Six-dimensional Potential Energy Surface Research Articles

Applying a Smolyak collocation method to Cl2CO

ABSTRACTPhosgene (Cl2C=O) is extremely poisonous, underscoring the importance of accurate infrared detection. Here, the computed vibrational energy levels of phosgene are reported for the first time from a six-dimensional potential energy surface (PES) that was constructed from 25,000 single-point energy computations at the CCSD(T)/cc-pVTZ level of theory. The computed points were fit using a neural network method, and the resulting PES was employed in the determination of vibrational energies and wavefunctions. Bond coordinates were utilised in conjunction with a collocation method to minimise problems that arise from the complicated nature of the kinetic energy operator. The collocation method makes possible the computation of energy levels without integral evaluation, and without the need to solve a generalised eigenvalue problem. Moreover, it is built on a nondirect product-pruned basis that is much smaller than the direct product basis that would be required to obtain the same accuracy.

Full-dimensional quantum dynamics of rovibrationally inelastic scattering between CN and H2.

We report six-dimensional (6D) potential energy surface (PES) and rovibrational scattering calculations for the CN-H2 collision system. The PES was computed using the high-level ab initio spin-restricted coupled-cluster with single, double, and perturbative triple excitations-F12B method and fitted to an analytic function using an invariant polynomial method in 6D. Quantum close-coupling calculations are reported for rotational transitions in CN by H2 and D2 collisions in 6D as well as four-dimensional (4D) within a rigid rotor model for collision energies of 1.0-1500 cm-1. Comparisons with experimental data and previous 4D calculations are presented for CN rotational levels j1 = 4 and 11. For the first time, rovibrational quenching cross sections and rate coefficients of CN (v1 = 1,j1 = 0) in collisions with para- and ortho-H2 are also reported in full-dimension. Agreement for pure rotational transitions is found to be good, but no experimental data on rovibrational collisional quenching for CN-H2 are available. Applications of the current rotational and rovibrational rate coefficients in astrophysical modeling are briefly discussed.

Experimental and theoretical study of rotationally inelastic diffraction of H2(D2) from methyl-terminated Si(111).

Fundamental details concerning the interaction between H2 and CH3-Si(111) have been elucidated by the combination of diffractive scattering experiments and electronic structure and scattering calculations. Rotationally inelastic diffraction (RID) of H2 and D2 from this model hydrocarbon-decorated semiconductor interface has been confirmed for the first time via both time-of-flight and diffraction measurements, with modest j = 0 → 2 RID intensities for H2 compared to the strong RID features observed for D2 over a large range of kinematic scattering conditions along two high-symmetry azimuthal directions. The Debye-Waller model was applied to the thermal attenuation of diffraction peaks, allowing for precise determination of the RID probabilities by accounting for incoherent motion of the CH3-Si(111) surface atoms. The probabilities of rotationally inelastic diffraction of H2 and D2 have been quantitatively evaluated as a function of beam energy and scattering angle, and have been compared with complementary electronic structure and scattering calculations to provide insight into the interaction potential between H2 (D2) and hence the surface charge density distribution. Specifically, a six-dimensional potential energy surface (PES), describing the electronic structure of the H2(D2)/CH3-Si(111) system, has been computed based on interpolation of density functional theory energies. Quantum and classical dynamics simulations have allowed for an assessment of the accuracy of the PES, and subsequently for identification of the features of the PES that serve as classical turning points. A close scrutiny of the PES reveals the highly anisotropic character of the interaction potential at these turning points. This combination of experiment and theory provides new and important details about the interaction of H2 with a hybrid organic-semiconductor interface, which can be used to further investigate energy flow in technologically relevant systems.

Full-dimensional quantum dynamics of CO in collision with H2.

Inelastic scattering computations are presented for collisions of vibrationally and rotationally excited CO with H2 in full dimension. The computations utilize a newly developed six-dimensional potential energy surface (PES) and the previously reported four-dimensional V12 PES [P. Jankowski et al., J. Chem. Phys. 138, 084307 (2013)] and incorporate full angular-momentum coupling. At low collision energies, pure rotational excitation cross sections of CO by para-, ortho-, and normal-H2 are calculated and convolved to compare with recent measurements. Good agreement with the measured data is shown except for j1 = 0 → 1 excitation of CO for very low-energy para-H2 collisions. Rovibrational quenching results are presented for initially excited CO(v1j1) levels with v1 = 1, j1 = 1-5 and v1 = 2, j1 = 0 for collisions with para-H2 (v2 = 0, j2 = 0) and ortho-H2 (v2 = 0, j2 = 1) over the kinetic energy range 0.1-1000 cm(-1). The total quenching cross sections are found to have similar magnitudes, but increase (decrease) with j1 for collision energies above ∼300 cm(-1) (below ∼10 cm(-1)). Only minor differences are found between para- and ortho-H2 colliders for rovibrational and pure rotational transitions, except at very low collision energies. Likewise, pure rotational deexcitation of CO yields similar cross sections for the v1 = 0 and v1 = 1 vibrational levels, while rovibrational quenching from v1 = 2, j1 = 0 is a factor of ∼5 larger than that from v1 = 1, j1 = 0. Details on the PES, computed at the CCSD(T)/aug-cc-pV5Z level, and fitted with an invariant polynomial method, are also presented.

Neural network exponential fitting of a potential energy surface with multiple minima: Application to HFCO

We have constructed a (semi)-global six-dimensional potential energy surface (PES) for HFCO, incorporating the equilibrium, cis- and trans- isomers (HOCF) as well as the transition states connecting them. The PES is based on a fit to 15000 CCSD(T)-F12/cc-pVTZ-F12 ab initio energies. The sum-of-products PES, obtained using neural network exponential fitting functions, was used to compute vibrational state frequencies using block improved relaxation with the multiconfiguration time dependent Hartree (MCTDH) approach. The PES is accurate (RMSE=130cm−1) up to 40,000cm−1 above the minimum energy. The equilibrium region of the PES was fit very well based on a comparison of the vibrational frequencies with those from a recent local HFCO PES (Pradhan and Brown, 2016) and experimental measurements (RMSE=10.9cm−1 compared to experiment). The vibrational frequencies for the trans- and cis-isomers are computed from the PES and compared to anharmonic MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ results; the trans- and cis-isomers have yet to be detected experimentally. Based on the accuracy of the vibrational energies at equilibrium, the present results for the cis- and trans-isomers could facilitate the identification of these species. The PES will also enable the study of intramolecular vibrational energy redistribution and its control leading to the elusive equilibrium HFCO to trans-HOCF conversion.

Numerical adiabatic potentials of orthorhombic Jahn-Teller effects retrieved from ultrasound attenuation experiments. Application to the SrF2:Cr crystal

A methodology is worked out to retrieve the numerical values of all the main parameters of the six-dimensional adiabatic potential energy surface (APES) of a polyatomic system with a quadratic T-term Jahn-Teller effect (JTE) from the ultrasound experiments. The method is based on a verified assumption that ultrasound attenuation and speed encounter anomalies when the direction of propagation and polarization of its wave of strain coincides with the characteristic directions of symmetry breaking in the JTE. For the SrF2:Cr crystal, employed as a basic example, we observed anomaly peaks in the temperature dependence of attenuation of ultrasound at frequencies of 50–160 MHz in the temperature interval of 40–60 K for the wave propagating along the [110] direction, for both the longitudinal and the shear modes, the latter with two polarizations along the [001] and [11¯0] axes, respectively. We show that these anomalies are due to the ultrasound relaxation by the system of non-interacting Cr2+ JT centers with orthorhombic local distortions. The interpretation of the experimental findings is based on the T2g⊗(eg+t2g) JTE problem including the linear and the quadratic terms of vibronic interactions in the Hamiltonian and the same-symmetry modes reduced to one interaction mode. Combining the experimental results with a theoretical analysis, we show that on the complicated six-dimensional APES of this system with three tetragonal, four trigonal, and six orthorhombic extrema points, the latter are global minima, while the former are saddle points, and we estimate numerically all the main parameters of this surface, including the linear and quadratic vibronic coupling constants, the primary force constants, the coordinates of all the extrema points and their energies, the energy barrier between the orthorhombic minima, and the tunneling splitting of the ground vibrational states. To our knowledge, such a based-on-experimental-data numerical reconstruction of the APES of a JTE problem in the five-dimensional space of all active tetragonal and trigonal displacements has not been reported before.

Vibrational energies for HFCO using a neural network sum of exponentials potential energy surface

A six-dimensional potential energy surface (PES) for formyl fluoride (HFCO) is fit in a sum-of-products form using neural network exponential fitting functions. The ab initio data upon which the fit is based were computed at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations [CCSD(T)-F12]/cc-pVTZ-F12 level of theory. The PES fit is accurate (RMSE = 10 cm(-1)) up to 10 000 cm(-1) above the zero point energy and covers most of the experimentally measured IR data. The PES is validated by computing vibrational energies for both HFCO and deuterated formyl fluoride (DFCO) using block improved relaxation with the multi-configuration time dependent Hartree approach. The frequencies of the fundamental modes, and all other vibrational states up to 5000 cm(-1) above the zero-point energy, are more accurate than those obtained from the previous MP2-based PES. The vibrational frequencies obtained on the PES are compared to anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The new PES will be useful for quantum dynamics simulations for both HFCO and DFCO, e.g., studies of intramolecular vibrational redistribution leading to unimolecular dissociation and its laser control.

Density functional theory study of nitrogen atoms and molecules interacting with Fe(1 1 1) surfaces

We present Density functional theory (DFT) calculations for the investigation of the structural relaxation of Fe(111), as well as for the study of the interaction of nitrogen atoms and molecules with this surface. We perform spin polarized DFT calculations using VASP (Vienna Ab-initio Simulation Package) code. We use the supercell approach and up to 19 slab layers for the relaxation of the Fe(111) surface. We find a contraction of the first two interlayer distances with a relative value of Δ12=-7.8% and Δ23=-21.7% with respect to the bulk reference. The third interlayer distance is however expanded with a relative change of Δ34=9.7%. Early experimental studies of the surface relaxation using Low Energy Electron Diffraction (LEED) and Medium Energy Ion Scattering (MEIS) showed contradictory results, even on the relaxation general trend. Our current theoretical results support the LEED conclusions and are consistent qualitatively with other recent theoretical calculations. In addition, we study the interaction energy of nitrogen atoms and molecules on the Fe(111) surface. The nitrogen atoms are adsorbed in the hollow site of the unit cell, with an adsorption energy consistent with the one found in previous studies. In addition, we find the three molecularly adsorbed states that are observed experimentally. Two of them correspond to the adsorbed molecule oriented normal to the surface and a third one corresponds to the molecule adsorbed parallel to the surface. We conclude that our results are accurate enough to be used to build a full six-dimensional potential energy surface for the N2 system.

Femtosecond-laser-driven molecular dynamics on surfaces: Photodesorption of molecular oxygen from Ag(110)

We simulate the femtosecond laser induced desorption dynamics of a diatomic molecule from a metal surface by including the effect of the electron and phonon excitations created by the laser pulse. Following previous models, the laser induced surface excitation is treated through the two temperature model, while the multidimensional dynamics of the molecule is described by a classical Langevin equation, in which the friction and random forces account for the action of the heated electrons. In this work, we propose the additional use of the generalized Langevin oscillator model to also include the effect of the energy exchange between the molecule and the heated surface lattice in the desorption dynamics. The model is applied to study the laser induced desorption of O$_2$ from the Ag(110) surface, making use of a six-dimensional potential energy surface calculated within density functional theory. Our results reveal the importance of the phonon mediated process and show that, depending on the value of the electronic density in the surroundings of the molecule adsorption site, its inclusion can significantly enhance or reduce the desorption probabilities.

Calculations of the active mode and energetic barrier to electron attachment to CF3 and comparison with kinetic modeling of experimental results.

To provide a deeper understanding of the kinetics of electron attachment to CF3, the six-dimensional potential energy surfaces of both CF3 and CF3- were developed by fitting ∼3000 ab initio points per surface at the AE-CCSD(T)-F12a/AVTZ level using the permutation invariant polynomial-neural network (PIP-NN) approach. The fitted potential energy surfaces for CF3 and CF3- had root mean square fitting errors relative to the ab initio calculations of 1.2 and 1.8 cm-1, respectively. The main active mode for the crossing between the two potential energy surfaces was identified as the umbrella bending mode of CF3 in C3v symmetry. The lowest energy crossing point is located at RCF = 1.306 Å and θFCF = 113.6° with the energy of 0.051 eV above the minimum of the CF3 electronic surface. This value is only slightly larger than the experimental data 0.026 ± 0.01 eV determined by kinetic modeling of electron attachment to CF3. The small discrepancy between the theoretical and experimentally measured values is analyzed.

Quantum dynamics on a three-sheeted six-dimensional ab initio potential-energy surface of the phosphine cation: Simulation of the photoelectron spectrum and the ultrafast radiationless decay dynamics.

A diabatic three-sheeted six-dimensional potential-energy surface has been constructed for the ground state and the lowest excited state of the PH3 (+) cation. Coupling terms of Jahn-Teller and pseudo-Jahn-Teller origin up to eighth order had to be included to describe the pronounced anharmonicity of the surface due to multiple conical intersections. The parameters of the diabatic Hamiltonian have been optimized by fitting the eigenvalues of the potential-energy matrix to ab initio data calculated at the CASSCF/MRCI level employing the correlation-consistent triple-ζ basis. The theoretical photoelectron spectrum of phosphine and the non-adiabatic nuclear dynamics of the phosphine cation have been computed by propagating nuclear wave packets with the multiconfiguration time-dependent Hartree method. The theoretical photoelectron bands obtained by Fourier transformation of the autocorrelation function agree well with the experimental results. It is shown that the ultrafast non-radiative decay dynamics of the first excited state of PH3 (+) is dominated by the exceptionally strong Jahn-Teller coupling of the asymmetric bending vibrational mode together with a hyperline of conical intersections with the electronic ground state induced by the umbrella mode. Time-dependent population probabilities have been computed for the three adiabatic electronic states. The non-adiabatic Jahn-Teller dynamics within the excited state takes place within ≈5 fs. Almost 80% of the excited-state population decay to the ground state within about 10 fs. The wave packets become highly complex and delocalized after 20 fs and no further significant transfer of electronic population seems to occur up to 100 fs propagation time.

Fingerprints of energy dissipation for exothermic surface chemical reactions: O2 on Pd(100).

We present first-principles calculations of the sticking coefficient of O2 at Pd(100) to assess the effect of phononic energy dissipation on this kinetic parameter. For this, we augment dynamical simulations on six-dimensional potential energy surfaces (PESs) representing the molecular degrees of freedom with various effective accounts of surface mobility. In comparison to the prevalent frozen-surface approach, energy dissipation is found to qualitatively affect the calculated sticking curves. At the level of a generalized Langevin oscillator model, we achieve good agreement with experimental data. The agreement is similarly reached for PESs based on two different semi-local density-functional theory functionals. This robustness of the simulated sticking curve does not extend to the underlying adsorption mechanism, which is predominantly directly dissociative for one functional or molecularly trapped for the other. Completely different adsorption mechanisms therewith lead to rather similar sticking curves that agree equally well with the experimental data. This highlights the danger of the prevalent practice to extract corresponding mechanistic details from simple fingerprints of measured sticking data for such exothermic surface reactions.

Influence of the van der Waals interaction in the dissociation dynamics of N2 on W(110) from first principles.

Using ab initio molecular dynamics (AIMD) calculations, we investigate the role of the van der Waals (vdW) interaction in the dissociative adsorption of N2 on W(110). Hitherto, existing classical dynamics calculations performed on six-dimensional potential energy surfaces based on density functional theory (DFT), and the semi-local PW91 and RPBE [Hammer et al. Phys. Rev. B 59, 7413 (1999)] exchange-correlation functionals were unable to fully describe the dependence of the initial sticking coefficient on the molecular beam incidence conditions as found in experiments. N2 dissociation on W(110) was shown to be very sensitive not only to short molecule-surface distances but also to large distances where the vdW interaction, not included in semilocal-DFT, should dominate. In this work, we perform a systematic study on the dissociative adsorption using a selection of existing non-local functionals that include the vdW interaction (vdW-functionals). Clearly, the inclusion of the non-local correlation term contributes in all cases to correct the unrealistic energy barriers that were identified in the RPBE at large molecule-surface distances. Among the tested vdW-functionals, the original vdW-DF by Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] and the ulterior vdW-DF2 give also an adequate description of the N2 adsorption energy and energy barrier at the transition state, i.e., of the properties that are commonly used to verify the quality of any exchange-correlation functional. However, the results of our AIMD calculations, which are performed at different incidence conditions and hence extensively probe the multi-configurational potential energy surface of the system, do not seem as satisfactory as the preliminary static analysis suggested. When comparing the obtained dissociation probabilities with existing experimental data, none of the used vdW-functionals seems to provide altogether an adequate description of the N2/W(110) interaction at short and large distances.

The dynamics of adsorption and dissociation of N2 in a monolayer of iron on W(110).

We study the adsorption dynamics of N2 on an expanded monolayer of Fe grown pseudomorphically on W(110). To this aim we have performed molecular dynamics simulations in a six-dimensional potential energy surface calculated within density functional theory. Our results show that N2 dissociation on this surface is a highly activated process with an energy barrier of around 1.25 eV. Regarding molecular adsorption, we find that the energetically most favorable adsorption well corresponds to a parallel orientation of the molecule with an adsorption energy of around 520 meV. However, at low molecular energies and surface temperatures, the molecules preferentially adsorb vertically to the surface with an adsorption energy of around 480 meV. A comparative analysis with the results previously obtained on a clean Fe(110) surface shows that while surface strain favors molecular adsorption of N2 in this system, it impedes dissociative adsorption. The former is consistent with the experimental observations showing that the inertness of Fe(110) towards N2 uptake is reduced in the strained surface. The latter leads us to suggest that the experimental observation of dissociated atomic N in the strained surface when increasing surface temperature must be related to the presence of step/defects at the surface.

A six-dimensional potential energy surface for Ru(0001)(2×2):CO.

We present a new global ground state potential energy surface (PES) for carbon monoxide at a coverage of 1/4, on a rigid Ru(0001) surface [Ru(0001)(2×2):CO]. All six adsorbate degrees of freedom are considered. For constructing the PES, we make use of more than 90,000 points calculated with periodic density functional theory using the RPBE exchange-correlation functional and an empirical van der Waals correction. These points are used for interpolation, utilizing a symmetry-adapted corrugation reducing procedure (CRP). Three different interpolation schemes with increasing accuracy have been realized, giving rise to three flavours of the CRP PES. The CRP PES yields in agreement with the DFT reference and experiments, the atop position of CO to be the most stable adsorption geometry, for the most accurate interpolation with an adsorption energy of 1.69 eV. The CRP PES shows that diffusion parallel to the surface is hindered by a barrier of 430 meV, and that dissociation is facilitated but still activated. As a first "real" application and further test of the new potential, the six-dimensional vibrational Schrödinger equation is solved variationally to arrive at fully coupled, anharmonic frequencies and vibrational wavefunctions for the vibrating, adsorbed CO molecule. Good agreement with experiment is found also here. Being analytical, the new PES opens an efficient way towards multidimensional dynamics.

Ab initio potential energy surface for methane and carbon dioxide and application to vapor-liquid coexistence.

A six-dimensional intermolecular potential energy surface for a rigid methane (CH4) and carbon dioxide (CO2) dimer was developed from the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory. A total of 466 grid points distributed to 46 orientations were calculated from the complete basis set limit extrapolation based on up to aug-cc-pVQZ basis set. A modified site-site pair potential function was proposed for rapid representation of the high level ab initio calculations. A nonadditive three-body interaction was represented by the Axilrod-Teller-Muto expression for mixtures with the polarizability and the London dispersion constant of each molecule. Second to fourth virial coefficients of CH4 and CO2 mixtures were calculated using both the Mayer sampling Monte Carlo method and the present potential functions. The virial equation of state derived from these coefficients was used to predict the pVT values and showed good agreement with experimental data below 200 bar at 300 K. The vapor-liquid coexistence curves of pure CH4, CO2 and their mixtures were presented with the aid of Gibbs ensemble Monte Carlo simulations. The predicted tie lines agreed with the experimental data within the uncertainties up to near the critical point.

Role of Physisorption States in Molecular Scattering: A Semilocal Density-Functional Theory Study onO2/Ag(111)

We simulate the scattering of O2 from Ag(111) with classical dynamics simulations performed on a six-dimensional potential energy surface calculated within semilocal density-functional theory. The enigmatic experimental trends that originally required the conjecture of two types of repulsive walls, arising from a physisorption and chemisorption part of the interaction potential, are fully reproduced. Given the inadequate description of the physisorption properties in semilocal density-functional theory, our work casts severe doubts on the prevalent notion to use molecular scattering data as indirect evidence for the existence of such states.

On the role of the simplest S-nitrosothiol, HSNO, in atmospheric and biological processes

Using state-of-the-art theoretical methods, we investigate the lowest electronic states of singlet and triplet spin multiplicities of HSNO. These computations are done using configuration interaction ab initio methods and the aug-cc-pV5Z basis set. One-dimensional cuts of the six-dimensional potential energy surfaces of these electronic states along the HS, SN stretches and HSN, SNO bending and torsion coordinates are calculated. Several avoided crossings and conical intersections are found. We computed also radiative lifetimes and spin-orbit couplings of these electronic states. Our work shows that the dynamics on these excited states is very complex, and suggest that multi-step mechanisms will populate the ground state via radiationless processes or lead to predissociation or intramolecular isomerization. For instance, these potentials are used to propose mechanisms for the IR, Vis, and UV light-induced cis-trans interconversions of HSNO and reactivity towards HS + NO and H + SNO products. Our findings are in good agreement with previous experimental studies on the photochemistry of HSNO. The atmospheric implication of HSNO is also discussed.

Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks

We constructed a six-dimensional potential energy surface (PES) for the dissociative chemisorption of HCl on Au(111) using the neural networks method based on roughly 70000 energies obtained from extensive density functional theory (DFT) calculations. The resulting PES is accurate and smooth, based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations. Time-dependent wave packet calculations show that the potential energy surface is very well converged with respect to the number of DFT data points, as well as to the fitting process. The dissociation probabilities of HCl initially in the ground rovibrational state from six-dimensional quantum dynamical calculations are quite different from the four-dimensional fixed-site calculations, indicating it is essential to perform full-dimensional quantum dynamical studies for the title molecule-surface interaction system.

Rovibrational energies of B2H2([formula omitted]) from an explicitly correlated potential energy surface

The six-dimensional potential energy surface of the X∼3Σg- electronic ground state of B2H2 was determined using spin-unrestricted explicitly correlated coupled cluster methodology. The analytic representation of this surface was used to compute the rovibrational energies of this boron hydride dimer. For the 11B2H2 species, the antisymmetric B–H stretching frequency is computed at 2693.2cm−1, and an isotopic shift of +10.7cm−1 is deduced for 10B2H2. Comparisons with the electronic ground state of diatomic fragments B2 and BH are discussed. The J=1←0 rotational transition is calculated at 50511.5MHz for 11B2H2 and at 53551.0MHz for 10B2H2. Spectroscopic constants of the deuterated isotopologues are reported.