Rigid Rotor Harmonic Oscillator Research Articles

Structural and thermochemical properties of methyl ethyl sulfide alcohols: HOCH2SCH2CH3, CH3SCH(OH)CH3, CH3SCH2CH2OH, and radicals corresponding to loss of H atom

AbstractSulfide alkoxy radicals are important intermediates during the partial oxidation of alkyl sulfides in atmospheric chemistry and in combustion. The atmospheric reaction sequence to formation of the alkoxy radicals includes (1) initial reaction with OH to create a radical on a carbon site, (2) the carbon radical then associates with 3O2 to form a peroxy radical, and (3) an NO radical reacts with the peroxy radical to form an alkoxy radical (RO•) plus NO2. This study determines structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (ΔfH°, S°, and Cp(T)) of 3 corresponding alcohols HOCH2SCH2CH3, CH3SCH(OH)CH3, and CH3SCH2CH2OH of methyl ethyl sulfides studied in order to characterize the thermochemistry of the respective alkoxy radicals. The lowest energy molecular structures were calculated using the B3LYP density functional level of theory with the 6‐311G(2d,d,p) basis set. Standard enthalpies of formation (ΔfH°298) for the radicals and their parent molecules were calculated using B3LYP/6‐31 + G(2d,p), CBS‐QB3, M062x/6‐311 + g(2d,p), and G3MP2B3 methods. Isodesmic reactions were used to determine ∆fH° values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31 + G(d,p) level theory. The contributions for S°298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by CBS‐QB3 calculations, with contributions from torsion frequencies replaced by internal rotor contributions. Group additivity and hydrogen bond increment values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxide molecules and their radicals.

A theoretical explanation of RbBH4’s fractionally occupied ground-state phase and the reorientational motion of the [BH4]− group

In this work, a pseudo-structure model is adopted to describe the fractionally occupied phase of RbBH4 at low temperatures. The fractionally occupied cubic ground state with Fm3m symmetry can be explained as a superposition and average of three well-defined pseudo-structures with P43m, F43m and P42/nmc symmetries. First, both mechanical and dynamical stability of these pseudo-structures are supported by the calculated elastic constants and phonon spectra, respectively. By comparing the electronic structure, elastic properties and thermodynamic properties of these well-defined pseudo-structures, it can be found that all pseudo-structures exhibit a certain degree of similarity. Second, the system is stabilized by charge transfer. Bader charge analysis of the pseudo-structures shows that charge transfer in RbBH4 contributes a constant shift in formation energy. Coulomb interaction energy and total electronic energy variations with the unit cell volume have been obtained. The results show that the larger the volume of the unit cell, the lower the difference of Coulomb interaction energy between the pseudo-structures P43m, F43m and P42/nmc. Third, the barrier energies calculated for paths of transitions between these pseudo-structures vary significantly with the volume. As the cell volume decreases from 512 to 216 Å3, the B–H covalent bonds are compressed from 1.242 to 1.208 Å. Meanwhile, the rotational barrier of [BH4]− anion increases rapidly, from 0.04 to 0.97 eV. Last, considering the temperature effect, the free energy and entropy contributions are calculated based on the rigid rotor harmonic oscillator approximation. The Gibbs free energy shows that at low temperature the P42/nmc structure is the preferred structure, and with increasing temperature, the P43m structure becomes the preferred structure. We found that the fractionally occupied phase of RbBH4 can be explained by the size of the Rb+ cation and a subtle balance between the Coulomb interaction energy, electronic total energy and thermal vibration energy.

Structures and thermochemistry of methyl ethyl sulfide and its hydroperoxides: HOOCH2SCH2CH3, CH3SCH(OOH)CH3, CH3SCH2CH2OOH, and radicals

AbstractHydroperoxides and the corresponding peroxy radicals are important intermediates during the partial oxidation of methyl ethyl sulfide (CH3SCH2CH3) in both atmospheric chemistry and in combustion. Structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (ΔHfo, So and Cp(T)) of 3 corresponding hydroperoxides CH2(OOH)SCH2CH3, CH3SCH(OOH)CH3, CH3SCH2CH2OOH of methyl ethyl sulfides, and the radicals formed via loss of a hydrogen atom are important to understanding the oxidation reactions of MES. The lowest energy molecular structures were identified using the density functional B3LYP/6‐311G(2d,d,p) level of theory. Standard enthalpies of formation (ΔHfo298) for the radicals and their parent molecules were calculated using the density functional B3LYP/6‐31G(d,p), B3LYP/6‐31 + G(2d,p), and the composite CBS‐QB3 ab initio methods. Isodesmic reactions were used to determine ∆Hfo values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31G(d,p) level theory. Contributions for So298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by the density functional calculations, with contributions from torsion frequencies replaced by internal rotor contributions. The recommended values for enthalpies of formation of the most stable conformers of CH3SCH2CH2, CH2(OOH)SCH2CH3, CH3SCH(OOH)CH3, and CH3SCH2CH2OOH are −14.0, −33.0, −37.2, and −32.7 kcal/mol, respectively. Group additivity values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxides. Groups for use in group additivity estimation of sulfur peroxide thermochemical properties were developed.

Anharmonicity of Coupled Torsions: The Extended Two-Dimensional Torsion Method and Its Use To Assess More Approximate Methods.

In this work we present the extended two-dimensional torsion (E2DT) method and use it to analyze the performance of several methods that incorporate torsional anharmonicity more approximately for calculating rotational-vibrational partition functions. Twenty molecules having two hindered rotors were studied for temperatures between 100 and 2500 K. These molecules present several kinds of situations; they include molecules with nearly separable rotors, molecules in which the reduced moments of inertia change substantially with the internal rotation, and molecules presenting compound rotation. Partition functions obtained by the rigid-rotor harmonic oscillator approximation, a method involving global separability of torsions and the multistructural methods without explicit potential coupling [MS-T(U)] and with explicit potential coupling [MS-T(C)] of torsions, are compared to those obtained with a quantized version - called the extended two-dimensional torsion (E2DT) method - of the extended hindered rotor approximation of Vansteenkiste et al. ( Vansteenkiste et al. J. Chem. Phys. 2006 , 124 , 044314 ). In the E2DT method, quantum effects due to the torsional modes were incorporated by the two-dimensional nonseparable method, which is a method that is based on the solution of the torsional Schrödinger equation and that includes full coupling in both the kinetic and potential energy. By comparing other methods to the E2DT method and to experimental thermochemical data, this study concludes that the harmonic approximation yields very poor results at high temperatures; the global separation of torsions from the rest of the degrees of freedom is not justified even when an accurate method to treat the torsions is employed; it is confirmed that methods based on less complete potential energy coupling of torsions, such as MS-T(U), are not accurate when dealing with rotors with different barrier heights, and more complete inclusion of torsional coupling to the method in MS-T(C) improves substantially the results in such a way that it could be used in cases where the E2DT method is unaffordable.

Thermodynamic functions and the enthalpies of formation of gaseous VOX3 vanadium oxotrihalides

A critical analysis of experimental and theoretical data on the structure and vibrational frequencies of gaseous VOX3 vanadium oxotrihalides is performed. The values of molecular constants are selected and the thermodynamic functions are calculated within a “rigid rotator–harmonic oscillator” approximation. Equations that approximate a temperature dependence of heat capacity within the temperature range of 298.15–3000 K are obtained. Analysis of the available experimental data allows the enthalpy of formation to be determined for gaseous VOCl3 molecules. The enthalpies of formation for VOF3, VOBr3, and VOI3 molecules are determined for the first time using this value and quantum-chemical calculations of energy of exchange reactions involving VOCl3. The obtained results are added to the database of the IVTANTERMO software.

State-of-the-Art Calculations of Sublimation Enthalpies for Selected Molecular Crystals and Their Computational Uncertainty.

A computational methodology for calculation of sublimation enthalpies of molecular crystals from first principles is developed and validated by comparison to critically evaluated literature experimental data. Temperature-dependent sublimation enthalpies for a set of selected 22 molecular crystals in their low-temperature phases are calculated. The computational methodology consists of several building blocks based on high-level electronic structure methods of quantum chemistry and statistical thermodynamics. Ab initio methods up to the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction with an estimated complete basis set description [CCSD(T)/CBS] are used to calculate the cohesive energies of crystalline phases within a fragment-based additive scheme. Density functional theory (DFT) calculations with periodic boundary conditions (PBC) coupled with the quasi-harmonic approximation are used to evaluate the thermal contributions to the enthalpy of the solid phase. The properties of the vapor phase are calculated within the ideal-gas model using the rigid-rotor harmonic-oscillator model with correction for internal rotation using a one-dimensional hindered rotor approximation and a proper treatment of the molecular rotational degrees of freedom in the vicinity of 0 K. All individual terms contributing to the sublimation enthalpy as a function of temperature are discussed and their uncertainties estimated by comparison to critically evaluated experimental data.

Thermodynamic functions of germanium oxide molecules in the gaseous phase: GeO2(g), Ge2O2(g), and Ge3O3(g)

Critical analysis of experimental and theoretical data on the structure and vibrational frequencies of GeO2, Ge2O2, and Ge3O3 molecules is performed. The values of molecular constants are chosen, and thermodynamic functions in the rigid rotator–harmonic oscillator approximation are calculated in temperature interval Т = 298.15–3000 K. The values obtained are introduced into the data base of the IVTANTERMO program complex.

Structural and thermochemical studies on CH3SCH2CHO, CH3CH2SCHO, CH3SC(═O)CH3, and radicals corresponding to loss of H atom

AbstractCH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 are intermediates during the partial oxidation of CH3SCH2CH3 in the atmosphere and in combustion processes. Thermochemical properties (ΔHfo, So and Cp(T)), structures, internal rotor potentials, and C─H bond dissociation energies of the parent molecules and their radicals formed after loss of a hydrogen atom are of value in understanding the oxidation processes of methyl ethyl sulfide. The lowest energy molecular structures were initially determined using the density functional B3LYP/6‐311G/(2d,d,p) level of theory. Standard enthalpies of formation (ΔHfo298) for the radicals and their parent molecules were calculated using the density functional B3LYP/6‐31G(d,p), B3LYP/6‐31 + G(2d,p), and the composite CBS‐QB3 ab initio methods using isodesmic reactions. Internal rotation potential energy diagrams and internal rotation barriers were investigated using B3LYP/6‐31 + G(d,p) level calculations. The contributions for So298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation on the basis of the structures and vibrational frequencies obtained by the density functional calculations, with contributions from torsion frequencies replaced by internal rotor contributions from the method of Pitzer‐Gwinn. The recommended values for enthalpies of formation of the most stable conformers of CH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 are −34.6 ± 0.8, −42.4 ± 1.2, and ‐49.7 ± 0.8 kcal/mol, respectively. The structural and thermochemical data presented for CH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 and their radicals are of value in understanding the mechanism and kinetics of methyl ethyl sulfide oxidation under varied temperatures and pressures. Group additivity values are developed for estimating properties of structurally similar, larger sulfur‐containing compounds.

Formation of the H2SO4 ·HSO−4 dimer in the atmosphere as a function of conditions: a simulation study

ABSTRACTThe detailed structure and clustering free energy of aerosol particles are important for understanding of new particle formation from molecules and ions in the atmosphere. In this paper, configurations of the H2SO4 ·HSO−4 dimer were sampled with meta-dynamics aided ab initio molecular dynamics (MTD-AIMD) simulations. Based on the rigid rotor harmonic oscillator (RRHO) approximation and the law of mass action, the binding free energies (ΔG) of the dimer in the most stable configuration were calculated for three atmospheric circumstances, i.e. at the ground level and in the middle and upper troposphere. The results show that, the most stable H2SO4 ·HSO−4 dimer is combined via triple O–H⋅⋅⋅O hydrogen bonds. It can be generated efficiently in both the middle and upper troposphere, but not at the ground level. All our simulations were carried out at the level of hybrid density functional theory (PBE0, hybrid-DFT), which is more accurate than DFT only.

Analytic energy-level densities of separable harmonic oscillators including approximate hindered rotor corrections

Energy-level densities are key for obtaining various chemical properties. In chemical kinetics, energy-level densities are used to predict thermochemistry and microscopic reaction rates. Here, an analytic energy-level density formulation is derived using inverse Laplace transformation of harmonic oscillator partition functions. Anharmonic contributions to the energy-level density are considered approximately using a literature model for the transition from harmonic to free motions. The present analytic energy-level density formulation for rigid rotor-harmonic oscillator systems is validated against the well-studied CO+O˙H system. The approximate hindered rotor energy-level density corrections are validated against the well-studied H2O2 system. The presented analytic energy-level density formulation gives a basis for developing novel numerical simulation schemes for chemical processes.

Thermodynamic properties of the gaseous lead phosphates

Wide use of phosphates in different areas motivates interest to investigation of these compounds. Knudsen effusion mass spectrometry was used to study thermodynamic properties of gaseous lead phosphates. On the basis of the measured constants of the equilibrium of gas-phase reactions the standard formation enthalpies of PbPO2, PbPO3 and PbP2O6 have been defined. For these gaseous lead phosphates thermodynamic function were calculated by statistical thermodynamic method in “rigid rotor-harmonic oscillator” approximation. The molecular parameters obtained by different quantum chemistry method.

Elucidation of Mechanisms and Selectivities of Metal-Catalyzed Reactions using Quantum Chemical Methodology.

Quantum chemical techniques today are indispensable for the detailed mechanistic understanding of catalytic reactions. The development of modern density functional theory approaches combined with the enormous growth in computer power have made it possible to treat quite large systems at a reasonable level of accuracy. Accordingly, quantum chemistry has been applied extensively to a wide variety of catalytic systems. A huge number of problems have been solved successfully, and vast amounts of chemical insights have been gained. In this Account, we summarize some of our recent work in this field. A number of examples concerned with transition metal-catalyzed reactions are selected, with emphasis on reactions with various kinds of selectivities. The discussed cases are (1) copper-catalyzed C-H bond amidation of indoles, (2) iridium-catalyzed C(sp(3))-H borylation of chlorosilanes, (3) vanadium-catalyzed Meyer-Schuster rearrangement and its combination with aldol- and Mannich-type additions, (4) palladium-catalyzed propargylic substitution with phosphorus nucleophiles, (5) rhodium-catalyzed 1:2 coupling of aldehydes and allenes, and finally (6) copper-catalyzed coupling of nitrones and alkynes to produce β-lactams (Kinugasa reaction). First, the methodology adopted in these studies is presented briefly. The electronic structure method in the great majority of these kinds of mechanistic investigations has for the last two decades been based on density functional theory. In the cases discussed here, mainly the B3LYP functional has been employed in conjunction with Grimme's empirical dispersion correction, which has been shown to improve the calculated energies significantly. The effect of the surrounding solvent is described by implicit solvation techniques, and the thermochemical corrections are included using the rigid-rotor harmonic oscillator approximation. The reviewed examples are chosen to illustrate the usefulness and versatility of the adopted methodology in solving complex problems and proposing new detailed reaction mechanisms that rationalize the experimental findings. For each of the considered reactions, a consistent mechanism is presented, the experimentally observed selectivities are reproduced, and their sources are identified. Reproducing selectivities requires high accuracy in computing relative transition state energies. As demonstrated by the results summarized in this Account, this accuracy is possible with the use of the presented methodology, benefiting of course from a large extent of cancellation of systematic errors. It is argued that as the employed models become larger, the number of rotamers and isomers that have to be considered for every stationary point increases and a careful assessment of their energies is therefore necessary in order to ensure that the lowest energy conformation is located. This issue constitutes a bottleneck of the investigation in some cases and is particularly important when analyzing selectivities, since small energy differences need to be reproduced.

The ratios of partition functions at different temperatures – Sensitivity to potential energy shape II

The ratios of partition functions at different temperatures are calculated and its dependence on potential energy shape is analyzed. The role of anharmonicity and non-rigidity of rotations is discussed in the context of the angular frequency and the shape of potential energy curve. A role of inflection point of potential energy curve for the quality of rigid rotor harmonic oscillator and rigid rotor Morse oscillator is elucidated.

The Virtual Multifrequency Spectrometer: a new paradigm for spectroscopy.

On going developments of hardware and software are changing computational spectroscopy from a strongly specialized research area to a general tool in the inventory of most researchers. Increased interactions between experimentally-oriented users and theoretically-oriented developers of new methods and models would result in more robust, flexible and reliable tools and studies for the systems of increasing complexity, which are of current scientific and technological interest. This is the philosophy behind this review, which presents the development of a so-called virtual multi-frequency spectrometer (VMS) including state-of-the-art approaches in a user-friendly frame. The current status of the VMS tool will be illustrated by a number of case studies with special reference to infrared and UV-vis regions of the electro-magnetic spectrum including also chiral spectroscopies. Only the basic theoretical background will be provided avoiding explicit equations as far as possible, and pointing out the most recent advancements beyond the standard rigid-rotor harmonic-oscillator model coupled to vertical electronic excitation energies.

Efficient yet accurate approximations for ab initio calculations of alcohol cluster thermochemistry.

We have calculated the binding enthalpies and entropies of gas phase alcohol clusters from ethanol to 1-decanol. In addition to the monomers, we have investigated dimers, tetramers, and pentamers. Geometries have been obtained at the B3LYP/TZVP level and single point energy calculations have been performed with the Resolution of the Identity-MP2 (RIMP2) method and basis set limit extrapolation using aug-cc-pVTZ and aug-cc-pVQZ basis sets. Thermochemistry is calculated with decoupled hindered rotor treatment for large amplitude motions. The results show three points: First, it is more accurate to transfer the rigid-rotor harmonic oscillator entropies from propanol to longer alcohols than to compute them with an ultra-fine grid and tight geometry convergence criteria. Second, the computational effort can be reduced considerably by using dimerization energies of longer alcohols at density functional theory (B3LYP) level plus a RIMP2 correction obtained from 1-propanol. This approximation yields results almost with the same accuracy as RIMP2 - both methods differ for 1-decanol only 0.4 kJ/mol. Third, the entropy of dimerization including the hindered rotation contribution is converged at 1-propanol with respect to chain length. This allows for a transfer of hindered rotation contributions from smaller alcohols to longer ones which reduces the required computational and man power considerably.

Thermochemical Properties Enthalpy, Entropy, and Heat Capacity of C1-C4 Fluorinated Hydrocarbons: Fluorocarbon Group Additivity.

Enthalpies of formation for 14 C2–C4 fluorinated hydrocarbons were calculated with nine popular ab initio and density functional theory methods: B3LYP, CBS-QB3, CBS-APNO, M06, M06-2X, ωB97X, G4, G4(MP2)-6X, and W1U via several series of isodesmic reactions. The recommended ideal gas phase ΔHf298° (kcal mol(–1)) values calculated in this study are the following: −65.4 for CH3CH2F; −70.2 for CH3CH2CH2F; −75.3 for CH3CHFCH3; −75.2 for CH3CH2CH2CH2F; −80.3 for CH3CHFCH2CH3; −108.1 for CH2F2; −120.9 for CH3CHF2; −125.8 for CH3CH2CHF2; −133.3 for CH3CF2CH3; −166.7 for CHF3; −180.5 for CH3CF3; −185.5 for CH3CH2CF3; −223.2 for CF4; and −85.8 for (CH3)3CF. Entropies (S298° in cal mol(–1) K(–1)) were estimated using B3LYP/6-31+G(d,p) computed frequencies and geometries. Rotational barriers were determined and hindered internal rotational contributions for S298°, and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation, with direct integration over energy levels of the intramolecular rotation potential energy curve. Thermochemical properties for the fluorinated carbon groups C/C/F/H2, C/C2/F/H, C/C/F2/H, C/C2/F2, and C/C/F3 were derived from the above target fluorocarbons. Previously published enthalpies and groups for 1,2-difluoroethane, 1,1,2-trifluoroethane, 1,1,2,2-tetrafluoroethane, 1,1,1,2-tetrafluoroethane, 1,1,1,2,2-pentafluoroethane, 2-fluoro-2-methylpropane that were previously determined via work reaction schemes are revised using updated reference species values. Standard deviations are compared for the calculation methods.

Thermodynamic Functions Molecular Polarizability of 2,6-dichloro-4-fluoro Phenol

The Laser-Raman and FT-IR spectra of 2,6-dichloro-4-fluoro phenol (2,6,4-DCFP) have been recorded. The thermodynamic functions, namely, the enthalpy, the heat capacity, the free energy and entropy of 2,6,4-DCFP have been calculated at a pressure of 1 atmosphere in the temperature range 200-1500 K under rigid rotorharmonic oscillator. The one-dimensional semi-empirical delta-function model of chemical binding has been used to evaluate the average molecular polarizability of 2,6,4-DCFP.

Theoretical Study of Intermolecular Chain Transfer to Polymer Reactions of Alkyl Acrylates

Mechanisms of intermolecular chain transfer to polymer (CTP) reactions in monomer self-initiated polymerization of alkyl acrylates, such as methyl acrylate, ethyl acrylate, and n-butyl acrylate, are studied using density functional theory calculations. Dead polymer chains with three different structures are considered, and three types of hybrid density functionals and four basis sets are used. The energy barrier and rate constant of each reaction are calculated using the transition state theory and the rigid rotor harmonic oscillator approximation. The study indicates that tertiary hydrogens of dead polymers formed by disproportionation reactions are most likely to be transferred to live polymer chains in CTP reactions. The length of the polymer chain has little effect on the calculated activation energies and transition-state geometries in all CTP mechanisms explored in this study. Moreover, CTP reactions of methyl, ethyl, and butyl acrylates have similar energy barriers and rate constants. The application of the integral equation formalism-polarizable continuum model results in higher CTP energy barriers. This increase in the predicted CTP energy barriers is larger in n-butanol than in p-xylene. However, the application of the conductor-like screening model does not affect the predicted CTP kinetic parameters.

Improved Force-Field Parameters for QM/MM Simulations of the Energies of Adsorption for Molecules in Zeolites and a Free Rotor Correction to the Rigid Rotor Harmonic Oscillator Model for Adsorption Enthalpies

Quantum mechanics/molecular mechanics (QM/MM) simulations provide an efficient avenue for studying reactions catalyzed in zeolite systems; however, the accuracy of such calculations is highly dependent on the zeolite MM parameters used. Previously reported parameters (P1), which were chosen to minimize the root mean square (RMS) deviations of adsorption energies compared with full QM ωB97X-D/6-31+G** adsorption energies, are shown to overestimate binding energies compared with experimental values, particularly for larger substrates. To address this issue, a new parameter set (P2) is derived by rescaling the previously reported characteristic energies of the Lennard-Jones potential in P1. The accuracy of the thermal correction for adsorption enthalpies determined by the rigid rotor-harmonic oscillator approximation (RRHO) is examined and shown to be improved by treating low-lying vibrational modes as free translational and rotational modes via a quasi-RRHO model. With P2 and quasi-RRHO, adsorption energies...

From orientation disordered to ordered--an ab initio simulation on ammonia borane phase transition within van der Waals corrections.

In this work, we report a detailed theoretical investigation of the phase transition of ammonia borane (NH(3) BH(3); AB), from a tetragonal I4mm (C(4v)(9)) phase with disordered orientation of hydrogen to an orthorhombic phase with Pmn2(1) (C(2v)(7)) symmetry, as a function of temperature based on Density Functional Theory calculations with semiempirical dispersion potential correction. We define a series of substructures with the NH(3) BH(3) moiety always in C(3v) symmetry and the partially occupied high temperature state can be described as a continuous transformation between these substructures. To understand the role of the van der Waals corrections to the physical properties, we use the empirical Grimme's dispersion potential correction (PBE-D2). Both Perdew-Burke-Emzerhof (PBE) and PBE-D2 functional yield almost the same energy sequence along the transition path. However, PBE-D2 functional shows obvious advantage in describing the lattice parameters of AB. The rigid rotor harmonic oscillator approximation is used to compute the free energy and the entropies contribution along the transition pathway. With knowledge of free energy surfaces along rotations of the --[NH(3)] and --[BH(3)] groups, complete transformation paths are mapped out. The phase transition is found to follow the sequence of partially occupied tetragonal system (I4mm) of a mixture of states with monoclinic (Cc), (CM) and orthorhombic (Pmn2(1)) symmetries to fully occupied quasitetragonal system (the intermediate phase, Pmn2(1)) to fully occupied orthorhombic system (Pmn2(1)).