Geometric analysis of anharmonic downward distortion following paths

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2^{f + 1} ? 2 , where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H₂O molecule in which pitchfork bifurcation is observed.     

Fast hydrogen elimination from the [Ru(PH3)3(CO)(H)2] complex in the first singlet excited states. A quantum dynamics study

The photodissociation dynamics of [Ru(PH₃)₃(CO)(H)₂] complex in the lowest two singlet excited electronic states has been theoretically analyzed. Reduced two-dimensional potential energy surfaces (PES) are built up by combining a time-dependent method to calculate the excited states energy with DFT (B3LYP) electronic calculations of the ground state. By means of a Fast Fourier Transform (FFT) algorithm the time evolution of the wavefunction upon vertical transition from the minimum of the ground state to both diabatic states has been followed. The propagation in S₁, the lowest in energy at the vertical transition point and the one with a larger transition probability from the ground state, discloses that the system is not evolving from the initial position at least in the time spanned by the calculations. Conversely the H₂ elimination is very fast (about 37 fs) in the S₂ state. In this state the vertical transition puts the system in a purely dissociative zone of the PES. In that state FFT results indicate that the lengthening of the Ru–H₂ distance and the shortening of the H–H one are taking place almost simultaneously.     

Mechanism of ketone hydrosilylation by Cu(I) catalysts: A theoretical study

The plausibility of the catalytic cycle suggested for the hydrosilylation of ketones by Cu(I) hydrides has been investigated by a theoretical DFT study. A model system made up of a CuH(PH₃)₂ catalyst, acetone and SiH₄ gives us the necessary insight into the intrinsic reactivity of the system. This reactivity is confirmed, by introducing the more rigid CuH[C₄H₄(PH₂)₂] catalyst, as well as tetra-coordinated, CuH(PH₃)₃ and CuH(PH₃)[C₄H₄(PH₂)₂] compounds. Computations show the activation of the copper fluoride pre-catalyst, as well as both steps of the catalytic cycle to involve a 4 center metathesis transition state as suggested in literature. These results show the reaction to be favored by the formation of a Van der Waals complex resembling the transition states. The formation of these latter is induced by stabilizing electrostatic interactions between those atoms involved in the bond breaking and bond forming. Both steps of the actual catalytic cycle show a free energy barrier of about 10 kcal/mol with respect to the isolated reactants, hereby confirming the plausibility of the suggested cycle. We have found a substantial overall exothermicity of the catalytic cycle of about 35 kcal/mol.     

Pseudorotation of trigonal bipyramidal molecules: Berry rotation contra “turnstile” rotation in PF5

The energy surface for the intramolecular nuclear motion in PF₅ is analysed with the aid of a modified CNDO/2 procedure. It is shown that intramolecular exchange of equatorial and apical fluorine atoms can only take place by a Berry pseudorotation mechanism and that the alternative “turnstile” processes correspond to special realization of rearrangement pathways in that “reaction valley“.     

Properties of variational transition states for association reactions

The relationships between the structures of microcanonical variational transition states for association reactions and potential energy surface properties are analyzed. The analysis is facilitated by the recent finding that in many cases the vibrational frequencies for the transitional modes in the association reaction vary exponentially with the reaction coordinate. An increase in the attenuation of the transitional mode frequencies results in a tighter transition state. Long-range minimum energy path potentials of the form −c/r″ have only one transition state at each energy. Certain types of association reactions may not have transition states.     

An ab initio investigation into the SN2 reaction: Frontside attack versus backside attack in the reaction of F− with CH3F

The energy hypersurface for the attack of fluoride ion on methyl fluoride has been explored with ab initio LCAO-SCF calculations at a split-valence basis set level. Transition states for frontside and backside attack have been located. In addition to transition states, two possible F^–-CH₃F clusters have been identified. The transition state for the substitution of fluoride with retention of configuration is found to be 56 kcal/mol higher than the transition state for inversion of configuration. The transition state for hydride displacement with inversion is 62 kcal/mol above the transition state for fluoride substitution with inversion.     

On the ion‐pair dissociation mechanisms in the small NaCl·(H2O)6 cluster: A perspective from reaction path search calculations

We performed reaction path search calculations for the NaCl·(H₂O)₆ cluster using the global reaction route mapping (GRRM) code to understand the atomic‐level mechanisms of the NaCl → Na⁺ + Cl⁻ ionic dissociation induced by water solvents. Low‐lying minima, transition states connecting two local minima and corresponding intrinsic reaction coordinates on the potential energy surface are explored. We found that the Na Cl distances at the transitions states for the dissociation pathways were distributed in a relatively wide range of 2.7–3.7 Å and that the Na Cl distance at the transition state did not correlate with the commonly used solvation coordinates. This suggests that the definition of the transition states with specific structures as well as good reaction coordinate is very difficult for the ionic dissociation process even in a small water cluster. © 2018 Wiley Periodicals, Inc.     

Theoretical study of potential energy surface and vibrational spectra of ArF2 system

Anab initio potential energy surface (PES) of ArF₂ system has been obtained by using MP4 calculation with a large basis set including bond functions. There are two local minimums on the PES: one is T-shaped and the other is L-shaped. The L-shaped minimum is the global minimum with a well depth of -119.62 cm^-1 atR = 0.3883nm. The T-shaped minimum has a well depth of -85.93cm^-1 atR = 0.3486 nm. A saddle point is found atR = 0.3486 and τ = 61° with the well depth of -61.53 cm^-1. The vibrational energy levels have been calculated by using VSCF-CI method. The results show that this PES supports 27 vibrational bound states, and the ground states are two degenerate states assigned to the L-type vibration.     

Ab initio calculations on the barrier to pseudorotation of model 2′-deoxyfuranose and 2′-deoxy-2′-fluorofuranose rings

Model ring systems 2′-deoxy-2′-fluororibofuranose and deoxyribofuranose have been investigated using ab initio calculations with the 3–21G basis set. The energy barrier to pseudorotation between the N and S states has been evaluated for the three preferred orientations of the (3′)-OH group. Positions of the energy minima and the transition state have been optimized with respect to the (3′)-OH orientation. The barrier to pseudorotation of 2′-deoxy-2′-fluorofuranose is high and asymmetrical (ΔE_N→S ≈ 20, ΔE_N←S ≈ 8 kJ/mol), whereas the barrier of 2′-deoxyfuranose is lower and almost symmetrical (ΔE ≈ 11–12 kJ/mol). The results obtained show that the preferred configuration of the 2′-deoxy-2′-fluororibo-furanose (N state) is stabilized by an internal O(3′)-H…?F interaction in accord with the crystallo-graphic data.     

Exploring the potential energy hypersurface of histamine monocation: Tautomerism in gas phase

The potential energy hypersurface of the histamine monocation is determined by ab initio methods at the STO -4G level using analytical gradient techniques. Three transition states and two minima have been found for the N_τ? H tautomer. One of the transition states connects the trans conformational region with a minimum gauche structure, where the proton of the ammonium group is approximately halfway between the N_π of the imidazole group and the N of the ammonium group, but nearer to the N_π. This minimum connects the potential energy surface of the N_τ? H tautomer with the imidazolium one. In the latter region, three transition states and two minima have been found. Critical points are discussed in relation with experimental data and histamine H₂ receptor models.     

Potential energy surface and proton HFI constants of the cyclopentane radical cation

According to the data of UB3LYP/6-31G* and UMP2/cc-pVTZ calculations, the adiabatic potential energy surface of the cyclopentane radical cation is very intricate and combines six types of stationary structures of C _s and C ₂ symmetry. Ten equivalent C _s structures with the totally symmetric electronic state (C _s (² A′)) correspond to global minima. Conformational transitions between the global minima occur along the inversion and pseudorotation coordinates, for each pair of minima the conformational transition occurring in one stage (through the only transition state). The inversion barrier is ～2 kcal/mol; pseudorotation barriers are ～4–8 kcal/mol. The structure of the potential surface provides the interpretation of the EPR data as a result of dynamic averaging over 20 C _s (² A′) and C ₂ (² A) stationary structures.     

The insertion and H<Subscript>2</Subscript> elimination reactions of H<Subscript>2</Subscript>GeFMgF germylenoid with RH (R = Cl,SH, PH<Subscript>2</Subscript>)

In present paper, the insertion and H₂ elimination reactions of H₂GeFMgF germylenoid with RH (R = Cl, SH, PH₂) were investigated by means of B3LYP and QCISD calculation methods. One transition state and one intermediate were found along the potential energy surface in each insertion reaction, while for the H₂ elimination reactions, only one transition state was found between the reactants and products in each reaction process. Both for the insertion and H₂ elimination reactions, RH reactivity increases in the following order: H–Cl > H–SH > H–PH₂. The insertion and H₂ elimination reactions were compared, and the results demonstrated that the H₂ elimination should be more favorable than the corresponding insertion. The solvent effects on these two types of reactions were considered. The calculated results indicated that the solvents could accelerate the reactions by reducing their barrier heights.     

An analytic hindered rotor model for calculating microcanonical variational unimolecular rate constants from reaction path properties

A model is proposed for performing microcanonical variational transition state theory calculations which incorporates ideas from vibrator and flexible variational transition state models. Vibrational frequencies, moments of inertia, and potential energy for the variational transition state are found by reaction path following as for the vibrator model. However, the transitional modes are treated as hindered rotors using an analytic potential and an analytic density of states, which are fit to barriers for hindered rotation determined from reaction path following. The model proposed here differs from the flexible transition state model in that the density of states for the transitional modes is analytic and transitional modes and external rotational angular momenta are uncoupled. For the H + CH₃ ? CH₄ system, rate constants calculated with this new model are only 6–23% smaller on average from those of the flexible transition state model for values of total angular momentum which correspond to average rotational temperatures of 0–2000 K. Harmonic frequencies calculated for the transitional modes from the hindered rotor Hamiltonian are in good agreement with the exact values found by a reaction path analysis. © 1994 John Wiley & Sons, Inc.     

Potential energy curves and photochemical cis-trans isomerism in styrene

Cis-trans photoisomerism of styrene is investigated from a theoretical point of view. Curves of the potential energy as a function of the rotation angle (ω) around the ethylenic bond were obtained for the ground state and a few excited states by the CIPSI PCILO method. The potential surface of the lowest excited singlet is found to have both an absolute minimum at ω = π/2 and a small relative minimum at ω = 0. These findings are consistent with the singlet mechanism for the direct cis-trans photoconversion. The origin of the two energy minima in the S₁ potential surface is explained in terms of weights of the local excitations in the zero-order wavefunction.     

Covalent-ionic nature of the potential energy surface of the Li-CO2 complex

Unrestricted Hartree-Fock calculations with large basis sets, including d-functions, and the estimation of the correlation energy, show that the potential energy surface for the Li-CO₂ complex is built from the crossing of two states, each of them corresponding to a different electron arrangement. One has a strong ionic character and the other is of van der Waals type. Each portion of the energy surface presents a minimum, which is stable in respect to the dissociation limit.     

Electronic structure and the hydrogen-shift isomerization of hydrogen nitryl HNO2

Summary Electronic structure of hydrogen nitryl HNO₂, a yet not identified entity, and the path of its possible isomerization totrans-HONO have been investigated byab initio SCF and MRD-CI computations using the 6-31G** basis set. HNO₂ isC _2v -symmetric and its ground state (¹ A ₁) is less stable thantrans-HONO by 66 kJ/mol (with the SCF vibrational zero-point energy correction). The lowest two excited singlet states (¹ A ₂ and¹ B ₁) are nearly degenerate, their vertical excitation energies being predicted to be 4.8 eV. The isomerization path is traced by the CASSCF procedure and the activation barrier height is evaluated by the CI treatment. HNO₂ in its ground state isomerizes totrans-HONO by maintaining the planar (C _s-symmetric) structure. The activation energy is calculated to be 171 kJ/mol, which is clearly lower than the calculated H-N bond energy (253 kJ/mol). The transition state seems to be more adequately described as an interacting system of proton and the nitrite anion rather than as a pair of two fragment radicals.     

Exploring the Reaction Paths on the Potential Energy Surfaces of the S1 and T1 States in Methylenecyclopropane

The reaction paths of methylenecyclopropane 1 on the potential energy surfaces (PESs) of the lowest triplet (T₁) state and the lowest excited singlet (S₁) state, as well as that of the ground state (S₀), were explored by using the nudged elastic band method at the MRMP2//MCSCF/6‐31++G(d,p) and DFT(B3LYP)/6‐31++G(d,p) levels of theory. After vertical excitation of 1, three transition states on the PES of the lowest triplet state and one transition state on the S₁ PES were found along the reaction path to produce a carbene, cyclobutylidene 2. All of these transition states are lower in energy than the S₁ state produced by vertical excitation at the S₀ energy minimum in 1. Fast transition is predicted to occur from the T₁ state or from the S₁ state to the S₀ state due to strong spin‐orbit coupling or nonadiabatic coupling in the geometrical vicinity of 2. On the MRMP2 S₀ PES, the energy barriers of 5.0, 10.3 and 13.5 kcal mol^?1 were obtained for C migration reaction (backward reaction), 1,2‐H migration reaction to cyclobutene 3, and 1,3‐H migration reaction to bicyclopropane 4, respectively, started at 2. The introduction of phenyl groups makes the energy barriers smaller due to the π conjugation between the carbene center and phenyl groups.     

Cycloreversion of cyclobutanes

Semiempirical MO calculations with the method SINDO1 were performed to study the potential energy surface of cyclobutane and several substituted cyclobutanes with substituents F, OCH₃ and CN. The reaction pathway with the lowest activation energy leading to two ethylenic fragments is nonconcerted. One carbon bond is broken after symmetric opening of two adjacent bond angles and twisting of the carbon framework. The first transition state is asymmetric and diradicaloid. The reaction proceeds to a diradicaloid, non-zwitterionic intermediate. The second transition state is characterized by bond breaking of the inner carbon-carbon bond. For the unsubstituted case, the barrier for free rotation of the outer methylenic groups was also calculated. In comparison, the unsubstituted reaction is characterized by transition states of almost equal energy, whereas in the substituted reactions the barriers for the second bond breaking are much higher than for the first bond breaking step.     

Relativity and the Jahn–Teller,Berry pseudorotations of TBP clusters: group theory,spin–orbit and combinatorial nuclear spin statistics of TBP Desargues–Levi isomerization graph

Jahn–Teller and Berry pseudorotations in transition metal and main group clusters such as Hf₅, Ta₅, W₅ and Bi₅ are interesting because of the competition between relativistic effects and pseudorotations. Topological representations of various isomerization pathways arising from the Berry pseudorotation of pentamers constitute the edges of the Desargues–Levi graph. We have computed the combinatorics for multinomial colorings of the vertices, edges and 10-faces of the Desargues–Levi isomerization graph for all irreducible representations and the nuclear spin statistics of spin-7/2 ¹⁸¹Ta₅ as well as the TBP composite cluster particles. Topological insights into Jahn–Teller and Berry pseudorotations and relativistic effects are provided.     

U+与CO2气相反应的密度泛函理论研究

运用密度泛函理论(DFT)中的B3LYP方法,U原子用含相对论有效原子实势(ECP)校正的基组(SDD),C、O原子采用6-311+G(d)基组,对气相中U+和CO2的反应进行了理论研究.通过研究二重和四重自旋态的反应势能面(PESs),优化得到了两条反应路径的反应物、中间体、过渡态和产物的结构.用"两态反应"(TSR)分析反应机理,结果表明体系的优先选择路径为高自旋态进入和低自旋态离开反应,发生在四重态和二重态的自旋多重度的改变使得整个反应系统能以一个低能反应途径进行.