Cluster-in-Cluster Approach for Computing MP2-Level Vibrational Infrared Spectra of Large Molecular Clusters.

Constructing the Hessian matrix (HM) for large molecules demands huge computational resources. Here, we report a cluster-in-cluster (CIC) procedure for efficiently evaluating HM and dipole derivatives for large molecular clusters by employing the second-order Møller-Plesset perturbation (MP2) theory. The highlight of the proposal is the separation of the estimations of Hartree-Fock (HF) and post-HF components. The parent cluster with n molecules is divided (virtually) into n subclusters centering each monomer and accommodating its near neighbors decided by a distance cutoff. The HF-level HM is obtained by doing full calculation (FC), while the correlation part is approximated by the respective subclusters. A software automating the procedure [followed by calculating infrared (IR) frequencies and intensities] is applied to deduce the IR spectrum for a variety of molecular clusters, particularly water clusters of various sizes, containing up to ∼2000 basis functions. The accuracy of the IR spectrum constructed using CIC is remarkable, with a substantial time advantage (with respect to its FC counterpart). The reduced computational resources and the tractability of the computations are other major benefits of the procedure.

Hydrogen bond energy estimation (H-BEE) in large molecular clusters: A Python program for quantum chemical investigations.

A procedure, derived from the fragmentation-based molecular tailoring approach (MTA), has been proposed and extensively applied by Deshmukh and Gadre for directly estimating the individual hydrogen bond (HB) energies and cooperativity contributions in molecular clusters. However, the manual fragmentation and high computational cost of correlated quantum chemical methods make the application of this method to large molecular clusters quite formidable. In this article, we report an in-house developed software for automated hydrogen bond energy estimation (H-BEE) in large molecular clusters. This user-friendly software is essentially written in Python and executed on a Linux platform with the Gaussian package at the backend. Two approximations to the MTA-based procedure, viz. the first spherical shell (SS1) and the Fragments-in-Fragments (Frags-in-Frags), enabling cost-effective, automated evaluation of HB energies and cooperativity contributions, are also implemented in this software. The software has been extensively tested on a variety of molecular clusters and is expected to be of immense use, especially in conjunction with correlated methods such as MP2, CCSD(T), and so forth.

REAlgo: Rapid and efficient algorithm for estimating MP2/CCSD energy gradients for large molecular clusters.

This work reports the development of an algorithm for rapid and efficient evaluation of energy gradients for large molecular clusters employing correlated methods viz. second-order Møller-Plesset perturbation theory (MP2) theory and couple cluster singles and doubles (CCSD). The procedure segregates the estimation of Hartree-Fock (HF) and correlation components. The HF energy and gradients are obtained by performing a full calculation. The correlation energy is approximated as the corresponding two-body interaction energy. Correlation gradients for each monomer are approximated from the respective monomer-centric fragments comprising its immediate neighbours. The programmed algorithm is explored for the geometry optimization of large molecular clusters using the BERNY optimizer as implemented in the Gaussian suite of software. The accuracy and efficacy of the method are critically probed for a variety of large molecular clusters containing up to 3000 basis functions, in particular large water clusters. The CCSD level geometry optimization of molecular clusters containing ∼800 basis functions employing a modest hardware is also reported.

Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins.

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.

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.

Development and testing of an algorithm for efficient MP2/CCSD(T) energy estimation of molecular clusters with the 2-body approach.

This work reports the development and testing of an automated algorithm for estimating the energies of weakly bound molecular clusters employing correlated theory. Firstly, the monomers and dimers of (homo/hetero) clusters are identified, and the sum of one-body and two-body contributions to correlation energy is calculated. The addition of this contribution to the Hartree-Fock full calculation (FC) energies provides a good estimate of the total energies at Møller-Plesset second-order perturbation theory (MP2)/coupled-cluster method with singles and doubles (CCSD) (T)-level theory using augmented Dunning basis sets. The estimated energies for several test clusters show an excellent agreement with their FC counterparts, with a substantial wall-clock time saving employing off-the-shelf hardware. Furthermore, the complete basis set (CBS) limit for MP2 energy computed using the two-body approach also agrees with its CBS energy with its FC counterpart.

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.

Pragmatic Many-Body Approach for Economic MP2 Energy Estimation of Molecular Clusters.

We propose a procedure, within the many-body analysis (MBA) framework, for an economic yet accurate estimation of the correlated method-based energies of large molecular clusters employing Dunning's augmented basis sets. The basis of the procedure is to segregate the Hartree-Fock ( EHF) and correlation energy ( EC) estimations. EHF is found to differ by tens of millihartrees (mH) from its full-calculation (FC) counterpart on truncating the MBA expansion at the two-body (MBA-2) level. On the contrary, EC is estimated with smaller error on modest hardware with limited computation time at the (MBA-2) level. In view of this, we adopt a pragmatic method wherein the EHF (accurate to five decimal places) is taken from the FC, whereas EC is estimated at the MBA-2 level. This method is applied to a variety of medium to large molecular clusters at the MP2 level. Preliminary results at the CCSD(T) level for (H2O)16 and (H2O)17 are also reported with tremendous savings in wall-clock time and resources. The typical errors in MP2 and CCSD(T) energies per monomer are up to 0.1 and 0.2 mH, respectively. Thus the present method, balancing accuracy and computational economy, opens a way for estimating energies of large molecular clusters using correlated theories with large basis sets.

Harmonizing accuracy and efficiency: A pragmatic approach to fragmentation of large molecules.

Fragmentation methods offer an attractive alternative for ab initio treatment of large molecules and molecular clusters. However, balancing the accuracy and efficiency of these methods is a tight-rope-act. With this in view, we present an algorithm for automatic molecular fragmentation within Molecular Tailoring Approach (MTA) achieving this delicate balance. The automated code is tested out on a variety of molecules and clusters at the Hartree-Fock (HF)- and Møller-Plesset second order perturbation theory as well as density functional theory employing augmented Dunning basis sets. The results show remarkable accuracy and efficiency vis-à-vis the respective full calculations. Thus the present work forms an important step toward the development of an MTA-based black box code for implementation of HF as well as correlated quantum chemical calculations on large molecular systems.