Anharmonic Corrections Research Articles

Synchrotron-based UV resonance Raman spectroscopy probes size confinement, termination effects, and anharmonicity of carbon atomic wires

Vibrational and electronic properties and anharmonicity of sp-carbon atomic wires (i.e., polyynes) have been studied using resonance Raman spectroscopy, focusing on the confinement effects connected to their structure (length and termination). We exploited the fine tunability of the synchrotron radiation to resonantly excite short H-, CH3-, and CN-capped carbon atomic wires at their vibronic transitions in the deep UV. We report for the first time the resonance Raman spectra of size-selected CH3-capped polyynic wires (HCnCH3, n = 8–12) and CN-capped wires (HC6CN and HC12CN). We observed that the degree of π-electron conjugation increases with the wire length and is related to the specific termination. The analysis of multiple quanta Raman overtone bands shows that the anharmonic correction of the vibrational potential energy becomes increasingly relevant as the wire length increases. Finally, studying the vibronic lines of the UV absorption spectra allows the determination of an effective displacement parameter between the minima of the ground and the low-lying excited state, proving that the strong electron-phonon coupling of these systems is sensitive to chain length and termination.

The Equilibrium Molecular Structure of Cyclic (Alkyl)(Amino) Carbene Copper(I) Chloride via Gas-Phase Electron Diffraction and Quantum Chemical Calculations.

Copper-centered carbene-metal-halides (CMHs) with cyclic (alkyl)(amino) carbenes (CAACs) are bright phosphorescent emitters and key precursors in the synthesis of the highly promising class of the materials carbene-metal-amides (CMAs) operating via thermally activated delayed fluorescence (TADF). Aiming to reveal the molecular geometry for CMH phosphors in the absence of the intermolecular contacts, we report here the equilibrium molecular structure of the (CAAC)Cu(I)Cl (1) molecule in the gas-phase. We demonstrate that linear geometry around a copper atom shows no distortions in the ground state. The structure of complex 1 has been determined using the electron diffraction method, supported by quantum chemical calculations with RI-MP2/def2-QZVPP level of theory and compared with the crystal structure determined by X-ray diffraction analysis. Mean vibrational amplitudes, uij,h1, and anharmonic vibrational corrections (rij,e • rij,a) were calculated for experimental temperature T = 20 °C, using quadratic and cubic force constants, respectively. The quantum theory of atoms in molecules (QTAIM) and natural bond order (NBO) analysis of wave function at MN15/def2TZVP level of theory revealed two Cu…H, three H…H, and one three-center H…H…H bond paths with bond critical points. NBO analysis also revealed three-center, four-electron hyperbonds, (3c4e), [π(N-C) nπ(Cu) ↔ nπ(N) π(N-Cu)], or [N-C: Cu ↔ N: C-Cu] and nπ(Cu) → π(C-N)* hyperconjugation, that is the delocalization of the lone electron pair of Cu atom into the antibonding orbital of C-N bond.

Fundamental vibrational frequencies of pnictogen (Pn) containing linear triatomic anions: OCPn - and SCPn - where Pn = N, P, As and Sb

The fundamental vibrational frequencies of the isolated OCAs − and SCAs − ions, as well as their heavier antimony analogues, are reported for the first time. A thorough analysis of basis set convergence of the bond lengths and harmonic vibrational frequencies, as well as the examination of anharmonic corrections, is conducted using the MP2 and CCSD(T) ab initio methods with robust basis sets for the OC P n − and SC P n − anions moving down the pnictogen series from Pn = N to Sb. Second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) theory are used to compute the fundamental vibrational frequencies of each triatomic anion approaching the MP2 and CCSD(T) complete basis set (CBS) limits. While fundamental vibrational frequencies have been reported for OCN − and SCN − in the gas phase, only experimental vibrational frequencies of the salts for the heavier pnictogen analogues (P and As) have been reported. Experimental Raman vibrational frequencies for OCAs − and SCAs − salts were found to be coincidentally in good agreement with the CCSD(T) VCI frequencies near the CBS limit, differing by at most 13 cm − 1 from the former and 9 cm − 1 from the latter. These modest differences are likely due to the presence of counter-ions and other environmental effects in the solid state, and the overall agreement between the salts and gas-phase frequencies is quite similar to that observed for the OCP − and SCP − ions.

Molecular structure of 3,3-pentamethylenediaziridine in gas and solution phases

The equilibrium molecular structure of the 3,3-penta-methylenediaziridine (PMDA) molecule in the gas phase was determined by gas-phase electron diffraction in combination with quantum chemical calculations up to the CCSD(T)-AE/cc-pwCVQZ level and estimation of the mean amplitudes and anharmonic vibrational corrections using quadratic and cubic force fields. 1D and 2D 1H and 13C NMR spectra of PMDA in a CDCl3 solution recorded at different temperatures revealed the temperature dependence of the chemical shifts of NH protons. Nonempirical simulations of small PMDA clusters, carried out at the DFT-B3LYP/6-31++G(2d,p) level, enabled us to suggest an interpretation of the NMR data

Anharmonic Correction to Free Energy Barriers from DFT-Based Molecular Dynamics Using Constrained Thermodynamic Integration.

For the calculation of anharmonic contributions to free energy barriers, constrained thermodynamic λ-path integration (λ-TI) from a harmonic reference force field to density functional theory is presented as an alternative to the established Blue Moon ensemble method (ξ-TI), in which free energy gradients along the reaction coordinate ξ are integrated. With good agreement in all cases, the λ-TI method is benchmarked against the ξ-TI method for several reactions, including the internal CH3 group rotation in ethane, a nucleophilic substitution of CH3Cl, a retro-Diels-Alder reaction, and a proton transfer in zeolite H-SSZ-13. An advantage of λ-TI is that one can use virtually any reference state to compute anharmonic contributions to reaction free energies or free energy barriers. This is particularly relevant for catalysis, where it is now possible to compute anharmonic corrections to the free energy of a transition state relative to any reference, for example, the most stable state of the active site and the reactants in the gas phase. This is in contrast to ξ-TI, where free energy barriers can only be computed relative to an initial state with all reactants coadsorbed. Finally, the Bennett acceptance ratio method combined with λ-TI is demonstrated to reduce the number of required integration grid points with tolerable accuracy, favoring thus λ-TI over ξ-TI in terms of computational efficiency.

Theoretical Study of Hydroxylation of α- and β-Pinene by a Cytochrome P450 Monooxygenase Model

Previous studies on biocatalytic transformations of pinenes by cytochrome P450 (CYP) enzymes reveal the formation of different oxygenated products from a single substrate due to the multistate reactivity of CYP and the many reactive sites in the pinene scaffold. Up until now, the detailed mechanism of these biocatalytic transformations of pinenes have not been reported. Hereby, we report a systematic theoretical study of the plausible hydrogen abstraction and hydroxylation reactions of α- and β-pinenes by CYP using the density functional theory (DFT) method. All DFT calculations in this study were based on B3LYP/LAN computational methodology using the Gaussian09 software. We used the B3LYP functional with corrections for dispersive forces, BSSE, and anharmonicity to study the mechanism and thermodynamic properties of these reactions using a bare model (without CYP) and a pinene-CYP model. According to the potential energy surface and Boltzmann distribution for radical conformers, the major reaction products of CYP-catalyzed hydrogen abstraction from β-pinene are the doublet trans (53.4%) and doublet cis (46.1%) radical conformer at delta site. The formation of doublet cis/trans hydroxylated products released a total Gibbs free energy of about 48 kcal/mol. As for alpha pinene, the most stable radicals were trans-doublet (86.4%) and cis-doublet (13.6%) at epsilon sites, and their hydroxylation products released a total of ~50 kcal/mol Gibbs free energy. Our results highlight the likely C-H abstraction and oxygen rebounding sites accounting for the multi-state of CYP (doublet, quartet, and sextet spin states) and the formation of different conformers due to the presence of cis/trans allylic hydrogen in α-pinene and β-pinene molecules.

Supersonic jet chirped pulse microwave spectroscopy of ring-like methanol : water pentamers.

The potential energy surfaces of pure methanol and mixed methanol-water pentamers have been explored using chirped pulse Fourier-transform microwave spectroscopy aided by ab initio calculations. Rotational constants, anharmonic corrections, dipole moments, and relative energies were calculated for different conformers. Predicted rotational transitions were then fit to experimental spectra from 10-18 GHz and the assignments were confirmed using double resonance experiments where feasible. The results show all 23 of the lowest energy conformers are bound in a planar ring of hydrogen bonding that display a steady decrease in the RO-O distance along this ring as methanol content is increased. Interspersed methanol and water conformers have comparable relative abundances to those with micro-aggregation, but structures with micro-aggregated methanol and water have a higher rigid rotor fitting error. The computational methods' high degree of accuracy when compared to our experimental results suggests the strong donor-acceptor hydrogen bonding in these clusters leads to well-defined minima on the intermolecular potential energy surface.

Ultralow lattice thermal conductivity of binary compounds A2B (A = Cs, Rb & B = Se, Te) with higher-order anharmonicity correction.

By employing first-principles calculations that integrate self-consistent phonon theory and the Boltzmann transport equation, we have delved into the thermal transport characteristics of hexagonal anisotropic materials A2B (A = Cs, Rb and B = Se, Te). Our computational results have disclosed that these A2B materials exhibit ultralow lattice thermal conductivity (κL) at room temperature. Specifically, in the case of Cs2Te, the κL values are a mere 0.15 W m-1 K-1 in the a(b) direction and 0.22 W m-1 K-1 in the c direction, both markedly less than the thermal conductivity of quartz glass, a conventional thermoelectric material (0.9 W m-1 K-1). Importantly, our calculations encompass higher-order anharmonic effects while computing the lattice thermal conductivities of these materials. This is essential since pronounced anharmonicity leads to a decrease in phonon group velocity, and consequently, lowers the κL values. Our results establish a theoretical foundation for exploring the thermal transport characteristics of anisotropic materials with substantial anharmonicity. Furthermore, the binary compounds A2B proffer a gamut of possibilities for a wide range of applications in thermoelectrics and thermal management, owing to their ultralow lattice thermal conductivity.

Anharmonic lattice dynamics and structural phase transition of SnTe monolayer from first principles

In this work we investigate the role of quartic anharmonicity on the lattice- and thermo-dynamic properties of rectangular () and square (β) phases of two-dimensional (2D) SnTe monolayer (ML) by using self-consistent phonon (SCP) theory, based on the first-principles calculations. For both phases, as compared to the usual harmonic approximation (HA), the renormalized phonon frequency at the optical modes (4–10) is found to be increased upon the inclusion of quartic anharmonicity via the SCP method, where the effects of cubic anharmonicity are neglected. At the experimentally observed transition temperature (T c = 270 K), the difference in the vibrational free-energy between the square and rectangular phases of SnTe ML, calculated by using the anharmonic SCP correction is found to be much closer to the structural energy gain as compared to that obtained by using only the quasi-harmonic contribution. This validates the significance of SCP approach over the HA to explain the lattice dynamics properties and predict the T c for SnTe ML and similar 2D compounds. The calculated lattice thermal conductivity of square SnTe ML (e.g. 10.67 W m−1K−1 at 300 K) is higher than that of the rectangular SnTe ML (e.g. 6.72 W m−1K−1 at 300 K) due to the relatively higher corresponding thermodynamic parameters: specific heat capacity, group velocity, and phonon lifetime obtained for the square SnTe ML. Particularly, the low energy phonon modes are found to transport most of the heat in the system and, hence, played major role to the total lattice thermal conductivity.

Anharmonic Aspects in Vibrational Circular Dichroism Spectra from 900 to 9000 cm-1 for Methyloxirane and Methylthiirane.

Vibrational circular dichroism (VCD) spectra and the corresponding IR spectra of the chiral isomers of methyloxirane and of methylthiirane have been reinvestigated, both experimentally and theoretically, with particular attention to accounting for anharmonic corrections, as calculated by the GVPT2 approach. De novo recorded VCD spectra in the near IR (NIR) range regarding CH-stretching overtone transitions, together with the corresponding NIR absorption spectra, were also considered and accounted for, both with the GVPT2 and with the local mode approaches. Comparison of the two methods has permitted us to better describe the nature of active “anharmonic” modes in the two molecules and the role of mechanical and electrical anharmonicity in determining the intensities of VCD and IR/NIR data. Finally, two nonstandard IR/NIR regions have been investigated: the first one about ≈2000 cm–1, involving mostly two-quanta bending mode transitions, the second one between 7000 and 7500 cm–1 involving three-quanta transitions containing CH-stretching overtones and HCC/HCH bending modes.

Thermal expansivity and Raman spectra of natural cordierite: A potential cordierite-garnet elastic thermometer

Cordierite is widely found in metamorphic rocks, and has important application for geothermometry and geobarometry, as well as a monitor of volatile concentrations in fluids or melts. In this study, we measured high-temperature powder X-ray diffraction (XRD) patterns on a natural sample (Na0.06[(Mg1.87Fe0.19)Al3.94Si5.00O18.00](CO2)0.09(H2O)0.22) up to 1500 K. The thermal expansion coefficient is fitted with an average value of 7.39(19) × 10−6 K−1. In situ high-temperature and high-pressure Raman spectra were also obtained on this sample, on the basis of which the isobaric and isothermal Grüneisen parameters are calculated. The anharmonic correction has positive contribution to the heat capacity, since the intrinsic anharmonic parameters show systematically negative values. Next, the isothermal bulk modulus (KT) at high temperatures is modeled by density functional theory (DFT), which is essential for constructing the P-V-T equation of state (EOS) as well as thermodynamic Grüneisen parameter (γV) for cordierite. The axial thermoelastic parameters and strain evolution along isochors at high temperatures are also evaluated. Cordierite is substantially softer with weaker anisotropy for axial compressibilities as compared with zircon and rutile, and consequently, significantly smaller strain effect is expected on the vibrational frequencies. Due to its smaller thermal expansivity and larger compressibility than garnets, the assemblage of cordierite trapped in garnet minerals can potentially be an elastic thermometer in the pressure range below 1 GPa. Entrapment isomekes are calculated with negative slopes of (∂P/∂T)V(inc-host), and positive residual inclusion pressures are expected at the ambient condition.

Trapping mechanism of metastable β-Ga disclosed by its lattice stability optimization and nucleation behavior exploration

Application of gallium-based liquid metals below 273 K calls for design of novel metastable materials with exceptionally low melting points. It is crucial to develop the thermodynamic database of metastable phases and to unveil their trapping mechanism. In this work, the thermodynamic assessment of metastable β-Ga and its lattice stability were evaluated by integrating experimental and ab-initio thermodynamics. We demonstrated that the lattice stability expression derived from a high-order modified Einstein modeling with anharmonic correction provided the most reliable and the most accurate description hitherto. Thereafter, the critical radius and the work for nucleation were derived by applying our optimized expressions of lattice stability and surface energy. Thereby the capturing of β-Ga at nano sizes and high supercooling were well explained. And it was confirmed that the classical nucleation theory played an important role in trapping metastable β-Ga phase. Furthermore, the significance of surfaces and interfaces in solidification process were highlighted. This work sheds light on designing metastable liquid metals with low melting points. Moreover, it provides a novel workflow for future studying of metastable multicomponent alloys.

Thermal decomposition of isopentanol: A theoretical calculation and kinetic modeling analysis

Isopentanol (3-methyl-1-butanol, 3M1B) is a prospective bioderived fuel with advantages over ethanol that make it a suitable substitute for gasoline. Although there have been studies on the combustion properties of 3M1B, reaction kinetics for its thermal decomposition is scarce. This study explores the reaction pathways for the thermal decomposition of 3M1B through theoretical calculations. Six reactions with tight transition states, and nine bond dissociation reactions (i.e., barrierless reactions) were considered. For reactions with tight transition states, the CCSD(T)/CBS//M06–2X-D3(0)/def2-TZVP method was used, and the MRCISD(+Q)/CBS//CASPT2/cc-pVDZ method was adopted for the bond dissociation reactions. The conventional transition state theory (CTST), including multi-structural torsional anharmonicity (MS-T) correction, addressed those reactions with tight transition states. The MS-T method thoroughly examined the co-effect of the multiple structures and torsional anharmonicity. Direct bond-breaking reactions were studied using the variational transition state theory (VTST). Subsequently, system-specific quantum Rice-Ramsperger-Kassel (SS-QRRK) theory and Rice-Ramsperger-Kassel-Marcus/Master Equation (RRKM/ME) were employed to obtain the rate constants for reactions with tight transition states and direct bond-breaking reactions at different temperatures and pressures (T/P) regimes (T = 298–2400 K, P = 0.01–100 atm), respectively. The results showed that water elimination and C-C bond dissociation play a significant role for 3M1B unimolecular decomposition, other molecular elimination and bond dissociation channels can be ignored. Combining the reaction pathways and the corresponding pressure dependent rate constants into the kinetic model resulted in good predictions of the speciation profiles during 3M1B pyrolysis. These data are valuable for the development of the combustion models of 3M1B.

ℏ2 expansion of the transmission probability through a barrier.

Ninety years ago, Wigner derived the leading order expansion term in ℏ2 for the tunneling rate through a symmetric barrier. His derivation included two contributions: one came from the parabolic barrier, but a second term involved the fourth-order derivative of the potential at the barrier top. He left us with a challenge, which is answered in this paper, to derive the same but for an asymmetric barrier. A crucial element of the derivation is obtaining the ℏ2 expansion term for the projection operator, which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (TST) reproduces the anharmonic corrections to the leading order of ℏ2. The efficacy of the resulting expression is demonstrated for an Eckart barrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, rather than the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of ℏ and, thus, provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics, and ring polymer molecular dynamics methods.

Theoretical study about the hydrogen abstraction reactions on methyl acetate on combustion conditions

Methyl acetate is considered a prototype molecule to study biodiesel ignition and combustion and is seen as a possible fuel or fuel additive. For this reason, methyl acetate decomposition paths have been investigated in recent years. In the present study, hydrogen abstraction reactions on methyl acetate by OH(2Π), HO2(2A'), H(2Σg), O(3P), and O2(3Σg) were conducted, and the effect of methodology and anharmonic corrections on the rate coefficients were evaluated. The M06-2X and B3LYP-D3 functionals with the cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ basis set were used for methodology evaluation and the CCSD(T)/cc-pVTZ//M06-2X/aug-cc-pVTZ for the rate coefficients calculation and literature comparisons. The rate coefficients were calculated in the range of 250-3500K, including tunneling corrections, methyl-hindered rotations, and anharmonic effects calculated by the VPT2 method. The methodology analysis showed that the B3LYP-D3 functional leads to lower activation energies for all elementary reactions studied, and the double-zeta basis is insufficient to calculate precise rate coefficients. The inclusion of anharmonic corrections consistently lowered the rate coefficients of all elementary reactions studied and changed the Arrhenius plot profile with the temperature. Significant anharmonic effects were observed at higher temperatures, being the reaction with O2(3Σg) the most affected by this correction. Differences superior to 105 cm3 molec-1s-1 in the rate coefficients were observed in some cases.

Crossover in dynamics in the Kob-Andersen binary mixture glass-forming liquid

Glass-forming liquids are broadly classified as being fragile or strong, depending on the deviation from Arrhenius behavior of their relaxation times. A fragile to strong crossover is observed or inferred in liquids like water and silica, and more recently also in metallic glasses and phase change alloys, leading to the expectation that such a crossover is more widely realised among glass formers. We investigate computationally the well-studied Kob-Andersen model, accessing temperatures well below the mode coupling temperature TMCT. We find that relaxation times exhibit a crossover in dynamics around TMCT, and discuss whether it bears characteristics of the fragile to strong crossover. Several aspects of dynamical heterogeneity exhibit behavior mirroring the dynamical crossover, whereas thermodynamic quantities do not. In particular, the Adam-Gibbs relation describing the relation between relaxation times and configurational entropy continues to hold below the dynamical crossover, when anharmonic corrections to the vibrational entropy are included.

Structures and spectroscopic properties of K+(H2O)n with n = 1–10 clusters based on density functional theory

Hydrated potassium ion clusters widely exist in salt solutions and biological cells. To explore the configuration of hydrated potassium ions, a global search for the structures from 4 to 10 hydrated potassium ion clusters is performed using the genetic algorithm with density functional theory, followed by high-level ab initio optimization and energetic calculation. Potassium ion remains on the surface of the clusters rather than surrounded by water molecules as the cluster size increases. The simulated infrared (IR) spectra with anharmonic correction of clusters could efficiently reproduce the experimental results. The interaction between the K+ cation and the water molecules resulted in little deviation (<300 cm−1) of the adjacent O–H stretching mode.

Attaching Onto or Inserting Into an Intramolecular Hydrogen Bond: Exploring and Controlling a Chirality-Dependent Dilemma for Alcohols

Prereactive complexes in noncovalent organocatalysis are sensitive to the relative chirality of the binding partners and to hydrogen bond isomerism. Both effects are present when a transiently chiral alcohol docks on a chiral α-hydroxy ester, turning such 1:1 complexes into elementary, non-reactive model systems for chirality induction in the gas phase. With the help of linear infrared and Raman spectroscopy in supersonic jet expansions, conformational preferences are investigated for benzyl alcohol in combination with methyl lactate, also exploring p-chlorination of the alcohol and the achiral homolog methyl glycolate to identify potential London dispersion and chirality effects on the energy sequence. Three of the four combinations prefer barrierless complexation via the hydroxy group of the ester (association). In contrast, the lightest complex predominantly shows insertion into the intramolecular hydrogen bond, such as the analogous lactate and glycolate complexes of methanol. The experimental findings are rationalized with computations, and a uniform helicality induction in the alcohol by the lactate is predicted, independent of insertion into or association with the internal lactate hydrogen bond. p-chlorination of benzyl alcohol has a stabilizing effect on association because the insertion motif prevents a close contact between the chlorine and the hydroxy ester. After simple anharmonicity and substitution corrections, the B3LYP-D3 approach offers a fairly systematic description of the known spectroscopic data on alcohol complexes with α-hydroxy esters.

Dynamical Behavior of Aromatic Trimer Complexes in Unimolecular Dissociation Reaction at High Temperatures. Case Studies on C6H6-C6F6-C6H6 and C6H6 Trimer Complexes.

The intramolecular vibrational energy redistribution (IVR) dynamics during unimolecular dissociation of aromatic trimers at high temperatures is the primary interest of this study. Chemical dynamics simulations are performed for the unimolecular dissociation of benzene-hexafluorobenzene-benzene (Bz-HFB-Bz) and benzene trimer (Bz-trimer) complexes at a temperature range of 1000-2000 K. Partial dissociation of both the complexes is observed, which leads to a dimer and a monomer in the dynamics. However, the probability of such dissociation was found much lower in the case of the Bz-trimer, which further decreases with the increase of temperature. The rate of partial dissociation of Bz-HFB-Bz is faster at 1500, 1800, and 2000 K, whereas the rate of complete dissociation of the Bz-trimer is significantly faster than Bz-HFB-Bz at all temperatures. This is just the opposite of the corresponding dimer's dissociation, where benzene-hexafluorobenzene (Bz-HFB) dissociates at a faster rate than the benzene dimer (Bz-dimer). Thus, the dissociation dynamics of the trimer is different than that of the dimer. Simulations with excited intramolecular and intermolecular modes of the trimer complexes reveal that energy flows from intermolecular to intramolecular modes of Bz-HFB-Bz more freely than the Bz-trimer, and the dissociation process becomes slower for the former. Calculated activation energies for both types of dynamics are much lower than the corresponding binding energies, which may be due to the anharmonicity. The Arrhenius equation with an anharmonic correction factor is considered to recalculate the activation energy and pre-exponential factor.

Equilibrium molecular structure of nicotinic acid hydrazide: joint study by means of gas electron diffraction and quantum chemistry

The conformational composition and molecular structure of gaseous nicotinic acid hydrazide (nicotinohydrazide) have been studied by means of gas electron diffraction (GED) supported by the results of quantum chemical (QC) calculations. According to QC calculations, eight conformers are possible for nicotinohydrazide. However, only two of them are in sufficient abundance to be detected by means of GED, with their ratio 7:3. Equilibrium structural parameters of the predominating conformers have been obtained with the use of anharmonic rovibrational corrections and standard enthalpy of formation of gaseous nicotinohydrazide has been calculated. The gas-phase molecular structure has been compared to the crystalline one, obtained via X-ray diffraction. Significant distinctions between the gaseous and solid structures have been revealed