Two-dimensional Potential Energy Surface Research Articles

Layered nested Markov chain Monte Carlo.

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many-body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded-volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. The proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

Interplay Between Microwave Spectroscopy and X-ray Diffraction: The Molecular Structure and Large Amplitude Motions of 2,3-Dimethylanisole.

To determine the structural properties of 2,3-dimethylanisole, a multidisciplinary approach was carried out where gas phase rotational spectroscopy recording a spectrum from 2 to 26.5 GHz using a pulsed molecular jet Fourier transform microwave spectrometer was combined with solid-state X-ray diffraction. Both methods revealed that only one conformer with a planar heavy-atom structure exists. In the solid state, the packing in the monoclinic space group is P21 /n with Z=4. In the gas phase spectrum, torsional splittings due to the internal rotations of two methyl groups attached to the phenyl ring were resolved and analyzed, providing an estimate of the barriers to methyl internal rotation of V3 =26.9047(5) and 518.7(12) cm-1 for the methyl groups at the ortho- and meta-position, respectively. The coupling between the two internal rotations is modeled on a two-dimensional potential energy surface, which was obtained by quantum chemical calculations at the B3LYP/6-311++G(d,p) level of theory.

Exploring potential energy surfaces with gentlest ascent dynamics in combination with the shrinking dimer method and Newtonian dynamics

We revisit the so-called gentlest ascent dynamics reaction path model for finding saddle points of any index in multidimensional potential energy surfaces. The variational nature of the method is analyzed in detail, and an algorithm for the integration of its equations of motion is proposed based on the optimization-based shrinking dimer method. By means of three different two-dimensional model potential energy surfaces, we argue that the combination of the proposed method with Newtonian (dissipative) dynamics could lead to a practical scheme for the exhaustive exploration of potential energy landscapes.

Testing Convergence of Different Free-Energy Methods in a Simple Analytical System with Hidden Barriers

In this work, we study the influence of hidden barriers on the convergence behavior of three free-energy calculation methods: well-tempered metadynamics (WTMD), adaptive-biasing forces (ABF), and on-the-fly parameterization (OTFP). We construct a simple two-dimensional potential-energy surfaces (PES) that allows for an exact analytical result for the free-energy in any one-dimensional order parameter. Then we chose different CV definitions and PES parameters to create three different systems with increasing sampling challenges. We find that all three methods are not greatly affected by the hidden-barriers in the simplest case considered. The adaptive sampling methods show faster sampling while the auxiliary high-friction requirement of OTFP makes it slower for this case. However, a slight change in the CV definition has a strong impact in the ABF and WTMD performance, illustrating the importance of choosing suitable collective variables.

Cross-sections and rate coefficients calculations for rotational excitation of cyanoethynylide ions () induced by collision with He atoms at low temperature

The focal points of the present paper are the calculations of cross-sections and rate coefficients for rotational (de-)excitation of C3N− induced by collision with He and H2 atoms for energies of up to 2000 cm−1 and temperatures ranging from 1 K to 300 K. For this study, the new two-dimensional potential energy surface (PES) of the C3N−−He complex has been calculated at the ab initio restricted coupled cluster level of theory, including single, double and perturbative triple excitation [RCCSD(T)-F12a] with the cc-pVTZ-F12 basis set augmented by mid-bond functions. Basis set superposition errors were taken into account. To allow for the dynamical calculations, the PES was then fitted to a global analytical form, the main features of which are discussed. Collisional cross-sections among the first 17 rotational levels were calculated and employed to compute downward and upward rate coefficients. A propensity towards was observed.

Photodissociation Dynamics of Benzaldehyde-d5 at 205 nm:The H Atom Production Channel.

Photodissociation dynamics of benzaldehyde-d5 (C6D5CHO) at 205 nm was investigated by measuring laser-induced fluorescence spectra of fragment H atoms. From the Doppler-broadened spectra, center-of-mass translational energy release into the C6D5CO + H channel was obtained as 68.8 ± 5.8 kJ/mol with the absolute quantum yield, 0.17 ± 0.03. The observed translational energy was successfully estimated from two-dimensional potential energy surfaces along the C-H dissociation coordinate and the CCO bent angle and the out-of-plane H angle, respectively calculated at the B3LYP/cc-pVDZ level. The dissociation of H should take place along the triplet surface via intersystem crossing from S1 after internal conversion from the initially excited S3 state and on the triplet surface, the dissociation proceeds along the CCO bent-linear-bent configuration with H being planar to nonplanar pathway.

The Role of High Excitations in Constructing Sub-spectroscopic Accuracy Intermolecular Potential of He-HCN: Critically Examined by the High-Resolution Spectra with Resonance States

Interpreting high-resolution rovibrational spectra of weakly bound complexes commonly requires spectroscopic accuracy (<1 cm−1) potential energy surfaces (PES). Constructing high-accuracy ab initio PES relies on the high-level electronic structure approaches and the accurate physical models to represent the potentials. The coupled cluster approaches including single and double excitations with a perturbational estimate of triple excitations (CCSD(T)) have been termed the “gold standard” of electronic structure theory, and widely used in generating intermolecular interaction energies for most van der Waals complexes. However, for HCN-He complex, the observed millimeter-wave spectroscopy with high-excited resonance states has not been assigned and interpreted even on the ab initio PES computed at CCSD(T) level of theory with the complete basis set (CBS) limit. In this work, an effective three-dimensional ab initio PES for HCN-He, which explicitly incorporates dependence on the Q1 (C–H) normal-mode coordinate of the HCN monomer has been calculated at the CCSD(T)/CBS level. The post-CCSD(T) interaction energy has been examined and included in our PES. Analytic two-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for v1(C–H)=0, and 1 to the Morse/Long-Range potential function form with root-mean-square deviations (RMSD) smaller than 0.011 cm−1. The role and significance of the post-CCSD(T) interaction energy contribution are clearly illustrated by comparison with the predicted rovibrational energy levels. With or without post-CCSD(T) corrections, the value of dissociation limit (D0) is 8.919 or 9.403 cm−1, respectively. The predicted millimeter-wave transitions and intensities from the PES with post-CCSD(T) excitation corrections are in good agreement with the available experimental data with RMS discrepancy of 0.072 cm−1. Moreover, the infrared spectrum for HCN-He complex is predicted for the first time. These results will serve as a good starting point and provide reliable guidance for future infrared studies of HCN doped in (He)n clusters.

The torsional barriers of two equivalent methyl internal rotations in 2,5-dimethylfuran investigated by microwave spectroscopy

The microwave spectrum of 2,5-dimethylfuran was recorded using two pulsed molecular jet Fourier transform microwave spectrometers which cover the frequency range from 2 to 40 GHz. The internal rotations of two equivalent methyl tops with a barrier height of approximately 439.15 cm−1 introduce torsional splittings of all rotational transitions in the spectrum. For the spectral analysis, two different computer programs were applied and compared, the PAM-C2v-2tops code based on the principal axis method which treats several torsional states simultaneously, and the XIAM code based on the combined axis method, yielding accurate molecular parameters. The experimental work was supplemented by quantum chemical calculations. Two-dimensional potential energy surfaces depending on the torsional angles of both methyl groups were calculated and parametrized.

Cold collisions of heavy Σ2 molecules with alkali-metal atoms in a magnetic field: Ab initio analysis and prospects for sympathetic cooling of SrOH(Σ+2) by Li(S2)

We use accurate ab initio and quantum scattering calculations to explore the prospects for sympathetic cooling of the heavy molecular radical SrOH($^2\Sigma$) by ultracold Li atoms in a magnetic trap. A two-dimensional potential energy surface (PES) for the triplet electronic state of Li-SrOH is calculated ab initio using the partially spin-restricted coupled cluster method with single, double and perturbative triple excitations and a large correlation-consistent basis set. The highly anisotropic PES has a deep global minimum in the skewed Li-HOSr geometry with $D_e=4932$ cm$^{-1}$ and saddle points in collinear configurations. Our quantum scattering calculations predict low spin relaxation rates in fully spin-polarized Li+SrOH collisions with the ratios of elastic to inelastic collision rates well in excess of 100 over a wide range of magnetic fields (1-1000 G) and collision energies (10$^{-5}-0.1$~K) suggesting favorable prospects for sympathetic cooling of SrOH molecules with spin-polarized Li atoms in a magnetic trap. We find that spin relaxation in Li+SrOH collisions occurs via a direct mechanism mediated by the magnetic dipole-dipole interaction between the electron spins of Li and SrOH, and that the indirect (spin-rotation) mechanism is strongly suppressed. The upper limit to the Li+SrOH reaction rate coefficient calculated for the singlet PES using adiabatic capture theory is found to decrease from $4\times 10^{-10}$~cm$^3$/s to a limiting value of $3.5\times 10^{-10}$ cm$^3$/s with decreasing temperature from 0.1 K to 1 $\mu$K.

Theoretical study on the thermal cis - Trans isomerization of novel acylhydrazone photoswitches

Quantum chemical calculations of a potent class of photoswitches acylhydrazones have been carried out with the goal to describe their thermal cis → trans isomerization. The effects of substituents, in particular their number, position and nature of the substituents (electron donating/withdrawing groups (EDGs/EWGs)), on activation energies incorporating solvent effects have been systematically researched with the ultimate goal to illuminate the isomerization process. Our results show that most parameters are highly dependent on the substitution pattern on the crucial positions (R1 and R2 position) of the backbone fragment, which in turn has a significant impact on the absorption spectra, the energy levels of molecular orbitals, the transition properties for the trans/cis isomers, the half-lives τ1/2 and the rate constants for the thermal cis → trans isomerization of the compounds. In summary, both relative strength of the donor/accept groups and solvent polarity have significant impact on the electric properties. Finally, the nature of the transition state(s) and its dependence on substituents and the environment are discussed. An ingenious approach to the construction of reaction path was realized, and energy barriers were determined from two-dimensional potential energy surfaces of the ground states.

Insight into the excited-state intramolecular double-proton transfer of the 2,5-bis(benzoxazol-2-yl)thiophene-3,4-diol: one-step or stepwise mechanism?

The excited-state double-proton transfer mechanism of 2,5-bis(benzoxazol-2-yl)thiophene-3,4-diol has been theoretically investigated based on the methods of density functional theory and time-dependent density functional theory. Geometric structure comparison and infrared vibrational spectra analysis confirm that the strengthening of the intramolecular hydrogen bond in the first excited state (S1) has facilitated the proton transfer process. The frontier molecular orbitals analysis illustrates that the nature of the hydrogen bond enhancement lies in the charge redistribution upon photo-excitation, which is further confirmed by NBO charge analysis quantitatively. The reduced dimensionality (two-dimensional) potential energy surfaces have been scanned for both the ground state (S0) and the first electronic excited state to reveal the mechanism and pathway of the two protons being transferred. Compared with the concerted path of proton transfer, the stepwise path with one proton being transferred first and then a second one followed exhibits a relatively mild energy barrier and seems to be more rational and favorable.

On the origins of intersecting potential energy surfaces

Techniques developed for investigating nonadiabatic processes in molecular systems are adapted to study the structure and properties of holomorphic and meromorphic functions of a complex variable, $$f(z)=\mathfrak {R}(f)+i\,\mathfrak {I}(f)$$ . The connection is that $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ are correlated two-dimensional scalar functions, interrelated by the Cauchy–Riemann equations. Exploiting this fact, it is demonstrated that $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ of f can be envisaged in Euclidean $${\mathbb {R}}^{3}$$ space as a two-state set of constrained, intersecting two-dimensional potential energy surfaces (PESs), called the graph of f. Importantly, the analytic and algebraic properties of f dictate the geometric structure evinced in the graph of f. This parallels multi-state sets of higher-dimensional, constrained, intersecting PESs linked with correlated electronic eigenstates of the parameterized molecular Hamiltonian operator. In view of this association, the language and mathematical infrastructure devised by chemists for discussing and analyzing intersections in higher-dimensional PESs are suitably modified for f. Notably, an algorithm capable of optimizing roots and poles of f through analysis of the real, two-dimensional $$\mathfrak {R}(f)$$ and $$\mathfrak {I}(f)$$ functions is derived, which is based on intersection-adapted coordinate and constrained Lagrangian methodologies. As constrained, intersecting PESs are indispensible for conceptualizing and characterizing the physics governing nonadiabatic phenomena, f represents a foundational bridge to these more abstract constructions.

Conformational preferences and internal rotation of methyl butyrate by microwave spectroscopy

The broadband rotational spectrum of methyl butyrate from 8 to 18GHz, recorded using a chirp-pulsed Fourier transform microwave (FTMW) spectrometer, was combined with high resolution FTMW measurements over the 2–26.5GHz region to provide a comprehensive account of its microwave spectrum under jet-cooled conditions. Two low-energy conformers, one with a fully extended, heavy-atom planar anti/anti structure (a,a), and the other with a gauche propyl chain (g±,a), were assigned in the spectrum. Torsional A/E splittings due to the internal rotation of the methoxy methyl group were resolved for both lower energy conformers, and were fitted using the program XIAM and BELGI, providing an estimate of the barrier to methyl internal rotation of V3≈420cm−1. The conformational landscape of methyl butyrate occurs on a two-dimensional potential energy surface, which was mapped out by quantum chemical calculations at the B2PLYP-D3BJ/aug-cc-pVTZ level of theory. The low torsional barrier about the CC(O)O bond leads to collisional removal of population originally in the (a,g±) and (g±,g±) minima into the (a,a) and (g±,a) minima, respectively, during the cooling in the expansion. Analysis of experimental intensities in the spectrum provide percent populations downstream in the expansion of 41±4% (a,a), and 59±6% (g±,a).

MP4 Study of the Anharmonic Coupling of the Shared Proton Stretching Vibration of the Protonated Water Dimer in Equilibrium and Transition States.

The structure and harmonic and anharmonic IR spectra of the protonated water dimer (PWD) were calculated in C1, C2, and Cs symmetry at the MP4/acc-pVTZ level of theory. We found that structure and IR spectra are practically identical in C2 and C1 symmetry, demonstrating that an equilibrium C1 configuration of the PWD is not realized. Anharmonic coupling of the shared proton stretching vibration with all other modes in the PWD in C2 and Cs symmetry was the focus of this investigation. For this purpose, 28 two-dimensional potential energy surfaces (2D PES) were built at the MP4/acc-pVTZ level of theory and the corresponding vibrational Schrödinger equations were solved using the DVR method. Differences in the coupling of the investigated mode with other modes in the C2 and Cs configurations, along with some factors that determine the red- or blue-shift of the stretching vibration frequency, were analyzed. We obtained a rather reasonable value of the stretching frequency of the bridging proton (1058.4 cm-1) unperturbed by Fermi resonance. The Fermi resonance between the fundamental vibration ν7 and the combined vibration ν2 + ν6 of the same symmetry was analyzed through anharmonic second-order perturbation theory calculations, as well as by 3D PES constructed using Q2, Q6, and Q7 as normal coordinates. A significant (up to 50%) transfer of intensity from the fundamental vibration to the combined one was found. We have estimated the frequency of the bridging proton stretching vibration in the Cs configuration of the PWD based on calculations of the intrinsic anharmonicity and anharmonic double modes interactions at the MP4/acc-pVTZ level of theory (1261 cm-1).

Cold interactions and chemical reactions of linear polyatomic anions with alkali-metal and alkaline-earth-metal atoms.

We consider collisional studies of linear polyatomic ions immersed in ultracold atomic gases and investigate the intermolecular interactions and chemical reactions of several molecular anions (OH-, CN-, NCO-, C2H-, C4H-) with alkali-metal (Li, Na, K, Rb, Cs) and alkaline-earth-metal (Mg, Ca, Sr, Ba) atoms. State-of-the-art ab initio techniques are applied to compute the potential energy surfaces (PESs) for these systems. The coupled cluster method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed and the scalar relativistic effects in heavier metal atoms are modeled within the small-core energy-consistent pseudopotentials. The leading long-range isotropic and anisotropic induction and dispersion interaction coefficients are obtained within the perturbation theory. The PESs are characterized in detail and their universal similarities typical for systems dominated by the induction interaction are discussed. The two-dimensional PESs are provided for selected systems and can be employed in scattering calculations. The possible channels of chemical reactions and their control are analyzed based on the energetics of the reactants. The present study of the electronic structure is the first step towards the evaluation of prospects for sympathetic cooling and controlled chemistry of linear polyatomic ions with ultracold atoms.

Low barrier methyl rotation in 3-pentyn-1-ol as observed by microwave spectroscopy

ABSTRACTThe rotational spectrum of 3-pentyn-1-ol, CH3−C≡C−CH2CH2OH, was measured using a molecular beam Fourier transform microwave spectrometer operating in the frequency range from 2 to 26.5 GHz. A two-dimensional potential energy surface was calculated at the MP2/6-311++G(d,p) level of theory for a conformational analysis, yielding five conformers. The most stable conformer exhibits C1 symmetry and was assigned in the spectrum by comparison with the results from quantum chemical calculations. The barrier to internal rotation of the propynyl methyl group CH3−C≡C− was found to be only 9.4552(94) cm−1. Molecular parameters and internal rotation parameters could be accurately determined using the program xiam and belgi-C1. The internal rotation barrier was compared with those of other molecules containing a propynyl methyl group.

Ultracold rotational deexcitation of CO (1Σ+) collision with proton

Ultracold rotational deexcitation cross sections and rate coefficients have been computed for CO collision with proton using close-coupling method on the two-dimensional ground state potential energy surface computed at the MRCI/cc-pVTZ level of theory. State-to-state rate coefficients have been obtained for temperature range from 10−5K to 200K. The system displays higher propensity with j′=0 cross section magnitude closer to j′=1 state, and j′=2 cross section closer to j′=3 state, from initial j=4 state. In ultracold region, the magnitude of cross section increases with the decrease in collision energy following Wigner’s threshold law.

Ab initio studies of the Rg-NO(+)(X(1)Σ(+)) van der Waals complexes (Rg = He, Ne, Ar, Kr, and Xe).

We used the explicitly correlated variant of the coupled clusters method with single, double, and noniterative triple excitations [CCSD(T)-F12] to compute two-dimensional potential energy surfaces of van der Waals complexes formed by rare gas atoms (Rg) and NO(+)(X(1)Σ(+)) cations. We used the correlation-consistent, triple-zeta (cc-pVTZ-F12) atomic basis sets, and for Kr and Xe rare gases, we employed corresponding pseudopotential cc-pVTZ-PP-F12 atomic basis sets. These basis sets were additionally augmented with mid-bond functions. The complexes are all of skewed T-shape type with Rg atom being closer to the N-side. Using analytical representation of the potentials, we have estimated zero-point energy corrected dissociation energies from anharmonic calculations with BOUND program and also from the harmonic approximation. The binding energies increase with the polarization of the Rg atom in series from He to Xe and are 196 cm(-1), 360 cm(-1), 1024 cm(-1), 1434 cm(-1), and 2141 cm(-1), respectively. Their corresponding dissociation energies are 132 cm(-1), 300 cm(-1), 927 cm(-1), 1320 cm(-1), and 1994 cm(-1) for the complexes with He to Xe, respectively. We find good agreement with previous theoretical and experimental results. The harmonic vibrational frequencies were calculated for the bending and stretching modes of the Rg-NO(+) complexes.

Hybrid MC/QC simulations of water-assisted proton transfer in nucleosides. Guanosine and its analog acyclovir

To provide an in-depth insight into the molecular basis of spontaneous tautomerism in DNA and RNA base pairs, a hybrid Monte Carlo (MC)–quantum chemical (QC) methodology is implemented to map two-dimensional potential energy surfaces along the reaction coordinates of solvent-assisted proton transfer processes in guanosine and its analog acyclovir in aqueous solution. The solvent effects were simulated by explicit inclusion of water molecules that model the relevant part of the first hydration shell around the solute. The position of these water molecules was estimated by carrying out a classical Metropolis Monte Carlo simulation of dilute water solutions of the guanosine (Gs) and acyclovir (ACV) and subsequently analyzing solute–solvent intermolecular interactions in the statistically-independent MC-generated configurations. The solvent-assisted proton transfer processes were further investigated using two different ab initio MP2 quantum chemical approaches. In the first one, potential energy surfaces of the ‘bare’ finite solute–solvent clusters containing Gs/ACV and four water molecules (MP2/6-31+G(d,p) level) were explored, while within the second approach, these clusters were embedded in ‘bulk’ solvent treated as polarizable continuum (C-PCM/MP2/6-31+G(d,p) level of theory). It was found that in the gas phase and in water solution, the most stable tautomer for guanosine and acyclovir is the 1H-2-amino-6-oxo form followed by the 2-amino-6-(sZ)-hydroxy form. The energy barriers of the water-assisted proton transfer reaction in guanosine and in acyclovir are found to be very similar – 11.74 kcal mol−1 for guanosine and 11.16 kcal mol−1 for acyclovir, and the respective rate constants (k = 1.5 × 101 s−1, guanosine and k = 4.09 × 101 s−1, acyclovir), are sufficiently large to generate the 2-amino-6-(sZ)-hydroxy tautomer. The analysis of the reaction profiles in both compounds shows that the proton transfer processes occur through the asynchronous concerted mechanism.

The molecular structure of phenetole studied by microwave spectroscopy and quantum chemical calculations

ABSTRACTA pulsed molecular beam Fourier transform microwave spectrometer operating in the frequency range 2–26.5 GHz was used to measure the spectrum of phenetole (ethyl phenyl ether or ethoxybenzene, C6H5OC2H5). The conformational landscape is completely determined by the orientations of the phenyl ring and the ethyl group. A two-dimensional potential energy surface was calculated at the MP2/6-311++G(d,p) level of theory. Two conformers were found: the trans conformer has a Cs symmetry, and the gauche conformer has the ethyl group tilted out of the phenyl plane by about 70°. Totally, 186 rotational transitions were assigned to the more stable planar trans conformer, and fitted using a semi-rigid rotor model to measure accuracy. Highly accurate rotational and centrifugal distortion constants were determined. Several method and basis set combinations were applied to check for convergence and to compare with the experimentally deduced molecular parameters.