Single Potential Energy Surface Research Articles

A nearly complete treatment of the effect of non-adiabaticity on rovibrational energies of H3+ (Part III).

In this article, significant contributions of non-adiabaticity for the rovibrational bound states up to 25 000 cm-1 and total angular momentum J = 0-20 of H3+ are investigated. A coupled-perturbed full configuration interaction (CP-FCI) treatment is applied to calculate all couplings between electronic states caused by the nuclear motion. These derivative couplings were evaluated up to the second order by means of a perturbation treatment and include all nuclear Cartesian first and second derivatives of the electronic wavefunctions. In particular, the coupling of special derivatives with respect to r and R in the Jacobi coordinate representation is more significant than thought. The perturbation approach is especially optimal for the treatment of weak non-adiabaticity in case of rovibrational energies in H3+ and had not been available before for H3+ or other triatomics. Using exclusively Gaussian basis functions for CP-FCI appears to be sufficient, because explicit correlated wavefunctions are already used for all other potential energy contributions. Our work is an extension of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses and which needs only a single potential energy surface for the dynamics. The implementation allows us to include all non-adiabatic effects up to the order of O(μ-2), μ being the reduced nuclear mass. Our treatment works for any isotopologue and for the whole potential energy curve or surface. By this treatment, a further reduction in deviations to experimental data for most rovibrational levels to less than 0.1 cm-1 is possible. For the related transition frequencies, 1366 of 1720 known rovibrational transitions in H3+ have deviations less than 0.1 cm-1 without using any empirically adjustable parameters or optimizing the nuclear mass for a specific transition. For many questionable assignments (deviations >0.3 cm-1) of observed transitions in H3+, a new labeling is proposed.

NeI2 Photofragmentation Dynamics Through Quasiclassical and Semiclassical Studies.

The triatomic system NeI$_2$ has been studied under the consideration the diatom is found in an excited electronic state (B). The vibrational levels $(v=13,\ldots,23)$ are taken into account in this research. For such a study, we use two well-known theoretical procedure: the QCT (Quasi-Classical Trajectories) method, where the classical equations motion for nuclei are solved on a single potential energy surface (PES), unlike the TSH (Trajectory Surface Hopping) method, where they are solved in a bunch of crossed vibrational PES (diabatic representation). We have incorporated the Trajectory Surface Hopping - Fewest Switches (TSH-FS) in order to minimize the number of hoppings, allowing us calculate the probability of hopping between the different PES's, and the kinetic mechanism to track the path followed for the system until dissociation. By using these methods we are able to obtain several observables like the lifetimes, vibrational and rotational energies (I$_2$), dissociation channels, among others. Our results are compared with previous experimental and theoretical work.

Nonadiabatic Coupling in Trajectory Surface Hopping: How Approximations Impact Excited-State Reaction Dynamics

Photochemical reactions are widely modeled using the popular trajectory surface hopping (TSH) method, an affordable mixed quantum-classical approximation to the full quantum dynamics of the system. TSH is able to account for nonadiabatic effects using an ensemble of trajectories, which are propagated on a single potential energy surface at a time and which can hop from one electronic state to another. The occurrences and locations of these hops are typically determined using the nonadiabatic coupling between electronic states, which can be assessed in a number of ways. In this work, we benchmark the impact of some approximations to the coupling term on the TSH dynamics for several typical isomerization and ring-opening reactions. We have identified that two of the schemes tested, the popular local diabatization scheme and a scheme based on biorthonormal wave function overlap implemented in the OpenMOLCAS code as part of this work, reproduce at a much reduced cost the dynamics obtained using the explicitly calculated nonadiabatic coupling vectors. The other two schemes tested can give different results, and in some cases, even entirely incorrect dynamics. Of these two, the scheme based on configuration interaction vectors gives unpredictable failures, while the other scheme based on the Baeck-An approximation systematically overestimates hopping to the ground state as compared to the reference approaches.

Representation and conservation of angular momentum in the Born-Oppenheimer theory of polyatomic molecules.

This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born-Oppenheimer parameter κ = (m/M)1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born-Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born-Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.

Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

Two state reactivity (TSR) and hydrogen tunneling reaction kinetics measured in the Co+ mediated decomposition of CH3CHO.

The electronic structure of a transition metal atom allows it to act as a catalytic active site by providing lower energy alternative pathways in chemical transformations. We have identified and kinetically characterized three such pathways in the title reaction. One is an adiabatic pathway that occurs on a single potential energy surface described within the Born-Oppenheimer approximation. A second pathway opens microseconds into the reaction as a portion of the reacting population competitively transitions from triplet to singlet multiplicity to circumvent energetic barriers on the triplet surface. These pathways are single- and two-state reactive (SSR and TSR) where the Co+ cation mediates an oxidative addition/reductive elimination sequence of the CH3CHO molecule. The third observed reaction pathway is the aldehyde hydrogen tunneling through an Eyring barrier to form high-spin products. First-order rate constants for the adiabatic and nonadiabatic energy lowered pathways, and the hydrogen tunneling pathway, are each measured using the single photon initiated dissociative rearrangement reaction (SPIDRR) experimental technique. We believe that this is the first experimental study where such disparate dynamic features (SSR, TSR, and H-tunneling) are disentangled in a system's chemistry, attributing specific rate constant values to each effect and quantifying the various competitions. Moreover, multi-reference CASSCF/CASPT2 calculations indicate that structures with covalent Co-H bonds are present exclusively along the excited singlet surface. This phenomenon significantly reduces these structures' energy relative to their triplet counterparts, thus enabling the surface crossing and spin inversion that cause the observed two-state reactivity.

Chemistry without the Born-Oppenheimer approximation.

Chemistry without the Born-Oppenheimer approximation.

Investigation of the global second-derivative non-adiabatic contributions: Rovibrational energies of [formula omitted], [formula omitted], and prospects for [formula omitted] (Part II)

The influence of the non-adiabaticity on the rovibrational bound states of H2+, H2, and H3+ is investigated. For this purpose a full configuration interaction (FCI) treatment using Gaussian basis functions is applied to calculate the energies of the electronic states as well as all couplings between them caused by the nuclear motion. These ‘derivative couplings’ were evaluated up to second order by means of a perturbation treatment. While this has been possible already for H2+ and H2, nothing equivalent has been available for H3+. The present work is an extension of the investigation of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses needed for only one single potential energy surface. Our new implementation allowed to include for the first time also for H3+ all non-adiabatic effects up to the order of O(μ-2), μ being the reduced nuclear mass. These new inclusions of all nonadiabatic effects could reduce also for H3+ the deviations to experimental data for most rovibrational levels to less than 0.1 cm−1 without any empirically adjustable parameters. For H3+, the accuracy is slightly improved when also relativistic and QED effects are taken into account. For two questionable assignments of observed transitions in H3+ we propose a new labeling.

Nonadiabatic quantum dynamics of the coherent excited state intramolecular proton transfer of 10-hydroxybenzo[h]quinoline

The photoinduced nonadiabatic dynamics of the enol-keto isomerization of 10-hydroxybenzo[h]quinoline (HBQ) are studied computationally using high-dimensional quantum dynamics. The simulations are based on a diabatic vibronic coupling Hamiltonian, which includes the two lowest pi pi ^* excited states and a npi ^* state, which has high energy in the Franck–Condon zone, but significantly stabilizes upon excited state intramolecular proton transfer. A procedure, applicable to large classes of excited state proton transfer reactions, is presented to parametrize this model using potential energies, forces and force constants, which, in this case, are obtained by time-dependent density functional theory. The wave packet calculations predict a time scale of 10–15 fs for the photoreaction, and reproduce the time constants and the coherent oscillations observed in time-resolved spectroscopic studies performed on HBQ. In contrast to the interpretation given to the most recent experiments, it is found that the reaction initiated by 1pi pi ^* longleftarrow S_0 photoexcitation proceeds essentially on a single potential energy surface, and the observed coherences bear signatures of Duschinsky mode-mixing along the reaction path. The dynamics after the 2pi pi ^* longleftarrow S_0 excitation are instead nonadiabatic, and the npi ^* state plays a major role in the relaxation process. The simulations suggest a mainly active role of the proton in the isomerization, rather than a passive migration assisted by the vibrations of the benzoquinoline backbone.Graphic

Nucleus–electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization

We present a novel theory and implementation for computing coupled electronic and quantal nuclear subsystems on a single potential energy surface, moving beyond the standard Born-Oppenheimer (BO) separation of nuclei and electrons. We formulate an exact self-consistent nucleus-electron embedding potential from the single product molecular wavefunction and demonstrate that the fundamental behavior of the correlated nucleus-electron can be computed for mean-field electrons that are responsive to a quantal anharmonic vibration of selected nuclei in a discrete variable representation. Geometric gauge choices are discussed and necessary for formulating energy invariant biorthogonal electronic equations. Our method is further applied to characterize vibrationally averaged molecular bonding properties of molecular energetics, bond lengths, and protonic and electron densities. Moreover, post-Hartree-Fock electron correlation can be conveniently computed on the basis of nucleus-electron coupled molecular orbitals, as demonstrated for correlated models of second-order Møllet-Plesset perturbation and full configuration interaction theories. Our approach not only accurately quantifies non-classical nucleus-electron couplings for revising molecular bonding properties but also provides an alternative time-independent approach for deploying non-BO molecular quantum chemistry.

Theoretical investigations on mechanisms and pathways of CH2FO2/CHF2O2 with ClO reactions in the atmosphere

The kinetics and mechanisms of the CH2FO2/CHF2O2 with ClO reactions have been investigated firstly by using the quantum chemical method. The single and triplet potential energy surfaces (PESs) of these two reactions have been obtained by using the BMC−CCSD method based on the geometries obtained at the B3LYP/6−311++G(d,p) level. For the CH2FO2 with ClO reaction, three activated intermediates, IM1 (CH2FOOOCl), IM2 (CH2FOOClO), and IM3 (CH2FOClO2) are generated along the reaction path, and then dissociate to various products. The similar production pathways are investigated for the CHF2O2 with ClO reaction. It should be noted that the isomerization of IM3 (CH2FOClO2) and the 1,3-Cl shift from IM1 (CH2FOOOCl) pathways were not found for the CH2FO2 with ClO reaction. The rate constants for the dominant product pathways are predicted by RRKM-TST theories. The major production pathway is the generation of IM1 (CH2FOOOCl)/IM1 (CHF2OOOCl) at 200−1200 K, and the generation of P1 (CHFO + HO2 +Cl)/P1 (CF2O + HO2 + Cl) by H-migration/elimination become dominant at higher temperatures for the CH2FO2/CHF2O2 + ClO reactions, respectively. The atmospheric lifetimes of CH2FO2 and CHF2O2 in ClO are around 11.38 and 8.65 h, respectively. Furthermore, on the basis of the analysis of the kinetics of all channels through which the addition and abstraction reactions proceed, we expect that the competitive power of reaction channels may vary with experimental conditions for the title reaction. The present study may be helpful for probing the mechanisms of the title reaction and understanding the halogen chemistry.

Thermophysical properties of supercritical [formula omitted] from Molecular Dynamics simulations

The ability to predict thermophysical properties of molecular hydrogen with high accuracy, especially at high pressures, is crucial to design and to operate processes involving compressed hydrogen. Molecular simulations comprise an adequate tool to investigate both thermodynamic and transport properties of different molecular systems using a single potential energy surface model. Such a potential is called a force field. Here we propose a new single-site force field for pure hydrogen using a Mie potential to describe the intermolecular interactions. The proposed force field yields better predictions of thermodynamic properties when compared to other available force fields that use Lennard-Jones interaction potential. The new force field is also able to predict transport properties with reasonable accuracy.

Analysis of QED and non-adiabaticity effects on the rovibrational spectrum of H3 + using geometry-dependent effective nuclear masses.

The influence of QED effects (including one- and two-electron Lamb-shift, Araki-Sucher term, one-loop self-energy, and finite nuclear size correction) together with non-adiabatic effects on the rovibrational bound states of H3 + has been investigated. Non-adiabaticity is modeled by using geometry-dependent effective nuclear masses together with only one single potential energy surface. In conclusion, for rovibrational states below 20 000 cm-1, QED and relativistic effects do nearly compensate, and a potential energy surface based on Born-Oppenheimer energies and diagonal adiabatic corrections has nearly the same quality as the one including relativity with QED; the deviations between the two approaches for individual rovibrational states are mostly below 0.02 cm-1. The inclusion of non-adiabatic effects is important, and it reduces deviations from experiments mostly below 0.1 cm-1.

Non-adiabatic quantum dynamics of the ultracold Li+LiNa→ Li2+Na chemical reaction

SynopsisWe report non-adiabatic dynamics of the Li+LiNa→Li2+Na chemical reaction at cold and ultracold temperatures employing accurate ab initio electronic potential energy surfaces in a quantum dynamics formulation employing a diabatic representation. Results are compared against those from a single adiabatic ground state potential energy surface and a universal model based on the long-range interaction potential. We discuss signatures of non-universal behavior in the total rate coefficients as well as strong non-adiabatic effects in the state-to-state rotationally resolved rate coefficients.

Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground

Highly accurate potential energy surfaces are of key interest for the detailed understanding and predictive modeling of chemical systems. In recent years, several new types of force fields, which are based on machine learning algorithms and fitted to ab initio reference calculations, have been introduced to meet this requirement. Here, we show how high-dimensional neural network potentials can be employed to automatically generate the potential energy surface of finite sized clusters at coupled cluster accuracy, namely CCSD(T*)-F12a/aug-cc-pVTZ. The developed automated procedure utilizes the established intrinsic properties of the model such that the configurations for the training set are selected in an unbiased and efficient way to minimize the computational effort of expensive reference calculations. These ideas are applied to protonated water clusters from the hydronium cation, H3O+, up to the tetramer, H9O4+, and lead to a single potential energy surface that describes all these systems at essentially converged coupled cluster accuracy with a fitting error of 0.06 kJ/mol per atom. The fit is validated in detail for all clusters up to the tetramer and yields reliable results not only for stationary points but also for reaction pathways and intermediate configurations as well as different sampling techniques. Per design, the neural network potentials (NNPs) constructed in this fashion can handle very different conditions including the quantum nature of the nuclei and enhanced sampling techniques covering very low as well as high temperatures. This enables fast and exhaustive exploration of the targeted protonated water clusters with essentially converged interactions. In addition, the automated process will allow one to tackle finite systems much beyond the present case.

Vibronic coupling in the F·CH4 prereactive complex

The F + CH4 → HF + CH3 reaction shows a counter-intuitive mode-selective chemistry and prominent resonances. The prereactive F·CH4 complex formed in the entrance channel is assumed to play an important role in the dynamics of the reaction. The present work investigates the effect of nonadiabatic transitions and the geometric phase on the low-lying quasibound states of the F·CH4 complex. Quantum dynamics calculations employing the multiconfigurational time-dependent Hartree approach and accurately accounting for vibronic as well as spin-orbit coupling are performed. Extending previous work [D. Schäpers and U. Manthe, J. Phys. Chem. A 120, 3186 (2016)], which was restricted to the dynamics on a single adiabatic potential energy surface and found the relative rotation of F and CH4 to proceed almost freely, we found chaotic patterns if vibronic coupling is included. While nonadiabatic transitions strongly affect individual resonances, their effect on averaged quantum state densities and the photodetachment spectrum of F⋅CH4 - is found to be minor.

Diabatic and adiabatic representations: Electronic structure caveats

In this Viewpoint issues in the construction and use of adiabatic and diabatic representations in describing spin-conserving electronically nonadiabatic processes using the Born-Huang ansatz are reviewed and illustrated. We address issues which limit the accuracy of commonly used approximate equations of motion. The following caveats are discussed. (i) The use of adiabatic states for Nstate > 2 is complicated by the fact that if states (I, J) and (J, K) have conical intersections then the derivative coupling f(a),I,J(R) may well be double-valued, rendering it inappropriate for nuclear dynamics. (ii) In the nonadiabatic tunneling regime, nuclear motion can be restricted to a single adiabatic potential energy surface on the basis of total energy. However, energetically inaccessible conical intersections make it necessary to take into account the geometric phase and the induced vector potential when formulating the nuclear Schrödinger equation. We review how a diabatization approach which takes explicit account of the derivative couplings can be used to accurately include these factors. (iii) Finally, we review how a commonly used class of two-state diabatizations based on smooth molecular properties can be subject to ruinous singularities inherent in equations defining the diabatization.

Theoretical elucidation on the mechanism of 1H‐1,2,4‐diazaphospholes synthesis from 1,3‐bis (amino)‐2‐phosphaallyl chlorides with hydrazine

AbstractThe mechanism of the reaction of 1,3‐bis (amino)‐2‐phosphaallyl chlorides with hydrazine for the synthesis of 1H‐1,2,4‐diazaphospholes in CHCl3 solvent has been extensively investigated at the B3LYP/6‐311G (d, p) level. The reaction is initiated by the elimination of HCl and formation of a key intermediate A, then A subsequently undergoes H‐migration‐cyclization (A → B) and Me2NH elimination reactions (B → C) to afford carbene intermediate C, and C can transform to F along both single and triplet potential energy surfaces in three steps. H‐migration‐cyclization (A → B) step was identified as a proton‐coupled electron transfer (PCET) process, and singlet‐triplet PES crossing should be important in decomposition of C to D1 and D2. For R═Me, Ph and H, the rate control step should be the decomposition of C, while for R═tBu, the first Me2NH removal step is the rate control one. Theoretical results suggested that tBu is a preferable group than Ph, Me, and H in this reaction, which can be attributed to hyperconjugation effects of tBu, showing good agreement with experimental data.

Investigation of non-adiabatic effects for the ro-vibrational spectrum of H3+: the use of a single potential energy surface with geometry-dependent nuclear masses

ABSTRACTThe influence of non-adiabatic effects on the ro-vibrational bound states of H+3 has been investigated using geometry-dependent reduced masses and only one single potential energy surface. The used potentials (BO electronic energy, adiabatic corrections and relativistic contributions) are based on explicitly correlated wavefunctions. For the first time, several different fully geometry-dependent reduced mass surfaces in three dimensions have been incorporated for the vibrational and rotational contributions.

Vibrational treatment of the formic acid double minimum case in valence coordinates.

One single full dimensional valence coordinate HCOOH ground state potential energy surface accurate for both cis and trans conformers for all levels up to 6000 cm-1 relative to trans zero point energy has been generated at CCSD(T)-F12a/aug-cc-pVTZ level. The fundamentals and a set of eigenfunctions complete up to about 3120 and 2660 cm-1 for trans- and cis-HCOOH, respectively, have been calculated and assigned using the improved relaxation method of the Heidelberg multi-configuration time-dependent Hartree package and an exact expression for the kinetic energy in valence coordinates generated by the TANA program. The calculated trans fundamental transition frequencies agree with experiment to within 5 cm-1. A few reassignments are suggested. Our results discard any cis trans delocalization effects for vibrational eigenfunctions up to 3640 cm-1 relative to trans zero point energy.