Gaseous bradykinin and its singly, doubly, and triply protonated forms: a first-principles study

The conformers of gaseous bradykinin, BK, (Arg(1)-Pro(2)-Pro(3)-Gly(4)-Phe(5)-Ser(6)-Pro(7)-Phe(8)-Arg(9)) and its protonated forms, [BK + H](+), [BK + 2H](2+), and [BK + 3H](3+), were examined theoretically using a combination of the Merck molecular force field, Hartree-Fock, and density functional theory. Neutral BK, [BK + H](+), and [BK + 2H](2+) exist in zwitterionic forms that are stabilized by internal solvation and have compact structures; [BK + 3H](3+) differs by the absence of a salt bridge and adopts an elongated form. The common structural feature in all four BK species is a beta-turn in the Ser(6)-Pro(7)-Phe(8)-Arg(9) sequence. The gas-phase basicity of [BK + H](+) estimated from the calculated protonation energy is in accord with published experimental basicity; population-weighted collision cross-sections of the three ionic forms are in agreement with experimental cross-sections in the literature.     

Beyond two-state conical intersections. Three-state conical intersections in low symmetry molecules: the allyl radical

Using multireference configuration interaction expansions comprised of over 7 million configuration state functions, three-state conical intersections are reported for the closely spaced, spectroscopically observed (tilde)B(2A1), (tilde)C(2B1), and (tilde)D(2B2) states (in C(2v) symmetry) of the allyl radical. These conical intersections of states which were previously assigned as the 3,4,5(2)A states and are here reassigned as the 4,5,6(2)A states, are expected to be accessible using optical probes. This conclusion is obtained from the structure of the minimum energy point on the 4,5,6(2)A three-state conical intersection seam which is similar to the equilibrium structure of the ground (tilde)X(2A2) state and only 1.1 eV above the (tilde)D(2B2) state at its equilibrium geometry. The seam of three-state degeneracies joins two two-state seams of conical intersection, the 4,5(2)A and 5,6(2)A conical intersection seams. The energy of the minimum energy point on the 4,5(2)A two-state seam is only 0.15 eV above that of the (tilde)D(2B2) state at its equilibrium structure. Three-state intersections are also reported for the 3,4,5(2)A states.     

Three-state conical intersections in cytosine and pyrimidinone bases

Three-state conical intersections have been located and characterized for cytosine and its analog 5-methyl-2-pyrimidinone using multireference configuration-interaction ab initio methods. The potential energy surfaces for each base contain three different three-state intersections: two different S(0)-S(1)-S(2) intersections (gs/pi pi(*)/n(N)pi(*) and gs/pi pi(*)/n(O)pi(*)) and an S(1)-S(2)-S(3) intersection (pi pi(*)/n(N)pi(*)/n(O)pi(*)). Two-state seam paths from these intersections are shown to be connected to previously reported two-state conical intersections. Nonadiabatic coupling terms have been calculated, and the effects of the proximal third state on these quantities are detailed. In particular, it is shown that when one of these loops incorporates more than one seam point, there is a profound and predictable effect on the phase of the nonadiabatic coupling terms, and as such provides a diagnostic for the presence and location of additional seams. In addition, it is shown that each of the three three-state conical intersections located on cytosine and 5-methyl-2-pyrimidinone is qualitatively similar between the two bases in terms of energies and character, implying that, like with the stationary points and two-state conical intersections previously reported for these two bases, there is an underlying pattern of energy surfaces for 2-pyrimidinone bases, in general, and this pattern also includes three-state conical intersections.     

Exploring molecular complexity: conical intersections and NH3 photodissociation

The role of conical intersections in the photodissociation of the A 1A2" state of NH3 is investigated using extended atomic basis sets and a configuration state function expansion of approximately 8.5 million terms. A previously unknown portion of the 1 1A-2 1A seam of conical intersections with only C(s) symmetry is located. This portion of the seam is readily accessible from the equilibrium geometry of the A 1A2" state. These conical intersections are expected to play a role in the competition between adiabatic and nonadiabatic pathways for NH3(A 1A2") photodissociation.     

On the location of conical intersections in CH2BrCl using MS-CASPT2 methods

Multiconfigurational second-order perturbation theory has been employed to calculate two-dimensional potential energy surfaces for the lowest low-lying singlet electronic states of CH2BrCl as a function of the two carbon-halogen bonds. The photochemistry of the system is controlled by a nonadiabatic crossing occurring between the A and B bands, attributed to the b1A' and c1A' states, which are found almost degenerate and forming a near-degeneracy line of almost equidistant C-Br and C-Cl bonds. A crossing point in the near-degeneracy line is identified as a conical intersection in this reduced two-dimensional space. The positions of the conical intersection located at CASSCF, single-state (SS)-CASPT2, and multistate (MS)-CASPT2 levels of theory are compared, also paying attention to the nonorthogonality problem of perturbative approaches. To validate the presence of the conical intersection versus an avoided crossing, the geometrical phase effect has been checked using the multiconfigurational MS-CASPT2 wave function.     

On the characterization of three-state conical intersections using a group homomorphism approach: the two-state degeneracy spaces

Second-order degenerate perturbation theory, in conjunction with the group homomorphism method for describing a similarity transformation, are used to characterize the subspace of two-state conical intersections contained in the branching space of a three-state conical intersection. It is shown by explicit calculation, using the lowest three-state conical intersection of (CH)3N2, that a second-order treatment yields highly accurate absolute energies, even at significant distances from the reference point of three-state intersection. The excellent agreement between the second order and ab initio results depends on the average energy component, which is computed using 5 first-order terms and 15 second-order terms. The second-order absolute energy change over the range rho = 0.0-0.3 au, where rho is the distance from the three-state conical intersection in the branching space coordinates, is approximately 6500 and 9500 cm(-1) for the E(1=2) and E(2=3) seams, respectively, with the maximum ab initio energy deviation from degeneracy of 200 cm(-1) occurring at rho = 0.3 au. The characteristic parameters gIJ and hIJ are also predicted to great accuracy, even at large rho, with the error growing to only 10-15% at rho = 0.3 au.     

Exploring the Jahn-Teller and pseudo-Jahn-Teller conical intersections in the ethane radical cation

We report a theoretical account on the static and dynamic aspects of the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) interactions in the ground and first excited electronic states of the ethane radical cation. The findings are compared with the experimental photoionization spectrum of ethane. The present theoretical approach is based on a model diabatic Hamiltonian and with the parameters derived from ab initio calculations. The optimized geometry of ethane in its electronic ground state (1A1g) revealed an equilibrium staggered conformation belonging to the D3d symmetry point group. At the vertical configuration, the ethane radical cation belongs to this symmetry point group. The ground and low-lying electronic states of this radical cation are of 2Eg, 2A1g, 2Eu, and 2A2u symmetries. Elementary symmetry selection rule suggests that the degenerate electronic states of the radical cation are prone to the JT distortion when perturbed along the degenerate vibrational modes of eg symmetry. The 2A1g state is estimated to be approximately 0.345 eV above the 2Eg state and approximately 2.405 eV below the 2Eu state at the vertical configuration. The symmetry selection rule also suggests PJT crossings of the 2A1g and the 2Eg electronic states of the radical cation along the vibrational modes of eg symmetry and such crossings appear to be energetically favorable also. The irregular vibrational progressions, with numerous shoulders and small peaks, observed below 12.55 eV in the experimental recording are manifestations of the dynamic (E x e)-JT effect. Our findings revealed that the PJT activity of the degenerate vibrational modes is particularly strong in the 2Eg-2A1g electronic manifold which leads to a broad and diffuse structure of the observed photoelectron band.     

Decomposition of neutral, singly and doubly protonated benzoquinone in the gas phase

The unimolecular fragmentations of singly and doubly protonated ortho-, meta-, and para-benzoquinones (BQH(+) and BQH(2)(2+), respectively) are studied by tandem mass spectrometry. The dominant fragmentation pathways lead to the elimination of a neutral CO molecule from BQH(+) and, by charge separation, to the expulsion of protonated CO from BQH(2)(2+). Reaction mechanisms are elucidated based on labeling experiments and UB3 LYP calculations. These results reveal that the respective reactions proceed in an analogous fashion to the decarbonylation of neutral benzoquinones, which decompose into carbon monoxide and cyclopentadienone. Single protonation facilitates all steps on the reaction pathway with neutral CO and O-protonated cyclopentadienone as final products. In contrast, double protonation leads to an increase of the barriers for the decomposition yielding CO.H(+) and O-protonated cyclopentadienone. This major process of BQH(2)(2+) is accompanied by two minor channels, which lead to the elimination of neutral carbon monoxide and water, respectively. The proton affinity of the para-BQH(+) monocation is estimated as 3.6+/-0.3 eV.     

On the characterization of three state conical intersections: a quasianalytic theory using a group homomorphism approach

In this work, degenerate perturbation theory through second order is used to characterize the vicinity of a three state conical intersection. This report extends our recent demonstration that it is possible to describe the branching space (in which the degeneracy is lifted linearly) and seam space (in which the degeneracy is preserved) in the vicinity of a two state conical intersection using second order perturbation theory. The general analysis developed here is based on a group homomorphism approach. Second order perturbation theory, in conjunction with high quality ab initio electronic structure data, produces an approximately diabatic Hamiltonian whose eigenenergies and eigenstates can accurately describe the three adiabatic potential energy surfaces, the interstate derivative couplings, and the branching and seam spaces in their full dimensionality. The application of this approach to the minimum energy three state conical intersection of the pyrazolyl radical demonstrates the potential of this method. A Hamiltonian comprised of the ten characteristic (linear) parameters and over 300 second order parameters is constructed to describe the branching space associated with a point of conical intersection. The second order parameters are determined using data at only 30 points. In the vicinity of the conical intersection the energy and derivative couplings are well reproduced and the singularity in the derivative coupling is analyzed.     

Quantum dynamics through conical intersections: combining effective modes and quadratic couplings

We present a detailed study for the short-time dynamics through conical intersections in molecular systems related to the quadratic vibronic coupling (QVC) Hamiltonian [Müller, H.; K?ppel, H.; Cederbaum, L. S. New J. Chem. 1993, 17, 7-29] and the effective-mode formalism [Cederbaum, L. S.; Gindensperger, E.; Burghardt, I. Phys. Rev. Lett. 2005, 94, 113003]. Our approach is based on splitting the nuclear degrees of freedom of the whole system into system modes and environment modes. It was found that only three-effective environmental modes together with the system's modes are needed to describe the short-time dynamics of the complex system correctly. In addition, a detailed mathematical proof is given in the appendix to demonstrate that the exact cumulants are recovered up to the second order within the cumulant expansion of the autocorrelation function. The butatriene molecule is studied as an explicit showcase example to stress the viability of our proposed scheme and to compare with other systems.     

Generation and dissociation pathways of singly and doubly protonated bisguanidines in the gas phase

Para-bisguanidinyl benzene 1 and its N-permethylated derivative 2 are both sufficiently strong bases to afford not only the monocations [1+H]+ and [2+H]+, but also the doubly protonated ions, [1+2H]2+ and [2+2H]2+, in the gas phase. The title ions generated via electrospray ionization are probed by collision-induced dissociation experiments which inter alia reveal that the dicationic species [1+2H]2+ and [2+2H]2+ can even undergo fragmentation reactions with maintenance of the 2-fold charge. Complementary results from density functional theory predict PAs above 1000 kJ mol(-1) for the neutral compounds, i.e., PA(1) = 1025 kJ mol(-1) and PA(2) = 1067 kJ mol(-1). Due to the stabilization of the positive charge in the guanidinium ions and the para-phenylene spacer separating the basic sites, even the monocations bear sizable proton affinities, i.e., PA([1+H]+) = 740 kJ mol(-1) and PA([2+H]+) = 816 kJ mol(-1).     

Two ion/ion charge inversion steps to form a doubly protonated peptide from a singly protonated peptide in the gas phase

An approach is described to increase the degree of protonation of a polypeptide ion in the gas phase. Sequential charge inversion reactions involving the reactions of oppositely charged ions are used to yield a net increase in ion charge. The approach is illustrated here with the conversion of singly protonated bradykinin to doubly protonated bradykinin. The first step involves conversion of the singly protonated peptide to the singly deprotonated peptide via reactions with multiply charged anions derived from carboxylate-terminated dendrimers. Some of the singly deprotonated peptide was then converted to doubly protonated peptide via reactions with multiply charged cations derived from amino-terminated dendrimers. The overall approach is illustrative of a general strategy for increasing the absolute charge states of large ions in the gas phase.     

An Ab initio study on the conformations of protonated,neutral, and deprotonated amidine

Ab initio SCF molecular orbital calculations have been performed to ascertain the conformational preferences of protonated, neutral, and deprotonated amidine [HC(?NH)NH₂], using the 3-21G split valence basis set. The states of eight stable species, eight transition states, and four higher-order saddle points have been determined by complete geometry optimization utilizing analytic energy gradient techniques. Protonation at the amidine ?NH is preferred over the –NH₂ site by 37.1 kcal/mol. Neutral amidine has rotational barriers of 9.6 and 11.7 kcal/mol for the HN?CN cis and trans isomers, respectively, while all the stable HC(NH₂)₂⁺ and HC(NH)₂^? species possess torsional barriers larger than 23 kcal/mol. There is, however, essentially free C—N single-bond rotation in HC(?NH)NH₃⁺, the calculated barriers being 0.7 and 1.8 kcal/mol for the cis and trans HN?CN isomers, respectively.     

Excited-state potential surfaces of ruthenium nitrosyl complexes: conical intersections and the Jahn-Teller effect

The Jahn-Teller effect in excited states of nitrosyl complexes was analyzed in terms of the density functional theory at the B3LYP level. This effect was shown to play a role in transitions between metastable isomers and their photoactivated relaxation to the ground state. In the compounds under study, the Jahn-Teller effect can be interpreted as the Renner-Teller effect. The characteristics of the Jahn-Teller potential energy surfaces were determined.     

Quantum dynamics through conical intersections in macrosystems: Combining effective modes and time-dependent Hartree

We address the nonadiabatic quantum dynamics of (macro)systems involving a vast number of nuclear degrees of freedom (modes) in the presence of conical intersections. The macrosystem is first decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment can be constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. The environment is described by a few effective modes augmented by a residual environment. In practice, the effective modes can be added to the system’s modes and the quantum dynamics of the entire macrosystem can be accurately calculated on a limited time-interval. For longer times, however, the residual environment plays a role. We investigate the possibility to treat fully quantum mechanically the system plus a few effective environmental modes, augmented by the dynamics of the residual environment treated by the time-dependent Hartree (TDH) approximation. While the TDH approximation is known to fail to correctly reproduce the dynamics in the presence of conical intersections, it is shown that its use on top of the effective-mode formalism leads to much better results. Two numerical examples are presented and discussed; one of them is known to be a critical case for the TDH approximation.     

Geometrical and substituent effects in conical intersections: linking chemical structure and photoreactivity in polyenes

The knowledge of the intersection space topography of electronic states is essential for deciphering and predicting photoinduced reactions. Michl and Bonaci?-Koutecky developed a two-electron two-orbital model that allowed first systematic studies of the chemical origin of conical intersections in strongly polar systems. We generalize this approach to arbitrary functionalized and unfunctionalized polyene systems. For the extended model, a set of mathematical conditions for the formation of conical intersections are derived. These conditions are translated into geometrical motions and electronic effects, which help to explain and predict the structure and energetics of conical intersections. A three-step strategy for the conceptual search of conical intersections is outlined. Its universal validity is demonstrated using the textbook example cyclohexadiene and its functionalized derivative trifluoromethyl-indolylfulgide, a chromophore studied for possible application as a molecular switch.     

Photoisomerization of naphthylquinolylethylenes in neutral and protonated forms

The quantum yield of the trans-cis photoisomerization of 1-(1-naphthyl)-2-(2-quinolyl)ethylene and 1-(2-naphthyl)-2-(2-quinolyl)ethylene is close to the theoretical limit (0.5) for diabatic photoisomerization and does not change on passing from the neutral to the protonated form. The data obtained indicate the absence of the α-effect for the test compounds, which consists in an increase in the trans-cis photoisomerization quantum yield to values of >0.5 upon protonation of some azadiarylethylenes with the nitrogen atom in the α-position to the ethylene group.     

On the simulation of photoelectron spectra in molecules with conical intersections and spin-orbit coupling: the vibronic spectrum of CH3S

A method to simulate photoelectron spectra for states coupled by conical intersections and the spin-orbit interaction is reported. The algorithm is based on the multimode vibronic coupling model and treats the spin-orbit interaction in a nonperturbative manner. Since the algorithm is not dependent on molecular symmetry, the approach is generally applicable to accidental conical intersections as well as the symmetry required intersections found in Jahn-Teller molecules. The method is also computationally efficient using energy gradient and derivative coupling information to limit the number of nuclear configurations at which ab initio data are required. This approach is applied to simulate the negative ion photoelectron spectrum of the methylthio radical. The two-state Hamiltonian employed to describe this system was determined employing ab initio gradients and derivative couplings at only 17 nuclear configurations.     

Hierarchy of effective modes for the dynamics through conical intersections in macrosystems

An extension of the effective-mode theory for the short-time dynamics through conical intersections in macrosystems [L. S. Cederbaum et al., Phys. Rev. Lett. 94, 113003 (2005)] is proposed. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective modes are needed-together with the system's modes-to accurately calculate low resolution spectra and the short-time dynamics of the entire macrosystem. Here, the authors propose an iterative scheme to construct a hierarchy of additional triplets of effective modes. This naturally extends the effective-mode formulation. By taking into account more and more triplets, the dynamics are accurately predicted for longer and longer times, and more resolved spectra can be calculated. Numerical examples are presented, computed using various numbers of additional effective modes.