Coupled Cluster in Condensed Phase. Part I: Static Quantum Chemical Calculations of Hydrogen Fluoride Clusters

Percolation transition and bimodal density distribution in hydrogen fluoride

Hydrogen-bond networks in associating fluids can be extremely robust and characterize the topological properties of the liquid phase, as in the case of water, over its whole domain of stability and beyond. Here, we report on molecular dynamics simulations of hydrogen fluoride (HF), one of the strongest hydrogen-bonding molecules. HF has more limited connectivity than water but can still create long, dynamic chains, setting it apart from most other small molecular liquids. Our simulation results provide robust evidence of a second-order percolation transition of HF's hydrogen bond network occurring below the critical point. This behavior is remarkable as it underlines the presence of two different cohesive mechanisms in liquid HF, one at low temperatures characterized by a spanning network of long, entangled hydrogen-bonded polymers, as opposed to short oligomers bound by the dispersion interaction above the percolation threshold. This second-order phase transition underlines the presence of marked structural heterogeneity in the fluid, which we found in the form of two liquid populations with distinct local densities.

Linear Scaling Incremental Scheme for Correlation Energies with Embedding Generated Virtuals

A novel incremental scheme is presented including an incremental expansion of the virtual space for the calculation of electron correlation energies, which is compatible with any size-extensive correlation method and scales asymptotically linear for large molecules. The performance is studied for organic molecules, water clusters, and a La(III)-water complex, where the compatibility with pseudopotentials is also examined. The computational requirements are already reduced tremendously for medium-sized water clusters and hydrocarbons with respect to the canonical CCSD as well as the ordinary incremental scheme references. Correlation energies within chemical accuracy have been observed for all studied systems. The novelty of the method is that relatively small virtual spaces are used in combination with tuples of localized occupied spaces. The corresponding orthonormal occupied and virtual orbitals are obtained from QM/QM embedding calculations and can thus be used with standard quantum chemistry codes for correlation calculations. It is presented how relevant virtual spaces are selected and the correlation energies are linked in the new virtual space expansion.

The effect of machine learning predicted anharmonic frequencies on thermodynamic properties of fluid hydrogen fluoride

Anharmonic effects play a crucial role in determining thermochemical properties of liquids and gases. For such extended phases, the inclusion of anharmonicity in reliable electronic structure methods is computationally extremely demanding, and hence, anharmonic effects are often lacking in thermochemical calculations. In this study, we apply the quantum cluster equilibrium method to transfer density functional theory calculations at the cluster level to the macroscopic, liquid, and gaseous phase of hydrogen fluoride. This allows us to include anharmonicity, either via vibrational self-consistent field calculations for smaller clusters or using a regression model for larger clusters. We obtain the structural composition of the fluid phases in terms of the population of different clusters as well as isobaric heat capacities as an example for thermodynamic properties. We study the role of anharmonicities for these analyses and observe that, in particular, the dominating structural motifs are rather sensitive to the anharmonicity in vibrational frequencies. The regression model proves to be a promising way to get access to anharmonic features, and the extension to more sophisticated machine-learning models is promising.

Unusually Large Hydrogen-Bond Cooperativity in Hydrogen Fluoride Clusters, (HF)n, n = 3 to 8, Revealed by the Molecular Tailoring Approach

In this work, our recently proposed molecular tailoring approach (MTA)-based method is employed for the evaluation of individual hydrogen-bond (HB) energies in linear (L) and cyclic (C) hydrogen fluoride clusters, (HF)_n (n = 3 to 8). The estimated individual HB energies calculated at the MP2(full)/aug-cc-pVTZ level for the L-(HF)_n are between 6.2 to 9.5 kcal/mol and those in the C-(HF)_n lie between 7.9 to 11.4 kcal/mol. The zero-point energy corrections and basis set superposition corrections are found to be very small (less than 0.6 and 1.2 kcal/mol, respectively). The cooperativity contribution toward individual HBs is seen to fall between 1.0 to 4.8 kcal/mol and 3.2 to 6.9 kcal/mol for linear and cyclic clusters, respectively. Interestingly, the HB energies in dimers, cleaved from these clusters, lie in a narrow range (4.4 to 5.2 kcal/mol) suggesting that the large HB strength in (HF)_n clusters is mainly due to the large cooperativity contribution, especially for n ≥ 5 (50 to 62% of the HBs energy). Furthermore, the HB energies in these clusters show a good qualitative correlation with geometrical parameters (H···F distance and F-H···F angles), stretching frequencies of F-H bonds, and electron density values at the (3, -1) bond critical points.

New Molecular-Mechanics Model for Simulations of Hydrogen Fluoride in Chemistry and Biology

Hydrogen fluoride (HF) is the most polar diatomic molecule and one of the simplest molecules capable of hydrogen-bonding. HF deviates from ideality both in the gas phase and in solution and is thus of great interest from a fundamental standpoint. Pure and aqueous HF solutions are broadly used in chemical and industrial processes, despite their high toxicity. HF is a stable species also in some biological conditions, because it does not readily dissociate in water unlike other hydrogen halides; yet, little is known about how HF interacts with biomolecules. Here, we set out to develop a molecular-mechanics model to enable computer simulations of HF in chemical and biological applications. This model is based on a comprehensive high-level ab initio quantum chemical investigation of the structure and energetics of the HF monomer and dimer; (HF)_n clusters, for n = 3-7; various clusters of HF and H₂O; and complexes of HF with analogs of all 20 amino acids and of several commonly occurring lipids, both neutral and ionized. This systematic analysis explains the unique properties of this molecule: for example, that interacting HF molecules favor nonlinear geometries despite being diatomic and that HF is a strong H-bond donor but a poor acceptor. The ab initio data also enables us to calibrate a three-site molecular-mechanics model, with which we investigate the structure and thermodynamic properties of gaseous, liquid, and supercritical HF in a wide range of temperatures and pressures; the solvation structure of HF in water and of H₂O in liquid HF; and the free diffusion of HF across a lipid bilayer, a key process underlying the high cytotoxicity of HF. Despite its inherent simplifications, the model presented significantly improves upon previous efforts to capture the properties of pure and aqueous HF fluids by molecular-mechanics methods and to our knowledge constitutes the first parameter set calibrated for biomolecular simulations.

Quantum Stabilization of the Frustrated Hydrogen Bonding Structure in the Hydrogen Fluoride Trimer

We performed ab initio path integral molecular dynamics (PIMD) and molecular dynamics (MD) simulations to discuss the thermal and nuclear quantum effects on the stabilities of hydrogen bonding network in a hydrogen fluoride trimer (HF)₃ cluster. By the conventional molecular orbital calculation, the (HF)₃ cluster has an equilateral triangle shape, which has a frustration in the chemical structure of the hydrogen bonds, whereas the hydrogen bonding structure of a hydrogen fluoride dimer (HF)₂ cluster is nearly perpendicular to the acceptor molecule. The ratio of the triangular structures with the three hydrogen bondings in the PIMD simulation is larger than that in the MD one, whereas nonhydrogen bonding conformations such as a dimerlike structure are often found in MD simulation. The nuclear quantum effect stabilizes the frustrated hydrogen bonding network of the triangular (HF)₃ cluster.

Anharmonicity of Vibrational Modes in Hydrogen Chloride-Water Mixtures

A thorough analysis of molecular vibrations in the binary system hydrogen chloride/water is presented considering a set of small mixed and pure clusters. In addition to the conventional normal-mode analysis based on the diagonalization of the Hessian, anharmonic frequencies were obtained from the perturbative VPT2 and PT2-VSCF method using hybrid density functional theory. For all normal modes, potential energy curves were modeled by displacing the atoms from the minimum geometry along the normal mode vectors. Three model potentials, a harmonic potential, a Morse potential, and a fourth order polynomial, were applied to fit these curves. From these data, it was possible not only to characterize distinct vibrations as mainly harmonic, anharmonic, or involving higher order terms but also to extract force constants, k, and anharmonicity constants, x_e. By investigating all different types of intramolecular vibrations including covalent stretching or bending vibrations and intermolecular vibrations such as librations, we could demonstrate that while vibrational frequencies can be obtained applying scaling factors to harmonic results, useful anharmonicity constants cannot be predicted in such a way and the usage of more elaborate vibrational methods is necessary. For each particular type of molecular vibration, we could however determine a relationship between the wavenumber or wavenumber shift and the anharmonicity constant, which allows us to estimate mode dependent anharmonicity constants for larger clusters in the future.

Hydrogen bonding between hydrides of the upper-right part of the periodic table

One of the most important electrostatic interactions between molecules is most definitely the hydrogen bond. Understanding the basis of this interaction may offer us the insight needed to understand its effect on the macroscopic scale. Hydrogen bonding is for example the reason for anomalous properties in compounds like water and naturally life as we know it. The strength of the bond depends on numerous factors, among them the electronegativity of participating atoms. In this work we calculated the strength of hydrogen bonds between hydrides of the upper-right part of the periodic table (C, N, O, F, P, S, Cl, As, Se, Br) using quantum-chemical methods. The aim was to determine what influences the strength of strong and weak hydrogen bonds in simple hydrides. Various relationships were checked. A relation between the strength of the bond and the electronegativity of the participating atoms was found. We also observed a correlation between the strength of hydrogen bonds and the inter-atomic distances, along with the dependence on the charge transfer on the atom of the donor. We also report characteristic geometries of different dimers.

Combining Accuracy and Efficiency: An Incremental Focal-Point Method Based on Pair Natural Orbitals

In this work, we present a new pair natural orbitals (PNO)-based incremental scheme to calculate CCSD(T) and CCSD(T0) reaction, interaction, and binding energies. We perform an extensive analysis, which shows small incremental errors similar to previous non-PNO calculations. Furthermore, slight PNO errors are obtained by using T_PNO = T_TNO with appropriate values of 10^-7 to 10^-8 for reactions and 10^-8 for interaction or binding energies. The combination with the efficient MP2 focal-point approach yields chemical accuracy relative to the complete basis-set (CBS) limit. In this method, small basis sets (cc-pVDZ, def2-TZVP) for the CCSD(T) part are sufficient in case of reactions or interactions, while some larger ones (e.g., (aug)-cc-pVTZ) are necessary for molecular clusters. For these larger basis sets, we show the very high efficiency of our scheme. We obtain not only tremendous decreases of the wall times (i.e., factors >10²) due to the parallelization of the increment calculations as well as of the total times due to the application of PNOs (i.e., compared to the normal incremental scheme) but also smaller total times with respect to the standard PNO method. That way, our new method features a perfect applicability by combining an excellent accuracy with a very high efficiency as well as the accessibility to larger systems due to the separation of the full computation into several small increments.

Quantum Chemical Methods for the Prediction of Energetic, Physical, and Spectroscopic Properties of Ionic Liquids

The accurate prediction of physicochemical properties of condensed systems is a longstanding goal of theoretical (quantum) chemistry. Ionic liquids comprising entirely of ions provide a unique challenge in this respect due to the diverse chemical nature of available ions and the complex interplay of intermolecular interactions among them, thus resulting in the wide variability of physicochemical properties, such as thermodynamic, transport, and spectroscopic properties. It is well understood that intermolecular forces are directly linked to physicochemical properties of condensed systems, and therefore, an understanding of this relationship would greatly aid in the design and synthesis of functionalized materials with tailored properties for an application at hand. This review aims to give an overview of how electronic structure properties obtained from quantum chemical methods such as interaction/binding energy and its fundamental components, dipole moment, polarizability, and orbital energies, can help shed light on the energetic, physical, and spectroscopic properties of semi-Coulomb systems such as ionic liquids. Particular emphasis is given to the prediction of their thermodynamic, transport, spectroscopic, and solubilizing properties.

Molecular Dipole Moments within the Incremental Scheme Using the Domain-Specific Basis-Set Approach

We present the first implementation of the fully automated incremental scheme for CCSD unrelaxed dipole moments using the domain-specific basis-set approach. Truncation parameters are varied, and the accuracy of the method is statistically analyzed for a test set of 20 molecules. The local approximations introduce small errors at second order and negligible ones at third order. For a third-order incremental CCSD expansion with a CC2 error correction, a cc-pVDZ/SV domain-specific basis set (tmain = 3.5 Bohr), and the truncation parameter f = 30 Bohr, we obtain a mean error of 0.00 mau (-0.20 mau) and a standard deviation of 1.95 mau (2.17 mau) for the total dipole moments (Cartesian components of the dipole vectors). By analyzing incremental CCSD energies, we demonstrate that the MP2 and CC2 error correction schemes are an exclusive correction for the domain-specific basis-set error. Our implementation of the incremental scheme provides fully automated computations of highly accurate dipole moments at reduced computational cost and is fully parallelized in terms of the calculation of the increments. Therefore, one can utilize the incremental scheme, on the same hardware, to extend the basis set in comparison to standard CCSD and thus obtain a better total accuracy.

Graph theoretical enumeration of topology-distinct structures for hydrogen fluoride clusters (HF)n (n ≤ 6)

A graph theoretical procedure to generate all the possible topology-distinct structures for hydrogen fluoride (HF) clusters is presented in this work. The hydrogen bond matrix is defined and used to enumerate the topology-distinct structures of hydrogen fluoride (HF)n (n = 2-8) clusters. From close investigation of the structural patterns obtained, several restrictions that should be satisfied for a structure of the HF clusters to be stable are found. The corresponding digraphs of generated hydrogen bond matrices are used as the theoretical framework to obtain all the topology-distinct local minima for (HF)n (n ≤ 6), at the level of MP2/6-31G**(d, p) of ab initio MO method and B3LYP/6-31G**(d, p) of density functional theory method. For HF clusters up to tetramers, the local minimum structures that we generated are same as those in the literature. For HF pentamers and hexamers, we found some new local minima structures which had not been obtained previously.

Structural properties of methanol–water binary mixtures within the quantum cluster equilibrium model

The Quantum Cluster Equilibrium (QCE) method computes cluster distributions and thermodynamic properties of binary methanol–water mixtures in agreement with experiments.

Incremental evaluation of coupled cluster dipole polarizabilities

In this work we present the first implementation of the incremental scheme for coupled cluster linear-response frequency-dependent dipole polarizabilities.

New accurate benchmark energies for large water clusters: DFT is better than expected

In this work, we use MP2 and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] as well as their corresponding explicitly correlated (F12) counterparts to compute the interaction energies of water icosamers. The incremental scheme is used to compute benchmark energies at the CCSD(T)/CBS(45) and CCSD(T)(F12*)/cc-pVQZ-F12 level of theory. The four structures, dodecahedron, edge sharing, face sharing, and fused cubes, are part of the WATER27 test set and therefore, highly accurate interaction energies are required. All methods applied in this work lead to new benchmark energies for these four systems. To obtain these values, we carefully analyze the convergence of the interaction energies with respect to the basis set. Furthermore, we investigate the influence of the basis set superposition error and the core-valence correlation. The interaction energies are: dodecahedron -198.6 kcal/mol, edge sharing -209.7 kcal/mol, face sharing -208.0 kcal/mol, and fused cubes -208.0 kcal/mol. For water clusters, we recommend to use the PW6B95 density functional of Truhlar in combination with Grimme's dispersion correction (D3), as the mean absolute error is 0.9 and the root mean-squared deviation is only 1.4 kcal/mol.