Ab-Initio Total Energy Studies of the Static and Dynamical Properties of Ice Ih

Descriptors of water aggregation

We rely on a total of 23 (cluster size, 8 structural, and 14 connectivity) descriptors to investigate structural patterns and connectivity motifs associated with water cluster aggregation. In addition to the cluster size n (number of molecules), the 8 structural descriptors can be further categorized into (i) one-body (intramolecular): covalent OH bond length (rOH) and HOH bond angle (θHOH), (ii) two-body: OO distance (rOO), OHO angle (θOHO), and HOOX dihedral angle (ϕHOOX), where X lies on the bisector of the HOH angle, (iii) three-body: OOO angle (θOOO), and (iv) many-body: modified tetrahedral order parameter (q) to account for two-, three-, four-, five-coordinated molecules (qm, m = 2, 3, 4, 5) and radius of gyration (Rg). The 14 connectivity descriptors are all many-body in nature and consist of the AD, AAD, ADD, AADD, AAAD, AAADD adjacencies [number of hydrogen bonds accepted (A) and donated (D) by each water molecule], Wiener index, Average Shortest Path Length, hydrogen bond saturation (% HB), and number of non-short-circuited three-membered cycles, four-membered cycles, five-membered cycles, six-membered cycles, and seven-membered cycles. We mined a previously reported database of 4 948 959 water cluster minima for (H2O)n, n = 3-25 to analyze the evolution and correlation of these descriptors for the clusters within 5 kcal/mol of the putative minima. It was found that rOH and % HB correlated strongly with cluster size n, which was identified as the strongest predictor of energetic stability. Marked changes in the adjacencies and cycle count were observed, lending insight into changes in the hydrogen bond network upon aggregation. A Principal Component Analysis (PCA) was employed to identify descriptor dependencies and group clusters into specific structural patterns across different cluster sizes. The results of this study inform our understanding of how water clusters evolve in size and what appropriate descriptors of their structural and connectivity patterns are with respect to system size, stability, and similarity. The approach described in this study is general and can be easily extended to other hydrogen-bonded systems.

Guest-Host Interactions in Clathrate Hydrates: Benchmark MP2 and CCSD(T)/CBS Binding Energies of CH4, CO2, and H2S in (H2O)20 Cages

We present benchmark binding energies of naturally occurring gas molecules CH₄, CO₂, and H₂S in the small cage, namely, the pentagonal dodecahedron (5¹²) (H₂O)₂₀, which is one of the constituent cages of the 3 major lattices (structures I, II, and H) of clathrate hydrates. These weak interactions require higher levels of electron correlation and converge slowly with an increasing basis set to the complete basis set (CBS) limit, necessitating the use of large basis sets up to the aug-cc-pV5Z and subsequent correction for basis set superposition error (BSSE). For the host hollow (H₂O)₂₀ cages, we have identified a most stable isomer with binding energy of -200.8 ± 2.1 kcal/mol at the CCSD(T)/CBS limit (-199.2 ± 0.5 kcal/mol at the MP2/CBS limit). Additionally, we report converged second order Møller-Plesset (MP2) CBS binding energies for the encapsulation of guests in the (H₂O)₂₀ cage of -4.3 ± 0.1 for CH₄@(H₂O)₂₀, -6.6 ± 0.1 for CO₂@(H₂O)₂₀, and -8.5 ± 0.1 kcal/mol for H₂S@(H₂O)₂₀, respectively. For CH₄@(H₂O)₂₀, exhibiting the weakest encapsulation affinity among the three, we report CCSD(T)/aug-cc-pVTZ binding energies and, based on them, a CCSD(T)/CBS estimate of -4.75 ± 0.1 kcal/mol. To the best of our knowledge, the CCSD(T)/aug-cc-pVTZ calculation for CH₄@(H₂O)₂₀ is the largest one reported to date (168 valence electrons, 1978 basis functions, and the correlation of 84 doubly occupied and 1873 virtual orbitals) and required a scalable implementation of the (T) module on 6144 nodes (350 208 cores) of the "Cori" supercomputer at the National Energy Research Supercomputing Center (NERSC) for a total execution time of 195 min (for the (T) part). These efficient scalable implementations of highly correlated methods offer the capability to obtain long-lasting benchmarks of intermolecular interactions in complex systems. They also provide a path toward parametrizing classical potentials needed to study the dynamical and transport properties in these complex systems as well as assess the accuracy of lower scaling electronic structure methods such as density functional theory (DFT) and MP2 including its spin-biased variants.

Molecular modeling and computational study of the chiral-dependent structures and properties of the self-assembling diphenylalanine peptide nanotubes, containing water molecules

DFT (VASP) and semi-empirical (HyperChem) calculations for the L- and D-chiral diphenylalanine (L-FF and D-FF) nanotube (PNT) structures, empty and filled with water/ice clusters, are presented and analyzed. The results obtained show that after optimization, the dipole moment and polarization of both chiral type L-FF and D-FF PNT and embedded water/ice cluster are enhanced; the water/ice cluster acquire the helix-like structure similar as L-FF and D-FF PNT. Ferroelectric properties of tubular water/ice helix-like-cluster obtained after optimization inside L-FF and D-FF PNT and total L-FF and D-FF PNT with embedded water/ice cluster are discussed.

Structures and Properties of the Self-Assembling Diphenylalanine Peptide Nanotubes Containing Water Molecules: Modeling and Data Analysis

The structures and properties of the diphenylalanine (FF) peptide nanotubes (PNTs), both L-chiral and D-chiral (L-FF and D-FF) and empty and filled with water/ice clusters, are presented and analyzed. DFT (VASP) and semi-empirical calculations (HyperChem) to study these structural and physical properties of PNTs (including ferroelectric) were used. The results obtained show that after optimization the dipole moment and polarization of both chiral type L-FF and D-FF PNT and embedded water/ice cluster are enhanced; the water/ice cluster acquire the helix-like structure similar as L-FF and D-FF PNT. Ferroelectric properties of tubular water/ice helix-like cluster, obtained after optimization inside L-FF and D-FF PNT, as well of the total L-FF and D-FF PNT with embedded water/ice cluster, are discussed.

Identifying pragmatic quasi-harmonic electronic structure approaches for modeling molecular crystal thermal expansion

Quasi-harmonic approaches provide an economical route to modeling the temperature dependence of molecular crystal structures and properties. Several studies have demonstrated good performance of these models, at least for rigid molecules, when using fragment-based approaches with correlated wavefunction techniques. Many others have found success employing dispersion-corrected density functional theory (DFT). Here, a hierarchy of models in which the energies, geometries, and phonons are computed either with correlated methods or DFT are examined to identify which combinations produce useful predictions for properties such as the molar volume, enthalpy, and entropy as a function of temperature. The results demonstrate that refining DFT geometries and phonons with single-point energies based on dispersion-corrected second-order Møller-Plesset perturbation theory can provide clear improvements in the molar volumes and enthalpies compared to those obtained from DFT alone. Predicted entropies, which are governed by vibrational contributions, benefit less clearly from the hybrid schemes. Using these hybrid techniques, the room-temperature thermochemistry of acetaminophen (paracetamol) is predicted to address the discrepancy between two experimental sublimation enthalpy measurements.

The mechanism for the formation of OH radicals in condensed-phase water under ultraviolet irradiation

OH radicals can be produced via direct water photolysis through concerted proton and electron transfer.

How important is thermal expansion for predicting molecular crystal structures and thermochemistry at finite temperatures?

Molecular crystals expand appreciably upon heating due to both zero-point and thermal vibrational motion, yet this expansion is often neglected in molecular crystal modeling studies. Here, a quasi-harmonic approximation is coupled with fragment-based hybrid many-body interaction calculations to predict thermal expansion and finite-temperature thermochemical properties in crystalline carbon dioxide, ice Ih, acetic acid and imidazole. Fragment-based second-order Möller-Plesset perturbation theory (MP2) and coupled cluster theory with singles, doubles and perturbative triples [CCSD(T)] predict the thermal expansion and the temperature dependence of the enthalpies, entropies and Gibbs free energies of sublimation in good agreement with experiment. The errors introduced by neglecting thermal expansion in the enthalpy and entropy cancel somewhat in the Gibbs free energy. The resulting ∼ 1-2 kJ mol(-1) errors in the free energy near room temperature are comparable to or smaller than the errors expected from the electronic structure treatment, but they may be sufficiently large to affect free-energy rankings among energetically close polymorphs.

Benchmark Calculations of Three-Body Intermolecular Interactions and the Performance of Low-Cost Electronic Structure Methods

Many-body noncovalent interactions are increasingly important in large and/or condensed-phase systems, but the current understanding of how well various models predict these interactions is limited. Here, benchmark complete-basis set coupled cluster singles, doubles, and perturbative triples (CCSD(T)) calculations have been performed to generate a new test set for three-body intermolecular interactions. This "3B-69" benchmark set includes three-body interaction energies for 69 total trimer structures, consisting of three structures from each of 23 different molecular crystals. By including structures that exhibit a variety of intermolecular interactions and packing arrangements, this set provides a stringent test for the ability of electronic structure methods to describe the correct physics involved in the interactions. Both MP2.5 (the average of second- and third-order Møller-Plesset perturbation theory) and spin-component-scaled CCSD for noncovalent interactions (SCS-MI-CCSD) perform well. MP2 handles the polarization aspects reasonably well, but it omits three-body dispersion. In contrast, many widely used density functionals corrected with three-body D3 dispersion correction perform comparatively poorly. The primary difficulty stems from the treatment of exchange and polarization in the functionals rather than from the dispersion correction, though the three-body dispersion may also be moderately underestimated by the D3 correction.

ADSORPTION STATES AND SITE CONVERSIONS OF PHENYLACETYLENE ON Si(100)2 × 1 CALCULATED BY DFT

The adsorption on Si(100)2 × 1 of PhenylAcetilene (PA), a bifunctional molecule with a phenyl ring and a triple bond, may occur through each group, selectively, or both functional groups simultaneously. The most favorable adsorption sites upon adsorption were calculated by DFT. Furthermore, several energy barriers were calculated: The ones connecting the physisorbed to the chemisorbed states, as well as the interconversion barriers of different chemisorbed states. The conversion of physisorbed-to-chemisorbed states has barriers of 0.11–0.19 eV. The barriers of sites inter-conversions are all higher (1.11–1.36 eV) and suggest a difficult post-chemisorption surface rearrangement.

A HREELS and DFT study of the adsorption of aromatic hydrocarbons on diamond (111)

Ultrathin layers of organic molecules can be assembled on group IV (e.g., silicon, germanium, diamond) semiconductor surfaces using surface analogues of cycloaddition reactions. We present a study of the chemisorption of benzene, toluene, and styrene on the Pandey chain of C(111) using high resolution electron energy loss spectroscopy and density functional theory calculations. Two cycloaddition reactions, namely, the [4 + 2] and [2 + 2], were examined. The [4 + 2] reaction is found to be thermodynamically unfavorable on C(111), while the [2 + 2] reaction involving the ring is slightly exothermic. In the case of aromatic molecules with an external unsaturated functional group, the reaction can proceed via the external functionality, thereby preserving the aromatic ring and providing further stability. Different reactivity patterns to the C(100) surface are rationalized on the basis of steric effects imposed by the geometrical structure of the Pandey chain. Our study demonstrates the potential of employing the Pandey chain as a template for assembling one-dimensional molecular structures on the diamond surface.

Ground-state properties of crystalline ice from periodic hartree-fock calculations and a coupled-cluster-based many-body decomposition of the correlation energy

Ground state properties of crystalline ice Ih are investigated by combining periodic Hartree-Fock calculations with a many-body expansion for the electron correlation energy using second-order many-body perturbation theory and coupled-cluster techniques. Very good agreement with experimental data can already be achieved by considering two-body correlation contributions up to the third coordination shell in crystalline ice. This hints at the possibility to accurately simulate ab initio water by using periodic Hartree-Fock calculations together with a parametrized two-body correlation potential.

High-level ab initio calculations for the four low-lying families of minima of(H2O)20. II. Spectroscopic signatures of the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms hydrogen bonding networks

We report the first harmonic vibrational spectra for each of the lowest lying isomers within the four major families of minima of (H2O)20, namely, the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms. These were obtained at the second-order Moller-Plesset perturbation level of theory (MP2) with the augmented correlation consistent basis set of double zeta quality (aug-cc-pVDZ) at the corresponding minimum energy geometries. The computed infrared (IR) spectra are the first ones obtained from first principles for these clusters. They were found to contain spectral features, which can be directly mapped onto the distinctive spectroscopic signatures of their constituent tetramer, pentamer, and octamer fragments. The dodecahedron spectra show the richest structure in the OH stretching region and are associated with the most redshifted OH vibrations with respect to the monomer. The lowest lying edge-sharing pentagonal prism isomer displays intense IR active vibrations that are redshifted by approximately 600 cm(-1) with respect to the water monomer. Furthermore the most redshifted, IR-active OH stretching vibrations for all four networks correspond to hydrogen bonded OH groups, which exhibit the following two common characteristics: (i) they belong to fragments which have a "free" OH stretch and (ii) they act as donors to a neighboring water molecule along a "dimerlike" (strong) hydrogen bond. The zero-point energy corrected MP2/CBS (complete basis set) limit binding energies D(0) for the four isomers are -163.1 kcal/mol (edge-sharing pentagonal prism), -160.1 kcal/mol (face-sharing pentagonal prism), -157.5 kcal/mol (fused cubes), and -148.1 kcal/mol (dodecahedron).

Dimensional Effects on the LO−TO Splitting in CF4: First-Principles and Infrared Absorption Studies

The development of longitudinal optical-transverse optical (LO-TO) modes in CF(4) has been studied experimentally and theoretically as a function of dimensionality. Infrared absorption experiments for CF(4) adsorbed on single-walled carbon nanotubes indicate a lack of LO-TO splitting at low coverage and a gradual appearance of LO-TO modes as the coverage of CF(4) on the nanotubes is increased. We have performed density functional perturbation theory calculations for the vibrational frequencies, IR absorption spectra, and phonon density of states for CF(4) in one, two, and three dimensions. The calculations demonstrate that LO-TO splitting in 1D is qualitatively different from that computed for 2D or the bulk. The magnitude of the splitting in 1D is about one-half that computed for the bulk, and the LO mode is very weakly blue-shifted in 1D. We predict that the phonon density of states changes dramatically as the dimensionality of the crystal is changed. This prediction can be tested experimentally via inelastic neutron scattering. We conclude that LO-TO splitting can be used as a probe to identify 1D states of matter.

Optical absorption of water: coulomb effects versus hydrogen bonding

The optical spectrum of water is not well understood. For example, the main absorption peak shifts upwards by 1.3 eV upon condensation, which is contrary to the behavior expected from aggregation-induced broadening of molecular levels. We investigate theoretically the effects of electron-electron and electron-hole correlations, finding that condensation leads to delocalization of the exciton onto nearby hydrogen-bonded molecules. This reduces its binding energy and has a dramatic impact on the line shape. The calculated spectrum is in excellent agreement with experiment.

Vibrational behavior of adsorbed CO2 on single-walled carbon nanotubes

We present theoretical and experimental evidence for CO(2) adsorption on different sites of single walled carbon nanotube (SWNT) bundles. We use local density approximation density functional theory (LDA-DFT) calculations to compute the adsorption energies and vibrational frequencies for CO(2) adsorbed on SWNT bundles. The LDA-DFT calculations give a range of shifts for the asymmetric stretching mode from about -6 to -20 cm(-1) for internally bound CO(2), and a range from -4 to -16 cm(-1) for externally bound CO(2) at low densities. The magnitude of the shift is larger for CO(2) adsorbed parallel to the SWNT surface; various perpendicular configurations yield much smaller theoretical shifts. The asymmetric stretching mode for CO(2) adsorbed in groove sites and interstitial sites exhibits calculated shifts of -22.2 and -23.8 cm(-1), respectively. The calculations show that vibrational mode softening is due to three effects: (1) dynamic image charges in the nanotube; (2) the confining effect of the adsorption potential; (3) dynamic dipole coupling with other adsorbate molecules. Infrared measurements indicate that two families of CO(2) adsorption sites are present. One family, exhibiting a shift of about -20 cm(-1) is assigned to internally bound CO(2) molecules in a parallel configuration. This type of CO(2) is readily displaced by Xe, a test for densely populated adsorbed species, which are expected to be present on the highest adsorption energy sites in the interior of the nanotubes. The second family exhibits a shift of about -7 cm(-1) and the site location and configuration for these species is ambiguous, based on comparison with the theoretical shifts. The population of the internally bound CO(2) may be enhanced by established etching procedures that open the entry ports for adsorption, namely, ozone oxidation followed by annealing in vacuum at 873 K. Xenon displacement experiments indicate that internally bound CO(2) is preferentially displaced relative to the -7 cm(-1) shifted species. The -7 cm(-1) shifted species is assigned to CO(2) adsorbed on the external surface based on results from etching and Xe displacement experiments.

Graph invariants for periodic systems: towards predicting physical properties from the hydrogen bond topology of ice

Ice-Ih consists of a disordered hydrogen-bonded network. The degree of disorder in ice-Ih, and possible phase transitions to an ordered phase have been debated in recent years. The dependence of energy, free energy, and other scalar physical properties on H-bond topology is needed to understand these phenomena. Graph invariants provide a means of linking physical properties to the topology of the H-bond network. We have previously shown the effectiveness of graph invariants for finite water clusters [J.-L. Kuo, J. V. Coe, S. J. Singer, Y. B. Band, and L. Ojamäe, J. Chem. Phys., 114, 2527 (2001)]. In this work, we develop a formalism for the graph invariants of periodic systems. We demonstrate that graph invariants for small unit cells are a subset of the graph invariants of larger unit cells, providing a hierarchy of approximations by which detailed calculations for small unit cells, such as periodic ab initio calculations as they become available, can be used to parametrize the energy of the astronomical number of H-bond arrangements present in large unit cells. We also present graph enumeration results for ice-Ih, analyzing conflicting results that have appeared previously in the literature and furnishing information on the statistical properties of the H-bond network of ice-Ih in the large system limit.

Thermodynamics of hydrogen bond patterns in supramolecular assemblies of water molecules

The PACHA (Partial Atomic Charges and Hardnesses Analysis) formalism is applied to various supramolecular assemblies of water molecules. After a detailed study of all available crystal structures for ice polymorphs, we shown that the hydrogen bond strength is roughly constant below 1 GPa and considerably weakened above that value. New hydrogen bond patterns are proposed for ice IV, V, and VI after (EB) (electrostatic balance) minimization. For other polymorphs, there is an almost perfect coincidence between experimental and predicted hydrogen bond patterns. The evolution of hydrogen bond energy as a function of molecular geometry in water clusters with up to 280 water molecules and in large supramolecular compounds is quantitatively described. Intermolecular hydrogen bonds are found to lie between -9 and -32 kJ mol-1, the stronger interaction occurs within the spherical fully disordered water droplet buried at the heart of Müller's superfullerene keplerate. The weakest one occurs in a chiral molecular snub cube built from six calix[4]resorcinarene and eight water molecules. Intramolecular hydrogen bonds are found in the range -10-100 kJ mol-1 and can thus be considerably stronger than intermolecular bonds. Finally, through the investigation of a clathrate type I compound, it was possible to obtain a deep insight of the host-guest interactions and self-assembly rules of water cages in these materials.