond energy is also discussed. This molecular system is of interest because of its biological function.     

Toward total structural analysis of cardiolipins: multiple-stage linear ion-trap mass spectrometry on the [M − 2H + 3Li]<Superscript>+</Superscript> ions

ESI multiple-stage linear ion-trap (LIT) mass spectrometric approaches for a near-complete structural characterization of cardiolipins (CLs), including identification of the fatty acyl substituents, assignment of the fatty acid substituents on the glycerol backbone, and location of the double-bond(s) or cyclopropyl group along the fatty acid chain are described. Upon collisionally activated dissociation (CAD) on the [M − 2H + 3Li]⁺ ions of CL in an ion-trap (MS²), two sets of fragment ions (designated as (a + 136) and (b + 136) ions) analogous to those previously reported for the [M − 2H + 3Na]⁺ ions were observed, leading to assignment of the phosphatidyl moieties attached to 1′- or 3′-position of the central glycerol. Further dissociation of the (a + 136) (or (b + 136)) ions (MS³) gives rise to the (a + 136 − R_{1(or 2)}CO₂Li) (or b + 136 − R_{1(or 2)}CO₂Li) ion pairs that identify the fatty acid moieties and their position on the glycerol backbone. This is followed by MS⁴ on the (a + 136 − R_{1(or 2)}CO₂Li) (or b + 136 − R_{1(or 2)}CO₂Li) ion to eliminate a tricylic glycerophosphate ester residue (136 Da) to yield the (a − R_{1(or 2)}CO₂Li) ion, which is then subjected to MS⁵. The MS5 spectrum contains the structural information that locates the double-bond(s) or cyclopropyl group of the fatty acid substituents. Finally, the subsequent MS⁶ on the dilithiated fatty acid ions generated from MS⁵ also yields feature ions that confirm the assignment.     

Analytical MCSCF energy gradients: Treatment of symmetry and CASSCF applications to propadienone

The formula for the first derivative of the MCSCF energy with respect to a nuclear coordinate is reviewed. The efficient utilization of symmetry in programs employing symmetry-adapted basis functions is described: Advantages that are also obtained for higher derivatives and for gradients of nonself-consistent wave functions are briefly discussed. Using CASSCF wave functions, the method is applied to the question of nonlinearity in the heavy atom chain of propadienone (CH₂CCO).     

Multiple Decay Mechanisms and 2D‐UV Spectroscopic Fingerprints of Singlet Excited Solvated Adenine‐Uracil Monophosphate

The decay channels of singlet excited adenine uracil monophosphate (ApU) in water are studied with CASPT2//CASSCF:MM potential energy calculations and simulation of the 2D‐UV spectroscopic fingerprints with the aim of elucidating the role of the different electronic states of the stacked conformer in the excited state dynamics. The adenine ¹L_a state can decay without a barrier to a conical intersection with the ground state. In contrast, the adenine ¹L_b and uracil S(U) states have minima that are separated from the intersections by sizeable barriers. Depending on the backbone conformation, the CT state can undergo inter‐base hydrogen transfer and decay to the ground state through a conical intersection, or it can yield a long‐lived minimum stabilized by a hydrogen bond between the two ribose rings. This suggests that the ¹L_b, S(U) and CT states of the stacked conformer may all contribute to the experimental lifetimes of 18 and 240 ps. We have also simulated the time evolution of the 2D‐UV spectra and provide the specific fingerprint of each species in a recommended probe window between 25 000 and 38 000 cm^?1 in which decongested, clearly distinguishable spectra can be obtained. This is expected to allow the mechanistic scenarios to be discerned in the near future with the help of the corresponding experiments. Our results reveal the complexity of the photophysics of the relatively small ApU system, and the potential of 2D‐UV spectroscopy to disentangle the photophysics of multichromophoric systems.     

Two polymorphs and the diethylammonium salt of the barbiturate eldoral

Polymorph (Ia) of eldoral [5‐ethyl‐5‐(piperidin‐1‐yl)barbituric acid or 5‐ethyl‐5‐(piperidin‐1‐yl)‐1,3‐diazinane‐2,4,6‐trione], C₁₁H₁₇N₃O₃, displays a hydrogen‐bonded layer structure parallel to (100). The piperidine N atom and the barbiturate carbonyl group in the 2‐position are utilized in N—H...N and N—H...O=C hydrogen bonds, respectively. The structure of polymorph (Ib) contains pseudosymmetry elements. The two independent molecules of (Ib) are connected via N—H...O=C(4/6‐position) and N—H...N(piperidine) hydrogen bonds to give a chain structure in the [100] direction. The hydrogen‐bonded layers, parallel to (010), formed in the salt diethylammonium 5‐ethyl‐5‐(piperidin‐1‐yl)barbiturate [or diethylammonium 5‐ethyl‐2,4,6‐trioxo‐5‐(piperidin‐1‐yl)‐1,3‐diazinan‐1‐ide], C₄H₁₂N⁺·C₁₁H₁₆N₃O₃⁻, (II), closely resemble the corresponding hydrogen‐bonded structure in polymorph (Ia). Like many other 5,5‐disubstituted derivatives of barbituric acid, polymorphs (Ia) and (Ib) contain the R₂²(8) N—H...O=C hydrogen‐bond motif. However, the overall hydrogen‐bonded chain and layer structures of (Ia) and (Ib) are unique because of the involvement of the hydrogen‐bond acceptor function in the piperidine group.