Reaction Coordinate Mode Research Articles

Action spectra associated with inelastic two-electron tunneling through a single molecule: Propene on Cu(211)

Inelastic electron tunneling through single molecules located in the tunnel junction between a surface and the tip of a scanning tunneling microscope may cause molecular surface dynamics. Vibrations excited by inelastically tunneling electrons may couple to other vibrational modes and finally induce processes like hopping or rotation. The reaction yield Y(V) as a function of a bias voltage V depict quasi an action spectrum of a certain dynamic event. Experimental results of action spectra are reproduced for rotation and hopping of a single propene molecule on a stepped Cu(211) surface. The good agreement between calculated and experimental Y(V) identify the respective vibrational modes excited by tunneling electrons. These induce then motions via intermode-coupling with the reaction coordinate modes. A general formula of a reaction rate R(V) in a two-electron process, exciting two different vibrational modes for enantiomer conversion of a single propene molecule is derived and the expected R(V) is calculated.

Computational Modeling of a Caged Methyl Cation: Structure, Energetics, and Vibrational Analysis.

DFT calculations for CH3+ within a constrained cage of water molecules permit the controlled manipulation of distances rax and req to "axial" and "equatorial" waters. Equatorial CH···O interactions catalyze methyl transfer (MT) between axial waters. Variation in rax has a greater effect on CH bond lengths and stretching force constants in the symmetric SN2-like transition structures than variation in req. In-plane bending frequencies are insensitive to these variations in cage dimensions, but axial interactions loosen the out-of-plane bending mode (OP) whereas equatorial interactions stiffen it. Frequencies for rotational and translational motions of CH3+ within the cage are influenced by rax and req. In particular, translation of CH3+ in the axial direction is always coupled to cage motion. With longer rax, CH3+ translation is coupled with asymmetric CO bond stretching, but with shorter rax, it is also coupled with OP (equivalent to the umbrella mode of trigonal bipyramidal O···CH3+···O); the magnitude of the imaginary MT frequency increases steeply as rax diminishes. This coupling between CH3+ and its cage is removed by eliminating the rows and columns associated with cage atoms from the full Hessian to obtain a reduced Hessian for CH3+ alone. Within a certain range of cage dimensions, the reduced Hessian yields a real frequency for MT. The importance of using a Hessian large enough to describe the reaction coordinate mode correctly is emphasized for modeling chemical reactions and particularly for kinetic isotope effects in enzymic MT.

Analysis of reaction rates of single molecules on metal surfaces

The experimental results of the action spectra i.e., reaction rate R(V) as a function of a bias voltage V are analyzed for rotation of a single CCH (D) molecule on a Cu (100) surface [5] and hopping of a single H(D)2O molecule on Pd(111) surface [6]. In the former system it is identified that rotation occurs if enough energy stored in the C-H (D) in-plane bending (IPB) mode excited by tunneling electron is transferred to the C-H (D) out of plane bending (OPB) mode (reaction coordinate mode) via the anharmonic mode coupling in a single electron process. The calculated R(V) shows an excellent agreement with the experimental results except at the low bias voltages below V ≃ 60 mV where no experimental data is available for the nonlinear current I dependence of R(I). A reproduction of the experimental R(V) at the higher voltage region allows us to determine the vibrational density of states of the C-H IPB mode and its coupling rate to the C-H (D) OPB mode as well as the inelastic tunneling current to excite IPB mode. A change of a conductance upon excitation of the C-H IPB mode enables us to evaluate the electron-vibration coupling strength inducing the rotation motion of CCH molecule. In the latter system investigated at a high temperature of about 40K, the constant R(V) due to thermal hopping followed by the rapid increase is satisfactory explained by anharmonic inter-mode coupling between the scissor mode excited by tunneling electrons and the frustrated translation mode for H(D)2O molecule on Pd(111).

STMを用いた単分子振動分光

Action spectroscopy (AS) of single molecules using a scanning tunneling microscope (STM) is presented. The AS obtained from the motion and reaction of a molecule, is applicable to understand molecular dynamics at metal surfaces. Combined study with the generic theory of STM-AS, not only the energy for the vibrational modes, but also versatile numbers such as reaction order, reaction constant, time constants of mode coupling between the excited vibrational mode and the reaction-coordinate mode, etc., can be obtained.

Rotation of a Single Acetylene Molecule on Cu(001) by Tunneling Electrons in STM

We study the elementary processes behind one of the pioneering works on scanning tunneling microscope controlled reactions of single molecules [Stipe et al., Phys. Rev. Lett. 81, 1263 (1998)]. Using the Keldysh-Green function approach for the vibrational generation rate in combination with density functional theory calculations to obtain realistic parameters we reproduce the experimental rotation rate of an acetylene molecule on a Cu(100) surface as a function of bias voltage and tunneling current. This combined approach allows us to identify the reaction coordinate mode of the acetylene rotation and its anharmonic coupling with the C-H stretch mode. We show that three different elementary processes, the excitation of C-H stretch, the overtone ladder climbing of the hindered rotational mode, and the combination band excitation together explain the rotation of the acetylene molecule on Cu(100).

Lateral hopping and desorption of a single CO molecule on a Cu(110) surface induced by femtosecond laser pulses

Lateral hopping and desorption of a single CO molecule on a Cu(110) surface [Bartels et al., Science 305, 648 (2004)] induced by femtosecond laser pulses are studied using an indirect heat-transfer model. In addition to a direct heating of the reaction coordinate (RC) mode [frustrated translation (FT) mode for hopping and center-of-mass (CM) mode for desorption] by laser-generated hot electrons in the substrate, we consider an indirect heating of the RC mode through intermode coupling between the frustrated rotation (FR) mode and the RC mode. We calculate the transient behavior of the effective temperature of the FT and the CM modes, and of the normalized reaction yield. The experimental result of a ratio of the hopping yield along and across a row on a Cu(110) surface is nicely calculated. Although no information is available for the attempt frequency in a form of the Arrhenius equation for thermally activated reactions, it is predicted under which condition the desorption rate becomes in the same order of magnitude as the hopping rate, although the barrier height for desorption is much higher than for hopping. The present analysis highlights the role of excitation of the FR mode in reactions of a CO molecule as has been confirmed in the real-time observation [Backus et al., Science 310, 1790 (2005)].

Wavepacket Motion via a Conical Intersection in the Photochemistry of Aqueous Transition-Metal Dianions

The photochemical reaction paths in aqueous PtBr62– and OsBr62– have been studied by femtosecond broad-band pump–probe spectroscopy supported by CASPT2 and DFT/TDDFT calculations. These paths lead to the separation of negative charges and propagate through distortions of nascent, penta-coordinated metal fragments caused by Jahn–Teller C4v and D3h conical intersections (CIs), respectively. Within 150 fs following 420 nm excitation of PtBr62–, the molecule undergoes internal conversion and intersystem crossing into the dissociative lowest triplet excited 3T1g state, loses a ligand, and relaxes via the C4v CI to the nearly trigonal bipyramid 3PtBr5– product in the triplet state. Direct 530 nm excitation of PtBr62– to 3T1g yields the same product. Oscillations observed in the bending and umbrella a1 modes of 3PtBr5– arise from impulsive excitation of, respectively, one of the reaction coordinate modes, which is parallel to the gradient difference vector of the C4v CI, and the “spectator” mode that preserves the electronic degeneracy.

Insight into Action Spectroscopy for Single Molecule Motion and Reactions through Inelastic Electron Tunneling

We propose a versatile formula that describes action spectra for vibrationally mediated reactions of single molecules with a scanning tunneling microscope. Spectral fitting of the formula to CO hopping and the configurational change of the cis-2-butene molecule on Pd(110) enables us to determine the vibrational energy, reaction order, and transition rate associated with anharmonic coupling between the modes excited by tunneling electrons and the reaction-coordinate modes. The formula proposed here is general and easy to apply to any vibrationally mediated motion and reaction of single molecules.

A pictorial representation of zero‐point energy and tunnelling contributions to primary hydrogen isotope effects

AbstractThe interpretation of primary hydrogen isotope effects in terms of isotopic sensitivities of zero‐point energies in the reactants and transition state is reviewed. The reader is reminded that the transition state for a hydrogen transfer reaction corresponds to the position of maximum energy on the minimum energy path defined by the motion of the heavy atoms between which hydrogen is transferred. Tunnelling occurs through the potential energy barrier separating the reactant and product channels of the potential energy surface for this reaction. It is a consequence of rapid vibrational motion of the hydrogen within a collision complex and the overlap of vibrational wave functions between reactant and product sides of the barrier. Comparing zero‐point energies of a tunnelling complex and a hydrogen bond confirms results of calculations indicating that the zero‐point energy of the complex is likely to be less than that of the reactants. It follows that there should be a compensation between contributions from zero‐point energy changes and tunnelling which may explain why tunnelling rarely leads to very large isotope effects at ambient temperatures. The isotopic sensitivity of the zero‐point energy of the transition state is discussed in terms of variations in force constants of reacting bonds within a three‐centre model. A shift in isotopic sensitivity from the reaction coordinate mode to real stretching vibration as the structure of the transition state becomes more reactant‐ or product‐like, which provides a basis for the Westheimer effect, contrasts with the behaviour of hydrogen bonds, for which there is no change in isotopic sensitivity of the two stretching modes. Copyright © 2010 John Wiley & Sons, Ltd.

Reaction force constant and projected force constants of vibrational modes along the path of an intramolecular proton transfer reaction

We have explored the relationships between the reaction force F( ξ), the reaction force constant κ( ξ) and the projected force constants of the intramolecular proton transfer HO−N S → O N−SH along the intrinsic reaction coordinate ξ. The structural changes and energetics associated with the reaction are analyzed in terms of the three regions defined by F( ξ): reactant, transition and product. The significance of the similarity between κ( ξ) and the variation of the force constant associated to the reaction coordinate mode, k ξ ( ξ), is discussed in detail.

Action spectroscopy for single-molecule motion induced by vibrational excitation with a scanning tunneling microscope

We propose an action spectroscopy for single-molecule motion induced by vibrational excitation with a scanning tunneling microscope (STM). Calculations of the inelastic tunneling current for excitation of the C-O stretch mode of the CO molecule on metal surfaces are combined with a theory which describes how the energy in the vibrational mode is transferred to a reaction coordinate mode to overcome the activation barrier. The calculated rate for CO hopping on Pd (110) as a function of the bias voltage agrees with the experimental result. It is proposed that the second derivative of the reaction rate with respect to the bias voltage is related to the vibrational density of states, which usually cannot be directly observed in STM inelastic electron tunneling spectroscopy when a molecule motion is induced by vibrational excitation.

Two-electron processes of desorption of a single ammonia molecule from Cu(1 0 0)

Novel two-electron processes are proposed for the desorption of a single ammonia molecule (NH 3) chemisorbed on a Cu(1 0 0) surface as induced by an inelastic tunneling current with the scanning tunneling microscope. According to density functional theory calculations, it is found that a single excitation of the high-frequency (HF) symmetric N–H stretch mode (408 meV) can induce the lateral translation of NH 3 via the transfer of energy to the frustrated-translation mode. In order to overcome the 600 meV desorption barrier, a double excitation of the symmetric N–H stretch mode is needed. A rate equation approach is employed to study different elementary processes for NH 3 desorption following the double excitation of the N–H mode by two tunneling electrons. After the double excitation of the HF mode, two possible reaction paths are possible: either the HF mode de-excites once creating and intermediate state with excited HF and reaction-coordinate (RC) modes that after decay leads to desorption, or the HF mode completely de-excites in the RC mode leading to desorption. In the first scenario, when the vibrational damping rate of the RC mode is lower than that of the HF mode, the intermode coupling from the excited state activates the RC mode above the barrier with help of energy transfer from the HF mode. Both, mode decay and intermode coupling, are made possible by energy transfer to the continuum of electronic excitations of the metallic surface: the electron–hole pair excitations.

Elementary processes of vibrationally mediated motions of single adsorbed molecules

Elementary processes of motions of single adsorbed molecules on metal surfaces induced by inelastic tunneling currents with scanning tunneling microscope are discussed in conjunction with novel experimental results. A coherent multiple-step vibrational ladder climbing following a direct excitation of the reaction coordinate (RC) mode, or an indirect excitation of the RC mode through the anharmonic coupling to the high-frequency mode excited by tunneling electrons, to overcome the potential barrier along the RC associated with the relevant motions are combined to gain a deep insight into how competing different reaction pathways can be selectively activated within a single adsorbed molecule.

Theoretical state-of-the art in adsorbate motions and reactions induced by inelastic tunneling current with STM

Current understanding of the physical mechanisms of motion and reaction of single adsorbates induced by inelastic tunneling current with scanning tunneling microscope (STM) is described in relation to various novel experimental results. It is a central issue to elucidate how the energy stored in the specific vibrational mode excited by tunneling electrons activates the configurational change of an adsorbate, in competing with the vibrational relaxation. There are two reaction paths, i.e., direct or indirect excitation of the reaction coordinate (RC) mode to overcome the relevant potential barrier. This includes vibrational ladder climbing in the potential well following a direct excitation of the RC mode, and indirect excitation of the RC mode through its anharmonic coupling to the vibrational mode excited by tunneling electrons. A unified picture is proposed for a qualitative scenario of mode selective control of different motions of single adsorbates by a combination of bias voltage and tunneling current.

Motions and Reactions of Single Adsorbed Molecules Induced by Vibrational Excitation with STM

Recent progress in the study of motions and reactions of single adsorbed molecules on metal surfaces induced by inelastic tunneling electrons with a scanning tunneling microscope (STM) is given an overview, with the focus on our current theoretical understanding of the elementary processes behind these phenomena. The selected topics include rotation and dissociation of O 2 on Pt (111), rotation of a C 2 H(D) 2 on Cu (100), lateral hopping of CO on Pd (110), lateral translation and desorption of NH 3 on Cu (100), and controlled manipulation of chemical transformation as well as bimolecular reaction of coadsorbed species on metal surfaces. Brief descriptions are presented of how an adsorbate to overcome the potential barrier for motion and reaction by incoherent stepwise and coherent single multistep climbing of the vibrational ladders in the potential well along the reaction coordinate, and indirect excitation of the reaction coordinate mode via anharmonic coupling to the vibrational mode excited by tunneling current. Elementary processes of the mode-selective control of different motions are also discussed in conjunction with a recent experimental result of lateral hopping and desorption of a single NH 3 molecule on Cu (100). Although still at a premature stage, these novel phenomena open a new world of "nano-surface-science," in which the manipulation and reaction of single adsorbates, and synthesis of a new molecular system are realized by a selective excitation of the relevant vibrational mode by tunneling electrons with an STM.

Unimolecular reaction dynamics of HSO. Analysis of the influence of different barrier samplings on the product energy distributions

Classical dynamics calculations are reported for the lowest energy unimolecular reaction channels of HSO. A recently published single-valued DMBE potential energy surface for HSO was employed in the dynamics calculations. The results predict that the isomerization channel HSO→HOS is the preferred one at the lowest energies of the study, while dissociation to give H+SO is increasingly important as the energy rises. For the energies selected, the vibrational coupling is not strong enough to keep the phase space uniform during the unimolecular dynamics. In addition, strong mode specific effects were found under initial excitation of the three normal modes of vibration. The product energy distributions obtained with classical and quasi-classical barrier sampling techniques are very similar. The results predicted by EMS (with and without ZPE restrictions) initialization at the barrier show a much higher vibrational energy content of the products than those obtained by the above sampling techniques. This arises from the separability of the reaction coordinate mode inherent to the QCBS and CBS models.

RISM-SCF study for the rate constant of S N2 reaction CH 3Cl+Cl − in aqueous solution

A method is proposed to evaluate the Grote–Hynes transmission coefficient based on the reference interaction site model self-consistent field (RISM-SCF) electronic structure calculations of reacting solute molecules combined with molecular dynamics simulation calculations of bulk solvent. The time dependent solvent friction acting on the reaction coordinate mode is derived using the linear response approximation. An application of the present method is made to the S N 2 reaction CH 3Cl+Cl − in aqueous solution. The transmission coefficient is calculated to be 0.71, which is consistent with the previous simulation studies.

A b i n i t i o calculation of transition state normal mode properties and rate constants for the H(T)+CH4(CD4) abstraction and exchange reactions

We present ab initio (GVB–POL–CI) calculations for enough of the region about the abstraction and exchange saddle points for H(T)+CH4(CD4) to perform a full normal mode analysis of the transition states. The resulting normal mode frequencies are compared to four other published surfaces: an ab initio UHF–SCF calculation by Carsky and Zahradnik, a semiempirical surface by Raff, and two semiempirical surfaces by Kurylo, Hollinden, and Timmons. Significant quantitative and qualitative differences exist between the POL–CI results and those of the other surfaces. Transition state theory rate constants and vibrationally adiabatic reaction threshold energies were computed for all surfaces and compared to available experimental values. For abstraction, the POL–CI rates are in good agreement with experimental rates and in better agreement than are the rates of any of the other surfaces. For exchange, uncertainties in the experimental values and in the importance of vibrationally nonadiabatic effects cloud the comparison of theory to experiment. Tentative conclusions are that the POL–CI barrier is too low by several kcal. Unless vibrationaly nonadiabatic effects are severe, the POL–CI surface is still in better agreement with experiment than are the other surfaces. The rates for a simple 3-atom transition state theory model (where CH3 is treated as an atom) are compared to the rates for the full 6-atom model. The kinetic energy coupling of reaction coordinate modes to methyl group modes is identified as being of primary importance in determining the accuracy of the 3-atom model for this system. Substantial coupling in abstraction, but not exchange, causes the model to fail for abstraction but succeed for exchange.

Model calculations of primary hydrogen isotope effects

Model calculations of primary hydrogen isotope effects for four and five-centre transition states, taking account of bending vibrations and proton tunnelling, are reported. The results reinforce those based on consideration of stretching vibrations alone, and suggest that both zero-point energy and tunnelling contributions are at a maximum for a symmetrical transition state. For proton transfer to halide ions, large isotope effects persist for product-like transition states owing to the low frequency of hydrogen bending vibrations. Swain's relation between deuterium and tritium isotope effects is well obeyed. It seems better to consider the reaction co-ordinate mode for an atom transfer reaction as deriving from a translation rather than from a vibration in the reactants.