Double-well Potential Energy Surface Research Articles

Solvent Polarity Effects on the Mechanochemistry of Spiropyran Ring Opening.

The spiropyran mechanophore (SP) is employed as a reporter of molecular tension in a wide range of polymer matrices, but the influence of surrounding environment on the force-coupled kinetics of its ring opening has not been quantified. Here, we report single-molecule force spectroscopy studies of SP ring opening in five solvents that span normalized Reichardt solvent polarity factors (ETN) of 0.1-0.59. Individual multimechanophore polymers were activated under increasing tension at constant 300 nm s-1 displacement in an atomic force microscope. The extension results in a plateau in the force-extension curve, whose midpoint occurs at a transition force f* that corresponds to the force required to increase the rate constant of SP activation to approximately 30 s-1. More polar solvents lead to mechanochemical reactions that are easier to trigger; f* decreases across the series of solvents, from a high of 415 ± 13 pN in toluene to a low of 234 ± 9 pN in n-butanol. The trend in mechanochemical reactivity is consistent with the developing zwitterionic character on going from SP to the ring-opened merocyanine product. The force dependence of the rate constant (Δx‡) was calculated for all solvent cases and found to increase with ETN, which is interpreted to reflect a shift in the transition state to a later and more productlike position. The inferred shift in the transition state position is consistent with a double-well (two-step) reaction potential energy surface, in which the second step is rate determining, and the intermediate is more polar than the product.

Cover Feature: Photoinduced Intervalence Charge Transfers: Spectroscopic Tools to Study Fundamental Phenomena and Applications (ChemPhysChem 20/2022)

The Cover Feature shows a molecule that forms, upon photon absorption, an excited state mixed valence system, which is characterized by a double-well potential energy surface. Inspection of the excited state with light reveals photoinduced intervalence charge transfers. More information can be found in the Concept by Alejandro Cadranel and co-workers.

Traversing Double-Well Potential Energy Surfaces: Photoinduced Concurrent Intralayer and Interlayer Structural Transitions in XTe2 (X = Mo, W)

The microscopic arrangement of atoms and molecules is the determining factor in how materials behave and perform; i.e., the structure determines the property, a traditional paradigm in materials science. Photoexcitation-driven manipulation of the crystal structure and associated electronic properties in quantum materials provides opportunities for the exploration of exotic physics and practical applications; however, a generalized mechanism for such symmetry engineering is absent. Here, by ultrafast electron diffraction, structure factor calculation, and TDDFT-MD simulations, we report the photoinduced concurrent intralayer and interlayer structural transitions in the Td and 1T' phases of XTe2 (X = Mo, W). We discuss the modification of multiple quantum electronic states associated with the intralayer and interlayer structural transitions, such as the topological band inversion and the higher-order topological state. The twin structures and the stacking faults in XTe2 are also identified by ultrafast structural responses. The comprehensive study of the ultrafast structural response in XTe2 suggests the traversal of all double-well potential energy surfaces (DWPES) by laser excitation, which is expected to be an intrinsic mechanism in the field of photoexcitation-driven global/local symmetry engineering and also a critical ingredient inducing the exotic properties in the non-equilibrium state in a large number of material systems.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces.

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Analytical gradients for nuclear–electronic orbital multistate density functional theory: Geometry optimizations and reaction paths

Hydrogen tunneling plays a critical role in many biologically and chemically important processes. The nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed to describe hydrogen transfer systems. In this approach, the transferring proton is treated quantum mechanically on the same level as the electrons within multicomponent DFT, and a nonorthogonal configuration interaction scheme is used to produce delocalized vibronic states from localized vibronic states. The NEO-MSDFT method has been shown to provide accurate hydrogen tunneling splittings for fixed molecular systems. Herein, the NEO-MSDFT analytical gradients for both ground and excited vibronic states are derived and implemented. The analytical gradients and semi-numerical Hessians are used to optimize and characterize equilibrium and transition state geometries and to generate minimum energy paths (MEPs), for proton transfer in the deprotonated acetylene dimer and malonaldehyde. The barriers along the resulting MEPs are lower when the transferring proton is quantized because the NEO-MSDFT method inherently includes the zero-point energy of the transferring proton. Analysis of the proton densities along the MEPs illustrates that the proton density can exhibit symmetric or asymmetric bilobal character associated with symmetric or slightly asymmetric double-well potential energy surfaces and hydrogen tunneling. Analysis of the contributions to the intrinsic reaction coordinate reveals that changes in the C-O bond lengths drive proton transfer in malonaldehyde. This work provides the foundation for future reaction path studies and direct nonadiabatic dynamics simulations of a wide range of hydrogen transfer reactions.

Boron Tunneling in the "Weak" Bond-Stretch Isomerization of N-B Lewis Adducts.

Some nitrile-boron halide adducts exhibit a double-well potential energy surface with two distinct minima: a "long bond" geometry (LB, a van der Waals interaction mostly based on electrostatics, but including a residual charge transfer component) and a "short bond" structure (SB, a covalent dative bond). This behavior can be considered as a "weak" form of bond stretch isomerism. Our computations reveal that complexes RCN-BX3 (R=CH3 , FCH2 , BrCH2 , and X=Cl, Br) exhibit a fast interconversion from LB to SB geometries even close to the absolute zero thanks to a boron atom tunneling mechanism. The computed half-lives of the meta-stable LB compounds vary between minutes to nanoseconds at cryogenic conditions. Accordingly, we predict that the long bond structures are practically impossible to isolate or characterize, which agrees with previous matrix-isolation experiments.

On the Role of Hydrogen Bonding in Gas-Phase SN2 Reactions at Silicon.

The shape of the potential energy surface (PES) of gas-phase SN2 reactions at silicon is determined by the type of nucleophile, the leaving group, and substituents which remain bonded to silicon. In this study, we present PES scans along the reaction coordinate of six symmetrical SN2 reactions: X- + SiR3X → XSiR3 + X-, where X = Cl or F and R = H, Me, or OMe. While the fluorine systems and the ClSiH3Cl system only give single-well PESs, ClSiMe3Cl and ClSi(OMe)3Cl give triple- and double-well PESs with stable pre- and post-reaction complexes. A complementary bonding analysis (energy decomposition analysis, quantum theory of atoms in molecules, and natural bond orbitals) reveals that the leaving group (X-) is stabilized by hydrogen bonding in the XSiMe3X and XSi(OMe)3X systems. It is shown that this so far neglected stabilizing contribution, along with σ-hole bonding, is responsible for the shapes of the PESs of ClSiMe3Cl and ClSi(OMe)3Cl in the gas phase.

Tunable quadruple-well ferroelectric van der Waals crystals.

The family of layered thio- and seleno-phosphates has gained attention as potential control dielectrics for the rapidly growing family of two-dimensional and quasi-two-dimensional electronic materials. Here we report a combination of density functional theory calculations, quantum molecular dynamics simulations and variable-temperature, -pressure and -bias piezoresponse force microscopy data to predict and verify the existence of an unusual ferroelectric property-a uniaxial quadruple potential well for Cu displacements-enabled by the van der Waals gap in copper indium thiophosphate (CuInP2S6). The calculated potential energy landscape for Cu displacements is strongly influenced by strain, accounting for the origin of the negative piezoelectric coefficient and rendering CuInP2S6 a rare example of a uniaxial multi-well ferroelectric. Experimental data verify the coexistence of four polarization states and explore the temperature-, pressure- and bias-dependent piezoelectric and ferroelectric properties, which are supported by bias-dependent molecular dynamics simulations. These phenomena offer new opportunities for both fundamental studies and applications in data storage and electronics.

Modeling the action of environment on proton tunneling in the adenine–thymine base pair

Effect of environment coupling on the quantum-biological phenomenon of proton tunneling in the hydrogen bonds of the adenine–thymine base pair in DNA was modeled within the framework of quantum statistics and perturbation theory. A number of important thermodynamic indicators including partition function, free energy, and entropy were then calculated and examined. The proton was then assumed to be subject to an attraction represented by a double-well potential energy surface with a small asymmetry, which was considered as the perturbation introduced to the system. The action of environment manifested itself in the form of a global minimum in the free energy curve, as an implicit implication of the tendency of the system toward randomness and disorder, at which no spontaneous change such as quantum tunneling will accordingly occur. Furthermore, assuming the free energy to be in a close neighborhood of its minimum truly explained the smallness of the contribution of environment coupling to the tunneling probability reported in the literature based on the fact that the closer the free energy to its minimum, the less the transition probability to this point.

Double-well potential energy surface in the interaction between h-BN and Ni(111).

Density functional theory calculations with non-local correlation functionals, properly accounting for dispersion forces, predict the presence of two minima in the interaction energy between h-BN and Ni(111). These can be described as a physisorbed state with no corrugation of the h-BN structure, and a chemisorbed state exhibiting noticeable corrugation and a shorter distance of h-BN to the metallic support. The latter corresponds indeed to the one reported in most experiments. The relative stability of the two minima depends on the specific density functional employed: of those investigated here only optB86b-vdW yields the correct order of stability. We also demonstrate that the effect of the metal support on the Raman frequency of the chemisorbed boron nitride monolayer cannot be reduced to the associated strain. This is important because the Raman frequency has been proposed as a signature to identify h-BN monolayers from multilayered samples. Our analysis shows that such signatures would be strongly dependent on the nature of the interaction between the support and h-BN.

Photoelectron Spectroscopy of the Methide Anion: Electron Affinities of (•)CH3 and (•)CD3 and Inversion Splittings of CH3(-) and CD3(-).

We report high-resolution photoelectron spectra of the simplest carbanions, CH₃⁻ and CD₃⁻. The vibrationally resolved spectra are dominated by a long progression in the umbrella mode (ν₂) of ˙CH₃ and ˙CD₃, indicating a transition from a pyramidal C(3v) anion to the planar D(3h) methyl radical. Analysis of the spectra provides electron affinities of ˙CH₃ (0.093(3) eV) and ˙CD₃ (0.082(4) eV). These results enable improved determination of the corresponding gas-phase acidities: Δ(acid)H(0K)°(CH₄) = 414.79(6) kcal/mol and Δ(acid)H(0K)°(CD₄) = 417.58(8) kcal/mol. On the basis of the photoelectron anisotropy distribution, the electron is photodetached from an orbital with predominant p-character, consistent with the sp³-hybridized orbital picture of the pyramidal anion. The double-well potential energy surface along the umbrella inversion coordinate leads to a splitting of the vibrational energy levels of the umbrella mode. The inversion splittings of CH₃⁻ and CD₃⁻ are 21(5) and 6(4) cm⁻¹, respectively, and the corresponding anion umbrella vibrational frequencies are 444(13) and 373(12) cm⁻¹, respectively. Quantum mechanical calculations reported herein show good agreement with the experimental data and provide insight regarding the electronic potential energy surface of CH₃⁻.

Dynamic Behavior of Hydrogen in Transition Metal Bis(silyl) Hydride Complexes

A series of rhodium complexes CpRh(SiMe2X)2(SiMe3)(H) (X = Me, Cl, Br, I), Cp1–Cp4, CpRh(SiMe2X)2(PMe3)(H)+ (X = Me, Cl, Br, I), Cp5–Cp8, CpRh(SiMe3)2(SiF3)(H), Cp9, CpRh(SiMe3)2(SiH3)(H), Cp10, TpRh(SiH3)2(SiMe3)(H), Tp1, TpRh(SiH3)2(PMe3)(H)+, Tp2, and TpRh(SiF3)2(PMe3)(H)+, Tp3, were studied computationally to understand the hydrogen behavior in the Si···H···Si moiety. The hydride ligand interacts with at least one of the silyls, and in many cases with both, but is located asymmetrically with regard to them, giving rise to a double-well potential energy surface (PES) for hydrogen motion. The hydrogen transfer barriers ΔE vary from 0.03 to 3 kcal·mol–1. For selected complexes Tp1, Tp2, Tp3, and Cp9 the three-dimensional PESs were constructed and the vibrational Schrödinger equation was solved. The PES is highly anharmonic in all four cases. The hydrogen is delocalized between two silicons in complexes Tp1, Tp3, and Cp9, but localized around the energy minima in complex Tp2. Complex Tp3 is an intermediate case with a substantial tunneling. The delocalized behavior is pertinent to systems with ΔE < 0.25 kcal·mol–1. For complexes Tp1, Tp2, Tp3, and Cp9 the J(Si–H) spin–spin coupling constants were calculated taking into account the vibrational motion of hydride. For Tp1, Tp3, and Cp9 both J(Si1–H) and J(Si2–H) are negative due to simultaneous Si1···H···Si2 interactions, while for Tp2J(Si2–H) is positive, indicating a single Si···H interaction only. Negative J(Si–H) values were obtained even for Si···H distances as large as 2.3 Å (complex Tp3). A possible effect of vibrations on the J(Si–H) values is also discussed.

Theoretical Study of Nucleophilic Identity Substitution Reactions at Nitrogen, Silicon and Phosphorus versus Carbon: Reaction Pathways, Energy Barrier, Inversion and Retention Mechanisms

AbstractGas‐phase identity SN2(N), SN2(Si) and SN2(P) versus SN2(C) reactions with Cl− are investigated by the ab initio method. Front‐side attack identity SN2 reactions considered have all double‐well potential energy surfaces (PES), and back‐side attack identity SN2(C) and SN2(N) reactions have also double‐well PES, while back‐side attack identity SN2(Si) and SN2(P) have single‐well PES. In addition, the geometrical transformations, potential energy profiles of front‐side and back‐side attack identity SN2(N), SN2(Si) and SN2(P) versus SN2(C) reactions based on the IRC calculations are described, the differences between them for the front‐side or back‐side attack reactions have been demonstrated.

Yb 2 + -doped SrCl2: Electronic structure of impurity states and impurity-trapped excitons

First-principles electronic structure calculations of the excited states of Yb(2+)-doped SrCl(2) crystals up to 65,000 cm(-1) reveal the existence of unexpected excited states with double-well potential energy surfaces and dual electronic structure lying above and very close in energy to the 4f(13)5d manifold, with which they interact strongly through spin-orbit coupling. The double-well energy curves result from avoided crossings between Yb-trapped exciton states (more stable at short Yb-Cl distances) and 4f(13)6s impurity states (more stable at long Yb-Cl distances); the former are found to be preionization states in which the impurity holds the excited electron in close lying empty interstitials located outside the YbCl(8) moiety. Spin-orbit coupling between the double-well states and the lower lying 4f(13)5d impurity states spreads the dual electronic structure character to lower energies and, hence, the instability of the divalent oxidation state is also spread. To some extent, the dual electronic structure (impurity-trapped exciton-impurity state) of some excited states expresses and gives support to hypotheses of interaction between Yb(2+) and Yb(3+) pairs proposed to understand the complex spectroscopy of the material and conciliates these hypotheses with interpretations in terms of the existence of only one type of Yb(2+) defect. The results presented confirm the presence of impurity states of the 4f(13)6s configuration among the 4f(13)5d manifolds, as proposed in literature, but their energies are very different from those assumed. The Yb-trapped excitons found in this chloride host can be seen as precursors of the luminescent Yb-trapped excitons characterized experimentally in the isomorphous SrF(2) crystals.

ChemInform Abstract: Reactions of Dihalobenzene Radical Cations with Ammonia in the Gas Phase. Reactivity Pattern for Nucleophilic Aromatic Substitution.

The reactions of homo- and heterodisubstituted dihalobenzene radical cations with NH3 were investigated by FT-ICR spectrometry. A halogen atom X (X = Cl, Br, I) is substituted in a gas-phase nucleophilic ipso substitution, yielding haloanilinium ions. The reaction efficiency, i.e., the percentage of reactive ion-molecule collisions, ranges from < 0.006% for 1-chloro-4-iodobenzene radical cations to 18% for 1-bromo-2-chlorobenzene radical cations. The reactivity of the halogenated benzene radical cations was found to be governed by two structural parameters. First, the radical cations with a low ionization energy, i.e., iodobenzene and its derivatives, react especially slowly regardless of the reaction exothermicity. Second, the reactivity of all dihalobenzene radical cations is strongly influenced by the substitution pattern. The reactivity of isomeric radical cations is always highest for the 1,2-isomer and lowest for the 1,4-isomer. These results show that the nucleophilic substitution of the halo- and dihalobenzene radical cations by NH3 proceeds by a multistep reaction mechanism with a double-well potential energy surface. The rate-determining step is the addition of NH3 to the aromatic radical cation in the collision complex. The structural parameters influencing this reaction step can be analyzed by the reactivity model of polar reactions of Shaik and Pross. From this the most important feature of the substitution reaction of mono- and dihalobenzene radical cations with NH3 is the different charge localization in reactants and products. This results in a strong influence of the difference of the ionization energies of the halogenated benzene and NH3 and of the dipole moment of the halogenated benzene, i.e., the precursor of the ionic reactant, on the activation energy of the addition step.

Theoretical Analysis of Gas-Phase Front-Side Attack Identity SN2(C) and SN2(Si) Reactions with Retention of Configuration

Gas-phase front-side attack identity S(N)2(C) and S(N)2(Si) reactions, CH(3)X1 + X2(-) --> CH(3)X2 + X1(-) and SiH(3)X1 + X2(-) --> SiH(3)X2 + X1(-) (X = F, Cl), are investigated by the ab initio method and molecular face (MF) theory. The computations have been performed at the CCSD(T)/aug-cc-pVTZ//MP2/6-311++G(3df,3pd) and CISD/aug-cc-pVDZ levels. Front-side attack identity S(N)2 reactions for both SiH(3)X and CH(3)X have double-well potential energy surfaces (PESs), but their transition-state positions are different relative to the positions of reactants and products: it is lower for SiH(3)X, and it is higher for CH(3)X. The minimum energy path for an S(N)2(Si) reaction with retention of configuration proceeds from a stable pentacoordinated anion intermediate of C(s) symmetry (TBP) via a C(s) transition state (SP) to a complementary pentacoordinated intermediate (TBP) and finally up to separate products. Berry pseudorotation has been observed in the front-side attack identity S(N)2(Si) reactions with F(-) and Cl(-) along the intrinsic reaction coordinate (IRC) routes. In addition, the geometrical transformations of front-side attack identity S(N)2(C) and S(N)2(Si) reactions based on the IRC calculations at the MP2/6-311++G(3df, 3pd) level of theory are described compared with those of corresponding back-side attack reactions. The difference between front-side attack identity S(N)2(C) and S(N)2(Si) reactions has been demonstrated. In MF theory, the potential acting on an electron in a molecule (PAEM) is an important quantity; in particular, its D(pb) can measure the strength of a chemical bond in a molecule. It is found that the difference between D(pb) values of reactant and transition state may be related to the activation energy for front-side and back-side attack S(N)2(C) and S(N)2(Si) reactions, and the D(pb) curves along the IRC routes have features similar to those of the potential energy profiles for all of the back-side attack S(N)2 reactions and front-side attack S(N)2(Si) reaction with F(-). Furthermore, according to the MF theory, the spatial dynamic changing features of the molecular shapes and the face electron density are vividly depicted for the course of the reactions.

Influence of the energy of H-bond protons on the electron transfer rate in photosynthetic reaction centers

We present here a theoretical interpretation of the temperature dependence of the rate of dark recombination between a primary quinone (QA) and a bacteriochlorophyll dimer in the reaction center of Rhodobacter sphaeroides. We were able to describe qualitatively the nonmonotonous character of this dependence using the energy of interaction between an excess electron and H-bond protons. We considered a molecular model of QA and two reaction center fragments that make H-bonds with QA: His(M219) and Asn(M259)-Ala(M260). We used the two-center approach with regard for electron-phonon interaction in order to calculate the characteristic time of electron tunneling during the recombination reaction. The energy of the phonon emitted/ absorbed during the electron tunneling was determined by the relative shift of donor and acceptor energy levels, the detuning of levels. The detuning was shown to depend on temperature nonmonotonously for H-bonds with double-well potential energy surface. The characteristic time (or the reaction rate) depended on temperature parametrically. The computed dependence was in qualitative agreement with the experimental one.

The umbrella motion of core-excited CH3 and CD3 methyl radicals

An accurate experimental and theoretical study of the lowest core excitation of CH(3) and CD(3) methyl radicals is presented. The complex vibrational structure of the lowest band of the x-ray absorption spectrum (XAS) is due to the large variation of the molecular geometry, which is planar in the ground state and pyramidal in the core-excited state. The XAS spectra of the two radicals were recorded at high resolution and assigned by theoretical simulations of the spectra, taking into account the coupling of symmetrical stretching and symmetrical bending (umbrellalike) deformations of the radicals. An excellent agreement between experimental and theoretical spectral profiles allowed us to accurately characterize the vibrational structure of the electronic transition. The similarities, as well as the differences, of the peculiar vibrational progression observed for the two radicals are explained by the strong anharmonicity along the umbrella coordinate and by the isotopic variation, leading to a different probing of the double-well potential energy surface of the core excited state during the nuclear motion.

Nucleophilic Substitution at Phosphorus Centers (SN2@P)

We have studied the characteristics of archetypal model systems for bimolecular nucleophilic substitution at phosphorus (SN2@P) and, for comparison, at carbon (SN2@C) and silicon (SN2@Si) centers. In our studies, we applied the generalized gradient approximation (GGA) of density functional theory (DFT) at the OLYP/TZ2P level. Our model systems cover nucleophilic substitution at carbon in X(-)+CH3Y (SN2@C), at silicon in X(-)+SiH3Y (SN2@Si), at tricoordinate phosphorus in X(-)+PH2Y (SN2@P3), and at tetracoordinate phosphorus in X(-)+POH2Y (SN2@P4). The main feature of going from SN2@C to SN2@P is the loss of the characteristic double-well potential energy surface (PES) involving a transition state [X--CH3--Y]- and the occurrence of a single-well PES with a stable transition complex, namely, [X--PH2--Y]- or [X--POH2--Y](-). The differences between SN2@P3 and SN2@P4 are relatively small. We explored both the symmetric and asymmetric (i.e. X, Y=Cl, OH) SN2 reactions in our model systems, the competition between backside and frontside pathways, and the dependence of the reactions on the conformation of the reactants. Furthermore, we studied the effect, on the symmetric and asymmetric SN2@P3 and S(N)2@P4 reactions, of replacing hydrogen substituents at the phosphorus centers by chlorine and fluorine in the model systems X(-)+PR2Y and X(-)+POR2Y, with R=Cl, F. An interesting phenomenon is the occurrence of a triple-well PES not only in the symmetric, but also in the asymmetric SN2@P4 reactions of X(-)+POCl2--Y.

Hydrogen-bond dynamics and Fermi resonance in high-pressure methane filled ice

High-pressure, variable temperature infrared spectroscopy and first-principles calculations on the methane filled ice structure (MH-III) at high pressures are used to investigate the vibrational dynamics related to pressure induced modifications in hydrogen bonding. Infrared spectroscopy of isotopically dilute solutions of H(2)O in D(2)O is employed together with first-principles calculations to characterize proton dynamics with the pressure induced shortening of hydrogen bonds. A Fermi resonance is identified and shown to dominate the infrared spectrum in the pressure region between 10 and 30 GPa. Significant differences in the effects of the Fermi resonance observed between 10 and 300 K arise from the double-well potential energy surface of the hydrogen bond and quantum effects associated with the proton dynamics.