Ring-Polymer Instanton Tunneling Splittings of Tropolone and Isotopomers using a Δ-Machine Learned CCSD(T) Potential: Theory and Experiment Shake Hands.

Tropolone, a 15-atom cyclic molecule, has received much interest both experimentally and theoretically due to its H-transfer tunneling dynamics. An accurate theoretical description is challenging owing to the need to develop a high-level potential energy surface (PES) and then to simulate quantum-mechanical tunneling on this PES in full dimensionality. Here, we tackle both aspects of this challenge and make detailed comparisons with experiments for numerous isotopomers. The PES, of near CCSD(T)-quality, is obtained using a Δ-machine learning approach starting from a pre-existing low-level DFT PES and corrected by a small number of approximate CCSD(T) energies obtained using the fragmentation-based molecular tailoring approach. The resulting PES is benchmarked against DF-FNO-CCSD(T) and CCSD(T)-F12 calculations. Ring-polymer instanton calculations of the splittings, obtained with the Δ-corrected PES are in good agreement with previously reported experiments and a significant improvement over those obtained using the low-level DFT PES. The instanton path includes heavy-atom tunneling effects and cuts the corner, thereby avoiding passing through the conventional saddle-point transition state. This is in contradistinction with typical approaches based on the minimum-energy reaction path. Finally, the subtle changes in the splittings for some of the heavy-atom isotopomers seen experimentally are reproduced and explained.

Constructing Potential Energy Surface with Correlated Theory for Dipeptides Using Molecular Tailoring Approach.

We demonstrate a cost-effective alternative employing the fragment-based molecular tailoring approach (MTA) for building the potential energy surface (PES) for two dipeptides viz. alanine-alanine and alanine-proline employing correlated theory, with augmented Dunning basis sets. About 1369 geometries are generated for each test dipeptide by systematically varying the dihedral angles Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . These conformational geometries are partially optimized by relaxing all the other Z-matrix parameters, fixing the values of Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . The MP2 level PES is constructed from the MTA-energies of chemically intact geometries using minimal hardware. The fidelity of MP2/aug-cc-pVDZ level PES is brought out by comparing it with its full calculation counterpart. Further, we bring out the power of the method by reporting the MTA-based CCSD/aug-cc-pVDZ level PES for these two dipeptides containing 498 and 562 basis functions respectively.

Hydration shell model for expeditious and reliable individual hydrogen bond energies in large water clusters.

Recently, we have developed and tested a method, based on the molecular tailoring approach (MTA-based) to directly estimate the individual hydrogen bond (HB) energies in molecular clusters. Application of this MTA-based method to large molecular clusters is prohibitively difficult due to the evaluation of the energy of large-sized fragments. We propose here a smaller model system called the shell model, to overcome this difficulty. The shell model represents the first hydration shell of water molecules involved in the formation of HB under consideration. Utilizing the shell model as a parent system, fragmentation is carried out, in a fashion similar to the actual MTA-based method, to estimate individual HB energies in large water clusters (Wn, n = 10-16, 18 and 20). The estimated individual HB energies in these Wn clusters, employing the shell model, fall between 0.2 and 12.5 kcal mol-1 at the MP2/aug-cc-pVTZ level, with no net loss in the cooperativity contribution. We have also applied this shell model-based approach to estimate individual HB energies in the two lowest energy conformers of ammonia octamers (NH3)8 and mixed hydrogen fluoride-water clusters. The estimated individual HB energies employing the shell model, in all these molecular clusters studied in this work, are in good agreement with their actual MTA-based counterparts. The typical difference is less than 1 kcal mol-1. Importantly, the shell model has a huge computational time advantage over the actual MTA-based method and it requires only modest hardware.

Enabling Rapid and Accurate Construction of CCSD(T)-Level Potential Energy Surface of Large Molecules Using Molecular Tailoring Approach.

The construction of a potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is arduous due to the high computational cost involved. The present study reports the possibility of efficiently constructing such a PES of molecules containing up to 15 atoms and 550 basis functions by employing the fragment-based molecular tailoring approach (MTA) on off-the-shelf hardware. The MTA energies at the CCSD(T)/aug-cc-pVTZ level for several geometries of three test molecules, viz., acetylacetone, N-methylacetamide, and tropolone, are reported. These energies are in excellent agreement with their full calculation counterparts with a time advantage factor of 3-5. The energy barrier from the ground to transition state is also accurately captured. Further, we demonstrate the accuracy and efficiency of MTA for estimating the energy gradients at the CCSD(T) level. As a further application of our MTA methodology, the energies of acetylacetone at ∼430 geometries are computed at the CCSD(T)/aug-cc-pVTZ level and used for generating a Δ-machine learning (Δ-ML) PES. This leads to the H-transfer barrier of 3.02 kcal/mol, well in agreement with the benchmarked barrier of 3.19 kcal/mol. The fidelity of this Δ-ML PES is examined by geometry optimization and normal mode frequency calculations of global minima and saddle point geometries. We trust that the present work is a major development for the rapid and accurate construction of PES at the CCSD(T) level for molecules containing up to 20 atoms and 600 basis functions using off-the-shelf hardware.

Molecular Tailoring Approach for Estimating Individual Intermolecular Interaction Energies in Benzene Clusters.

There is no general method available for the estimation of individual intermolecular interaction energies in weakly bound molecular clusters, and such studies are limited only to the dimer. Recently, we proposed a molecular tailoring approach-based method for the estimation of individual O-H···O hydrogen bond energies in water clusters. In the present work, we extend the applicability of this method for estimating the individual intermolecular interaction energies in benzene clusters, which are expected to be small. The basis set superposition error (BSSE)-corrected individual intermolecular interaction energies in linear (LN) benzene clusters, LN-(Bz)n n = 3-7, were calculated to be in the range from -1.75 to -2.33 kcal/mol with the cooperativity contribution falling between 0.05 and 0.20 kcal/mol, calculated at the MP2.5/aug-cc-pVDZ level of theory. In the case of non-linear (NLN) benzene clusters, NLN-(Bz)n n = 3-5, the BSSE-corrected individual intermolecular interaction energies exhibit a wider range from -1.16 to -2.55 kcal/mol with cooperativity contribution in the range from 0.02 to -0.61 kcal/mol. The accuracy of these estimated values was validated by adding the sum of interaction energies to the sum of monomer energies. These estimated molecular energies of clusters were compared with their actual calculated values. The small difference (<0.3 kcal/mol) in these two values suggests that our estimated individual intermolecular interaction energies in benzene clusters are quite reliable.

Encaged molecules in external electric fields: A molecular "tug-of-war".

Response of polar molecules CH3OH and H2O2 and a non-polar molecule, CO2, as "guests" encapsulated in the dodecahedral water cage (H2O)20 "host," to an external, perturbative electric field is investigated theoretically. We employ the hybrid density-functionals M06-2X and ωB97X-D incorporating the effects of damped dispersion, in conjunction with the maug-cc-pVTZ basis set, amenable for a hydrogen bonding description. While the host cluster (cage) tends to confine the embedded guest molecule through cooperative hydrogen bonding, the applied electric field tends to rupture the cluster-composite by stretching it; these two competitive effects leading to a molecular "tug-of-war." The composite remains stable up to a maximal sustainable threshold electric field, beyond which, concomitant with the vanishing of the HOMO-LUMO gap, the field wins over and the cluster breaks down. The electric-field effects are gauged in terms of the changes in the molecular geometry of the confined species, interaction energy, molecular electrostatic potential surfaces, and frequency shifts of characteristic normal vibrations in the IR regime. Interestingly, beyond the characteristic threshold electric field, the labile, distorted host cluster fragmentizes, and the guest molecule still tethered to a remnant fragment, an effect attributed to the underlying hydrogen-bonded networks.

CH3OH⋯(H2O)n [n = 1-4] clusters in external electric fields.

For hydrogen-bonded neutral molecular clusters, response to an externally applied electric field can critically affect molecular cooperativity. In this light, response of dilute methanol-water admixtures to an external, perturbative electric field is studied at the simplest molecular level in the cluster configurations CH3OH⋯(H2O)n with "n" chosen to range from 1 to 4, employing the M06-2X hybrid functional in conjunction with the 6-311++G(2d,2p) basis set, well-suited for hydrogen bonding. Methanol is seen to favorably bond with the water molecules at its hydroxyl end up to certain characteristic maximum threshold field strengths beyond which the HOMO-LUMO energy-gap abruptly drops to zero culminating into a complete breakdown of the cluster. In the interim regime prior to breakdown, the electric field significantly alters the hydrogen bonding pattern primarily by elongating the cluster, resulting in a marked enhancement in its electric dipole moment leading to alterations in the molecular electrostatic potential. With the application of electric field, certain "exotic" O-H vibration bands appear that at the threshold field fall in the frequency range of 2510 cm(-1)-1880 cm(-1) in the IR spectra, in contrast with their normal (zero-field) counterparts that occur in the range of ∼3300-3900 cm(-1).