Vapour-liquid equilibrium of the acetone---methanol system in the presence of KSCN and comparison with other salts

The effect of KSCN at salt mole fractions of 0.01–0.05 and at saturation on the VLE of the binary acetone-methanol system has been experimentally investigated at 101.32 kPa using a modified Othmer equilibrium still. The experimental data were correlated by the electrolytic NRTL model [B. Mock, L.B. Evans and C.C. Chen, AIChE J., 32 (1986) 1655–1664], the extended UNIQUAC equation [B. Sander, A. Fredensland and P. Rasmussen, Chem. Eng. Sci., 41 (1986) 1171–1183] and the modified Wilson and NRTL models proposed by Tan [T.C. Tan, AIChE J., 31 (1985) 2083–2085; Chem. Eng. Res. Des., 65 (1987) 355–366; Trans. Inst. Chem. Eng., 68 (1990) 93–102]. The results were compared with those obtained by Tan's predictive models. A crossover between the salting-out and salting-in effects on acetone and a non-azeotropic minimum in the temperature-composition diagram were observed at low and high salt concentrations. Based on the solubility data in the mixture, comparisons with the effect of other salts on the same mixed solvent were made.     

Designing novel nicotinic agonists by searching a database of molecular shapes

Summary We introduce an approach by which novel ligands can be designed for a receptor if a pharmacophore geometry has been established and the receptor-bound conformations of other ligands are known. We use the shape-matching method of Kuntz et al. [J. Mol. Biol., 161 (1982) 269–288] to search a database of molecular shapes for those molecules which can fit inside the combined volume of the known ligands and which have interatomic distances compatible with the pharmacophore geometry. Some of these molecules are then modified by interactive modeling techniques to better match the chemical properties of the known ligands. Our shape database (about 5000 candidate molecules) is derived from a subset of the Cambridge Crystallographic Database [Allen et al., Acta Crystallogr., Sect. B,35 (1979) 2331–2339]. We show, as an example, how several novel designs for nicotinic agonists can be derived by this approach, given a pharmacophore model derived from known agonists [Sheridan et al., J. Med. Chem., 29 (1986) 889–906]. This report complements our previous report [DesJarlais et al., J. Med. Chem., in press], which introduced a similar method for designing ligands when the structure of the receptor is known.     

Molecular dynamics simulations of hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) using a combined Sorescu-Rice-Thompson AMBER force field

We present the results of molecular dynamics simulations of crystalline hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) using the SRT-AMBER force field (P. M. Agrawal et al., J. Phys. Chem. B 2006, 110, 5721), which combines the rigid-molecule force field developed by Sorescu-Rice-Thompson (D. C. Sorescu, B. M. Rice, and D. L. Thompson, J. Phys. Chem. B 1997, 101, 798) with the intramolecular interactions obtained from the Generalized AMBER Force Field (Wang et al., J. Comput. Chem. 2004, 25, 1157). The calculated crystal density at room conditions is about 10% lower than the measured value, while the lattice parameters and thermodynamic melting point are within about 5% at ambient pressure. The chair and inverted chair conformation, bond lengths, and bond angles of the RDX molecule are accurately predicted; however, there are some inaccuracies in the calculated orientations of the NO2 groups. The SRT-AMBER force field predicts overall reasonable results, but modifications, probably in the torsional parameters, are needed for a more accurate force field.     

Supercooled water's thermodynamic behaviour and a conflict between Arrhenius relaxation and configurational entropy

The increase in the time- and temperature-dependent heat capacity, C_p, in the glass–liquid transition range of water has been investigated using earlier data [G.P. Johari, A. Hallbrucker, E. Mayer, Nature 330 (1987) 552], new computation of the manner of C_p increase in the glass–liquid transition range and theoretical views. The investigation shows that the temperature dependence of structural relaxation time of water in the 136–148 K range remains non-Arrhenius, like the dielectric relaxation time [G.P. Johari, J. Chem. Phys. 105 (1996) 7079] and the self-diffusion coefficient [R.C. Smith, B.D. Kay, Nature 398 (1999) 788]. Theoretical reasons for the broadening of the heat-capacity endotherm are given and verified by computation. Analysis shows that for an Arrhenius-type relaxation-dynamics, the configurational entropy of a liquid will remain constant on its cooling, which violates the consequences of the third law of thermodynamics. When the relaxation time is taken as 10² s at T_g and as 10⁻¹⁴ s at infinite temperature for analysing a liquid's relaxation [K. Ito, C.T. Moynihan, C.A. Angell, Nature 398 (1999) 492; R. Richert, C.A. Angell, J. Chem. Phys. 108 (1998) 9016], the Arrhenius energy becomes unjustifiably proportional to the T_g of a liquid. In its glass transition features, water is not as analogous with molten silica as is believed.     

A versatile method for systematic conformational searches: application to CheY

A novel molecular structure prediction method, the Z Method, is described. It provides a versatile platform for the development and use of systematic, grid‐based conformational search protocols, in which statistical information (i.e., rotamers) can also be included. The Z Method generates trial structures by applying many changes of the same type to a single starting structure, thereby sampling the conformation space in an unbiased way. The method, implemented in the CHARMM program as the Z Module, is applied here to an illustrative model problem in which rigid, systematic searches are performed in a 36‐dimensional conformational space that describes the relative positions of the 10 secondary structural elements of the protein CheY. A polar hydrogen representation with an implicit solvation term (EEF1) is used to evaluate successively larger fragments of the protein generated in a hierarchical build‐up procedure. After a final refinement stage, and a total computational time of about two‐and‐a‐half CPU days on AMD Opteron processors, the prediction is within 1.56 Å of the native structure. The errors in the predicted backbone dihedral angles are found to approximately cancel. Monte Carlo and simulated annealing trials on the same or smaller versions of the problem, using the same atomic model and energy terms, are shown to result in less accurate predictions. Although the problem solved here is a limited one, the findings illustrate the utility of systematic searches with atom‐based models for macromolecular structure prediction and the importance of unbiased sampling in structure prediction methods. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Modification of the integral isoconversional method to account for variation in the activation energy

Integral isoconversional methods may give rise to noticeable systematic error in the activation energy when the latter strongly varies with the extent of conversion. This error is eliminated by using an integration technique that properly accounts for the variation in the activation energy. The technique is implemented as a modification of the earlier proposed advanced isoconversional method [Vyazovkin, S. J Comput Chem 1997, 18, 393]. The applications of the modified method are illustrated by simulations as well as by processing of data on the thermal decomposition of calcium oxalate monohydrate and ammonium nitrate. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 178–183, 2001     

Quantitative analysis of the calorimetric parameters associated with the temperature induced aggregation of aqueous solutions of polyoxypropylene

High sensitivity differential scanning calorimetry (HSDSC)—coupled with the application of a previously outlined thermodynamic model [Patterson et al., Langmuir 13 (1997) 2219]—has been used to the obtain thermodynamic parameters that characterise thermal aggregation in aqueous solutions of polyoxypropylene (POP) of molecular mass 1000 g mol⁻¹ over a range of concentrations (2.5–51.5 g dm⁻³). An important aspect of the derived thermodynamic values, which complements previously reported HSDSC data [Armstrong et al., J. Phys. Chem. 99 (1995) 4590], is the elaboration of heat capacity changes which accompany the aggregation transition. The concentration dependence of the POP thermodynamic data, obtained in this investigation, has been established. These observations provide the means for establishing functional relationships between enthalpy and temperature as well as heat capacity and temperature. The parameters describing the quadratic relationship between enthalpy change associated with aggregation and temperature are in close agreement with those describing the linear relationship between heat capacity change and temperature.     

Drainage and critical thickness of foam films from aqueous solutions of mixed nonionic surfactants

The thinning and the critical thickness (of rupture or “black spots” formation) of foam films from aqueous solutions of mixed nonionic surfactants are studied under varied experimental conditions, as a function of film radius (0.05–0.15 mm), surfactant concentration (0.01–1.0 CMC) and ionic strength (0.001–0.1 M NaCl). The experimental values of the drainage coefficient (), determined from the film thickness versus time dependences, were used to calculate the theoretical values of the film critical thickness.

The real velocity of film thinning is a major factor in the process of reaching the state of kinetic instability when approaching the critical thickness (Scheludko's criterion). The classical equation used to describe the film thinning rate, proposed and named by Scheludko (1955) “Reynolds Law”, is applicable for small film radii (r < 0.05 mm). At larger radii the velocity of thinning follows the equation of Manev et al. [E.D. Manev, R. Tsekov, B. Radoev, J. Colloid Interf. Sci. 18 (1997) 769], which takes into account the effect of the film thickness local non-homogeneity.

The studied stabilizing surfactants include n-dodecyl-β-d-maltoside (β-C12G2) and hexaethyleneglycol monododecyl ether (C12E6). Along with confirming the dependences following from the theories of the critical thickness [B. Radoev, A. Scheludko, E.D. Manev, J. Colloid Interf. Sci. 95 (1983) 254] and film thinning [E.D. Manev, R. Tsekov, B. Radoev, J. Colloid Interf. Sci. 18 (1997) 769], the results of the present investigation established also certain deviations for films stabilized with mixed surfactants (β-C12G2 + C12E6). The effectiveness of the empirical equation, employing the drainage coefficient () to describe the film thinning, is emphatically proven here.     

Interprotein electron transfer in a confined space: uncoupling protein dynamics from electron transfer by sol-gel encapsulation

In this paper, we describe the first observations of photoinitiated interprotein electron transfer (ET) within sol-gels. We have encapsulated three protein-protein complexes, specifically selected because they represent a full range of affinities, are sensitive to different types of dynamic processes, and thus are expected to respond differently to sol-gel encapsulation. The three systems are (i) the [Zn, Fe(3+)L] mixed-metal hemoglobin hybrids, where the alpha(1)-Zn and beta(2)-Fe subunits correspond to a "predocked" protein-protein complex with a crystallographically defined interface (Natan, M. J.; Baxter, W. W.; Kuila, D.; Gingrich, D. J.; Martin, G. S.; Hoffman, B. M. Adv. Chem. Ser. 1991, 228 (Electron-Transfer Inorg., Org., Biol. Syst.), 201-213), (ii) the Zn-cytochrome c peroxidase complex with cytochrome c, [ZnCcP, Fe(3+)Cc], having an intermediate affinity between its partners (Nocek, J. M.; Zhou, J. S.; De Forest, S.; Priyadarshy, S.; Beratan, D. N.; Onuchic, J. N.; Hoffman, B. M. Chem. Rev. 1996, 96, 2459-2489), and (iii) the [Zn-deuteromyoglobin, ferricytochrome b(5)] complex, [ZnDMb, Fe(3+)b(5)], which is loosely bound and highly dynamic (Liang, Z.-X.; Nocek, J.; Huang, K.; Hayes, R. T.; Kurnikov, I. V.; Beratan, D. N.; Hoffman, B. M. J. Am. Chem. Soc. 2002, 124, 6849-6859. Intersubunit ET within the hybrid does not involve second-order processes or subunit rearrangements, and thus is influenced only by perturbations of high-frequency motions coupled to ET. For the latter two complexes, sol-gel encapsulation eliminates second-order processes: protein partners encapsulated as a complex must stay together throughout a photoinitiated ET cycle, while proteins encapsulated alone cannot acquire a partner. It further modulates intracomplex motions of the two partners.     

Implementation of empirical dispersion corrections to density functional theory for periodic systems

A recently developed empirical dispersion correction (Grimme et al., J. Chem. Phys. 2010, 132, 154104) to standard density functional theory (DFT‐D3) is implemented in the plane‐wave program package VASP. The DFT‐D3 implementation is compared with an implementation of the earlier DFT‐D2 version (Grimme, J. Comput. Chem. 2004, 25, 1463; Grimme, J. Comput. Chem. 2006, 27, 1787). Summation of empirical pair potential terms is performed over all atom pairs in the reference cell and over atoms in shells of neighboring cells until convergence of the dispersion energy is obtained. For DFT‐D3, the definition of coordination numbers has to be modified with respect to the molecular version to ensure convergence. The effect of three‐center terms as implemented in the original molecular DFT‐D3 version is investigated. The empirical parameters are taken from the original DFT‐D3 version where they had been optimized for a reference set of small molecules. As the coordination numbers of atoms in bulk and surfaces are much larger than in the reference compounds, this effect has to be discussed. The results of test calculations for bulk properties of metals, metal oxides, benzene, and graphite indicate that the original parameters are also suitable for solid‐state systems. In particular, the interlayer distance in bulk graphite and lattice constants of molecular crystals is considerably improved over standard functionals. With the molecular standard parameters (Grimme et al., J. Chem. Phys. 2010, 132, 154104; Grimme, J. Comput. Chem. 2006, 27, 1787) a slight overbinding is observed for ionic oxides where dispersion should not contribute to the bond. For simple adsorbate systems, such as Xe atoms and benzene on Ag(111), the DFT‐D implementations reproduce experimental results with a similar accuracy as more sophisticated approaches based on perturbation theory (Rohlfing and Bredow, Phys. Rev. Lett. 2008, 101, 266106). © 2012 Wiley Periodicals, Inc.     

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451–459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements H Br. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.     

Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator [T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)] and the long-range Ewald operator [T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)]) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use.     

Molecular dynamics simulations of peptide carboxylate hydration

Aqueous solvation of carboxylate groups, as present in the glycine zwitterion and the dipeptide aspartylalanine, is studied employing a force-field that includes distributed multipole electrostatics and induction contributions (Amoebapro: P. Ren and J. W. Ponder, J. Comput. Chem., 2002, 23, 1497; P. Ren and J. W. Ponder, J. Phys. Chem. B, 2003, 107, 5933; J. W. Ponder and D. A. Case, Adv. Protein Chem., 2003, 66, 27). Radial and orientation distribution functions, as well as hydration numbers, are calculated and compared with existing simulation data derived from Car-Parrinello molecular dynamics (CPMD), and also distributed-charge force-fields. Connections are also made with experimental data for solvation of carboxylates in water. Our findings show that Amoebapro yields carboxylate solvation properties in very good agreement with CPMD results, significantly closer agreement than can be obtained from traditional force-fields. We also demonstrate that the influence of solvation on the conformation of the dipeptide is markedly different using Amoebapro compared with the other force-fields.     

Structural and optical properties of highly hydroxylated fullerenes: stability of molecular domains on the C60 surface

The excitation spectra and the structural properties of highly hydroxylated C(60)(OH)(x) fullerenes (so-called fullerenols) are analyzed by comparing optical absorption experiments on dilute fullerenol-water solutions with semiempirical and density functional theory electronic structure calculations. The optical spectrum of fullerenol molecules with 24-28 OH attached to the carbon surface is characterized by the existence of broad bands with reduced intensities near the ultraviolet region (below approximately 500 nm) together with a complete absence of optical transitions in the visible part of the spectra, contrasting with the intense absorption observed in C(60) solutions. Our theoretical calculations of the absorption spectra, performed within the framework of the semiempirical Zerner intermediate neglect of diatomic differential overlap method [Reviews in Computational Chemistry II, edited by K. B. Lipkowitz and D. B. Boyd (VCH, Weinheim, 1991), Chap. 8, pp. 313-316] for various gas-phase-like C(60)(OH)(26) isomers, reveal that the excitation spectra of fullerenol molecules strongly depend on the degree of surface functionalization, the precise distribution of the OH groups on the carbon structure, and the presence of impurities in the samples. Interestingly, we have surprisingly found that low energy atomic configurations are obtained when the OH groups segregate on the C(60) surface forming molecular domains of different sizes. This patchy behavior for the hydroxyl molecules on the carbon surface leads in general to the formation of fullerene compounds with closed electronic shells, large highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps, and existence of an excitation spectrum that accounts for the main qualitative features observed in the experimental data.     

Molecular dynamics simulations of shock waves in oriented nitromethane single crystals: plane-specific effects

Molecular dynamics simulations of supported shock waves (shock pressure P(s) ～ 15 GPa) propagating along the [110], [011], [101], and [111] directions in crystalline nitromethane initially at T = 200 K were performed using the nonreactive Sorescu-Rice-Thompson force field [D. C. Sorescu, B. M. Rice, and D. L. Thompson, J. Phys. Chem. B 104, 8406 (2000)]. These simulations, combined with those from a preceding study of shocks propagating along [100], [010], and [001] directions in nitromethane for similar conditions of temperature and shock pressure [L. He, T. D. Sewell, and D. L. Thompson, J. Chem. Phys. 134, 124506 (2011)], have been used to study the post-shock relaxation phenomena. Shocks along [010] and [101] lead to a crystal-crystal structure transformation. Shocks propagating along [011], [110], [111], [100], and [001] exhibit plane-specific disordering, which was characterized by calculating as functions of time the 1D mean square displacement (MSD), 2D radial distribution function (RDF), and 2D orientation order parameter P(2)(θ) in orthogonal planes mutually perpendicular to the shock plane; and by calculating as functions of distance behind the shock front the Cartesian components of intermolecular, intramolecular, and total kinetic energies. The 2D RDF results show that the structural disordering for shocks along [100], [110], and [111] is strongly plane-specific; whereas for shocks along [001] and [011], the loss of crystal structural order is almost equivalent in the orthogonal planes perpendicular to the shock plane. Based on the entire set of simulations, there is a trend for the most extensive disordering to occur in the (010) and (110) planes, less extensive disordering to occur in the (100) plane, and essentially no disordering to occur in the (001) plane. The 2D P(2)(θ) and 1D MSD profiles show, respectively, that the orientational and translational disordering is plane-specific, which results in the plane-specific structural disordering observed in the 2D RDF. By contrast, the kinetic energy partitioning and redistribution do not exhibit plane specificity, as shown by the similarity of spatial profiles of the Cartesian components of the intermolecular, intramolecular, and total kinetic energies in orthogonal planes perpendicular to the shock plane.     

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, [linear span]R(g)(2)[linear span], was found to scale as N(4/5) for an intermediate regime and N(2/3) for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204905 (2011)]. Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

Flexible docking simulations: Scaled collective variable Monte Carlo minimization approach using Bezier splines,and comparison with a standard Monte Carlo algorithm

An algorithm for docking a flexible ligand onto a flexible or rigid receptor, using the scaled‐collective‐variables Monte Carlo with energy minimization approach, is presented. Energy minimization is shown to be one of the best techniques for distinguishing between native‐ and nonnative‐generated conformations. Incorporation of this technique into a Monte Carlo procedure enables one to distinguish the native conformation directly during the conformational search. It avoids the generation of a large number of ligand conformers for which more sophisticated energy evaluation tools would have had to be applied to identify the nativelike conformations. The efficiency of the Monte Carlo minimization was greatly improved by incorporating a new grid‐based energy evaluation technique using Bezier splines for which the energy function, as well as all of its derivatives, can be deduced from the values at the grid points. Comparison between our ECEPP/3‐based algorithm and the Monte Carlo algorithm presented elsewhere (Hart, T. N.; Read, R. J. Prot Struct Funct Genet 1992, 13, 206–222) has been made for docking NH₂ D Phe Pro Arg COOH, the noncovalent analog of NH₂ D Phe Pro Arg chloromethylketone (PPACK), onto the active site of human α‐thrombin. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 244–252, 1999     

Molecular dynamics simulations of spontaneous bile salt aggregation

Bile salts are surfactants in bile that facilitate digestion, adsorption and excretion of various compounds. They have planar hydrophobic and hydrophilic faces and therefore exhibit some unusual properties; including the shape and size of the micelles that they form. Molecular dynamics simulations of the spontaneous aggregation of six bile salts (cholate (CHD), glycocholate (GCH), taurocholate (TCH), glycochenodeoxycholate (GCD), glycodeoxycholate (GDX) and glycolithocholate (GLC)) were performed in an aqueous phase to gain insight into their micellar structure. The aggregates that formed spontaneously from a random distribution of molecules ranged in size from 8 to 17 molecules. The structures are highly dynamic in nature and are on average oblate, but can vary from oblate, to spherical or prolate. Intermolecular hydrogen bonding within the micelles was found to be an important factor in determining the micelle size, structure and dynamics. The molecular arrangement within the micelles maximises the hydration of the hydrophilic chains and some favourable orientations for adjacent molecules were acquired. The dynamics of the micelles were investigated using the hydrogen-bond lifetime autocorrelation function correlation time, which exhibited a relationship with the degree of hydroxylation. Comparison of the proposed model to the three literature models showed some features of the disk shaped models of Cary and Small [M.C. Cary, D.M. Small, Arch. Intern. Med. 130 (1972) 506–527] and Kawamura et al. [H. Kawamura, Y. Murata, T. Yamaguchi, H. Igimi, M. Tanaka, G. Sugihara, J.P. Kratohvil, J. Phys. Chem. 93 (1989) 3321–3326], whereas the third, inverted helix model of Giglio et al. [E. Giglio, S. Loreti, N.V. Pavel, J. Phys. Chem. 92 (1988) 2858–2862] can be discounted. The proposed model is better than the existing models, which assumed a rigid and structured molecular arrangement.     

A quantum-classical treatment of non-adiabatic transitions

We have carried out molecular dynamics simulations of non-adiabatic processes with the help of a newly formulated potentially exact quantum-classical approach derived from a method proposed earlier [J. Chem. Phys. 118 (2003) 5302]. In this method, time-dependent Schroedinger equation is solved by representing Ψ on a moving Gauss–Hermite DVR grid, the motion of grid-centre being handled classically, but self consistently with the quantum evolution of the wavefunction. Electronic transitions are allowed anywhere in the configuration space among any number of coupled states. We have tested the method on three model problems proposed by J.C. Tully [J. Chem. Phys. 93 (1990) 1061]. These models are relevant to a wide range of gas-phase and condensed-phase phenomena occurring even at low energies. Excellent agreement of computed transition probabilities with corresponding quantum mechanical (DVR/FFT) results even in the deep quantum regime and its cost-efficiency (computational) are encouraging.