Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning

Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.

Low scaling quantum mechanics calculations and machine learning can be employed to efficiently predict the molecular energies, forces, and optical and electrical properties of molecular materials and their aggregates.     

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields

We introduce an initial implementation of the LICHEM software package. LICHEM can interface with Gaussian, PSI4, NWChem, TINKER, and TINKER–HP to enable QM/MM calculations using multipolar/polarizable force fields. LICHEM extracts forces and energies from unmodified QM and MM software packages to perform geometry optimizations, single‐point energy calculations, or Monte Carlo simulations. When the QM and MM regions are connected by covalent bonds, the pseudo‐bond approach is employed to smoothly transition between the QM region and the polarizable force field. A series of water clusters and small peptides have been employed to test our initial implementation. The results obtained from these test systems show the capabilities of the new software and highlight the importance of including explicit polarization. © 2016 Wiley Periodicals, Inc.     

Iridium cyclometalated complexes with axial symmetry: time-dependent density functional theory investigation of trans-bis-cyclometalated complexes containing the tridentate ligand 2,6-diphenylpyridine

A new series of iridium cyclometalated complexes with a C/N/C dppy-type ligand and a N/N/N tpy-type ligand have been synthesized and characterized by various techniques such as mass spectrometry, 1H and 13C NMR, cyclic voltammetry, both steady-state and time-resolved emission and absorption studies, and time-dependent DFT (TDDFT) calculations. The complexes exhibit strong visible absorptions and long-lived (1.6-2.0 micros) emissions (lambdamax, ca. 680 nm) in room-temperature solution. DFT calculations on the ground-state geometry match that of an X-ray crystal structure. TDDFT calculations give accurate predictions of the electronic absorption energies and intensities, while geometry optimizations on the lowest energy triplet state give accurate energies for the emission. Examination of the relevant molecular orbitals shows that the inherent asymmetry of the coordination environment offers a unique directional character to the emitting excited state, which is predominately LLCT (dppy --> tpy) in nature.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Probing the structural and electronic factors affecting the adsorption and reactivity of alkenes in acidic zeolites using DFT calculations and multivariate statistical methods

Quantum mechanical (QM) cluster calculations have been performed on a model of ZSM-5 at DFT and MP2 levels. We investigated how the adsorption energies and the energetics of alkoxide intermediate formation of six different alkene substrates, ethene, propene, 1-butene, cis/trans butene, and isobutene, vary in this zeolite model. An analysis of the DFT geometric, electronic, and energetic parameters of the zeolite-substrate complexes, transition states, and alkoxide intermediates is performed using principal components analysis (PCA) and partial least squares (PLS). These deliver an insight into the correlated changes that occur between molecular structure and energy along the reaction coordinate between the physisorbed and chemisorbed species within the zeolite. To the best of our knowledge, this is the first occasion multivariate techniques such as PCA or PLS have been employed to profile the changes in electronics, distances, and angles in QM calculations of catalytic systems such as zeolites. We find the calculated adsorption and the alkoxide intermediate energies correlate strongly with the absolute charge on the substrate and the length of the substrate double bond. The transition states' energies are not affected by the zeolite framework as modeled, which explains why they correlate strongly with the gas-phase substrate protonation energy. Our cluster results show that for ethene, propene, 1-butene, and isobutene, the relative energetics associated with the formation of the alkoxide intermediate in ZSM-5 follow the same trends as calculations where the effects of the framework are included.     

Conformational Analysis of Free and Bound Retinoic Acid

The conformational profiles of unbound all-trans and 9-cis retinoic acid (RA) have been determined using classical and quantum mechanical calculations. Sixty-six all-trans-RA (ATRA) and forty-eight 9-cis-RA energy minimum conformers were identified via HF/6-31G* geometry optimizations in vacuo. Their relative conformational energies were estimated utilizing the M06, M06-2x and MP2 methods combined with the 6-311+G(d,p), aug-cc-pVDZ and aug-cc-pVTZ basis sets, as well as complete basis set MP2 extrapolations using the latter two basis sets. Single-point energy calculations performed with the M06-2x density functional were found to yield similar results to MP2/CBS for the low-energy retinoic acid conformations. Not unexpectedly, the conformational propensities of retinoic acid were governed by the orientation and arrangement of the torsion angles associated with the polyene tail. We also used previously reported QM/MM X-ray refinement results on four ATRA-protein crystal structures plus one newly refined 9-cis-RA complex (PDB ID 1XDK) in order to investigate the conformational preferences of bound retinoic acid. In the re-refined RA conformers the conjugated double bonds are nearly coplanar, which is consistent with the global minimum identified by the Omega/QM method rather than the corresponding crystallographically determined conformations given in the PDB. Consequently, a 91.3% average reduction of the local strain energy in the gas phase, as well as 92.1% in PCM solvent, was observed using the QM/MM refined structures versus the PDB deposited RA conformations. These results thus demonstrate that our QM/MM X-ray refinement approach can significantly enhance the quality of X-ray crystal structures refined by conventional refinement protocols, thereby providing reliable drug-target structural information for use in structure-based drug discovery applications.     

Fragmentation-based QM/MM simulations: length dependence of chain dynamics and hydrogen bonding of polyethylene oxide and polyethylene in aqueous solutions

Molecular fragmentation quantum mechanics (QM) calculations have been combined with molecular mechanics (MM) to construct the fragmentation QM/MM method for simulations of dilute solutions of macromolecules. We adopt the electrostatics embedding QM/MM model, where the low-cost generalized energy-based fragmentation calculations are employed for the QM part. Conformation energy calculations, geometry optimizations, and Born-Oppenheimer molecular dynamics simulations of poly(ethylene oxide), PEO(n) (n = 6-20), and polyethylene, PE(n) ( n = 9-30), in aqueous solution have been performed within the framework of both fragmentation and conventional QM/MM methods. The intermolecular hydrogen bonding and chain configurations obtained from the fragmentation QM/MM simulations are consistent with the conventional QM/MM method. The length dependence of chain conformations and dynamics of PEO and PE oligomers in aqueous solutions is also investigated through the fragmentation QM/MM molecular dynamics simulations.     

Benzoxazine oligomers: evidence for a helical structure from solid-state NMR spectroscopy and DFT-based dynamics and chemical shift calculations

A combination of molecular modeling, DFT calculations, and advanced solid-state NMR experiments is used to elucidate the supramolecular structure of a series of benzoxazine oligomers. Intramolecular hydrogen bonds are characterized and identified as the driving forces for ring-shape and helical conformations of trimeric and tetrameric units. In fast MAS (1)H NMR spectra, the resonances of the protons forming the hydrogen bonds can be assigned and used for validating and refining the structure by means of DFT-based geometry optimizations and (1)H chemical-shift calculations. Also supporting these proposed structures are homonuclear (1)H[bond](1)H double-quantum NMR spectra, which identify the local proton-proton proximities in each material. Additionally, quantitative (15)N[bond](1)H distance measurements obtained by analysis of dipolar spinning sideband patterns confirm the optimized geometry of the tetramer. These results clearly support the predicted helical geometry of the benzoxazine polymer. This geometry, in which the N...H...O and O...H...O hydrogen bonds are protected on the inside of the helix, can account for many of the exemplary chemical properties of the polybenzoxazine materials. The combination of advanced experimental solid-state NMR spectroscopy with computational geometry optimizations, total energy, and NMR spectra calculations is a powerful tool for structural analysis. Its results provide significantly more confidence than the individual measurements or calculations alone, in particular, because the microscopic structure of many disordered systems cannot be elucidated by means of conventional methods due to lack of long-range order.     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

Structures in solutions from joint experimental-computational analysis: applications to cyclic molecules and studies of noncovalent interactions

The potential of an approach combining nuclear magnetic resonance (NMR) spectroscopy, molecular dynamics (MD) simulations, and quantum mechanical (QM) calculations for full structural characterizations in solution is assessed using cyclic organic compounds, namely, benzazocinone derivatives 1-3 with fused five- and eight-membered aliphatic rings, camphoric anhydride 4, and bullvalene 5. Various MD simulations were considered, using force field and semiempirical QM treatments, implicit and explicit solvation, and high-temperature MD calculations for selecting plausible molecular geometries for subsequent QM geometry optimizations using mainly B3LYP, M062X, and MP2 methods. The QM-predicted values of NMR parameters were compared to their experimental values for verification of the final structures derived from the MD/QM analysis. From these comparisons, initial estimates of quality thresholds (calculated as rms deviations) were 0.7-0.9 Hz for (3)J(HH) couplings, 0.07-0.11 ? for interproton distances, 0.05-0.08 ppm for (1)H chemical shifts, and 1.0-2.1 ppm for (13)C chemical shifts. The obtained results suggest that the accuracy of the MD analysis in predicting geometries and relative conformational energies is not critical and that the final geometry refinements of the structures selected from the MD simulations using QM methods are sufficient for correcting for the expected inaccuracy of the MD analysis. A unique example of C(sp(3))-H···N(sp(3)) intramolecular noncovalent interaction is also identified using the NMR/MD/QM and the natural bond orbital analyses. As the NMR/MD/QM approach relies on the final QM geometry optimization, comparisons of geometric characteristics predicted by different QM methods and those from X-ray and neutron diffraction measurements were undertaken using rigid and flexible cyclic systems. The joint analysis shows that intermolecular noncovalent interactions present in the solid state alter molecular geometries significantly compared to the geometries of isolated molecules from QM calculations.     

YinYang atom: a simple combined ab initio quantum mechanical molecular mechanical model

A simple interface is proposed for combined quantum mechanical (QM) molecular mechanical (MM) calculations for the systems where the QM and MM regions are connected through covalent bonds. Within this model, the atom that connects the two regions, called YinYang atom here, serves as an ordinary MM atom to other MM atoms and as a hydrogen-like atom to other QM atoms. Only one new empirical parameter is introduced to adjust the length of the connecting bond and is calibrated with the molecule propanol. This model is tested with the computation of equilibrium geometries and protonation energies for dozens of molecules. Special attention is paid on the influence of MM point charges on optimized geometry and protonation energy, and it is found that it is important to maintain local charge-neutrality in the MM region in order for the accurate calculation of the protonation and deprotonation energies. Overall the simple YinYang atom model yields comparable results to some other QM/MM models.     

Protein-cofactor interactions in bacterial reaction centers from Rhodobacter sphaeroides R-26: effect of hydrogen bonding on the electronic and geometric structure of the primary quinone. A density functional theory study

The effect of hydrogen bonding to the primary quinone (Q(A) and Q(*)(-)(A)) in bacterial reaction centers was studied using density functional theory (DFT) calculations. The charge neutral state Q(A) was investigated by optimizing the hydrogen atom positions of model systems extracted from 15 different X-ray structures. From this analysis, mean values of the H-bond lengths and directions were derived. It was found that the N(delta)-H of His M219 forms a shorter H-bond to Q(A) than the N-H of Ala M260. The H-bond of His M219 is linear and more twisted out of the quinone plane. The radical anion Q(*)(-)(A) in the protein environment was investigated by using a mixed quantum mechanics/molecular mechanics (QM/MM) approach. Two geometry optimizations with a different number of flexible atoms were performed. H-bond lengths were obtained and spectroscopic parameters calculated, i.e. the hyperfine and nuclear quadrupole couplings of magnetic nuclei coupled to the radical. Good agreement was found with the results provided by EPR/ENDOR spectroscopy. This implies that the calculated lengths and directions of the H-bonds to Q(*)(-)(A) are reliable values. From a comparison of the neutral and reduced state of Q(A) it was concluded that the H-bond distances are shortened by approximately 0.17 Angstroms (His M219) and approximately 0.13 Angstroms (Ala M260) upon single reduction of the quinone. It is shown that the point-dipole approximation can not be used for an estimation of H-bond lengths from measured hyperfine couplings in a system with out-of-plane H-bonding. In contrast, the evaluation of the nuclear quadrupole couplings of (2)H nuclei substituted in the hydrogen bonds yields H-bond lengths close to the values that were deduced from DFT geometry optimizations. The significance of hydrogen bonding to the quinone cofactors in biological systems is discussed.     

Peptide hydrolysis catalyzed by matrix metalloproteinase 2: a computational study

The MMP-2 reaction mechanism is investigated by using different computational methodologies. First, quantum mechanical (QM) calculations are carried out on a cluster model of the active site bound to an Ace-Gly approximately Ile-Nme peptide. Along the QM reaction path, a Zn-bound water molecule attacks the Gly carbonyl group to give a tetrahedral intermediate. The breaking of the C-N bond is completed thanks to the Glu 404 residue that shuttles a proton from the water molecule to Ile-N atom. The gas-phase QM energy barrier is quite low ( approximately 14 kcal/mol), thus suggesting that the essential catalytic machinery is included in the cluster model. A similar reaction path occurs in the MMP-2 catalytic domain bound to an octapeptide substrate according to hybrid QM and molecular mechanical (QM/MM) geometry optimizations. However, the rupture of the Gly( P 1) approximately Ile( P 1') amide bond is destabilized in the static QM/MM calculations, owing to the positioning of the Ile( P 1') side chain inside the MMP-2 S 1' pocket and to the inability of simple energy miminization methodologies to properly relax complex systems. Molecular dynamics simulations show that these steric limitations are overcome easily through structural fluctuations. The energetic effect of structural fluctuations is taken into account by combining QM energies with average MM Poisson-Boltzmann free energies, resulting in a total free energy barrier of 14.8 kcal/mol in good agreement with experimental data. The rate-determining event in the MMP-2 mechanism corresponds to a H-bond rearrangement involving the Glu 404 residue and/or the Glu 404-COOH --> N-Ile( P 1') proton transfer. Overall, the present computational results and previous experimental data complement each other well in order to provide a detailed view of the MMPs catalytic mechanism.     

Improved density functional theory/electrostatic calculation of the His291 protonation state in cytochrome C oxidase: self-consistent charges for solvation energy calculation

The protonation state of His291 in cytochrome c oxidase (CcO), a ligand to the Cu(B) center of the enzyme, has been recently studied in this group by using combined density functional theory (DFT)/electrostatic (QM/MM) calculations. On the basis of these calculations, a model of the proton pumping mechanism of CcO has been proposed. Due to certain technical difficulties, the procedure used in the previous calculation to find partial atomic charges of the QM system for the solvation energy evaluation was not entirely satisfactory; i.e., it was not self-consistent. Here, we describe a procedure that resolves the problem and report on the improved calculations of the protonation state of the His residue. The new procedure fits the protein and reaction field potentials in the region of the QM system with artificial point charges placed on a surface of a sphere surrounding the QM system and a few charges inside the sphere and allows one to perform DFT calculations that involve an inhomogeneous dielectric environment in a self-consistent way. The procedure improves the accuracy of calculations in comparison with previous work. The improved results show, however, that although the absolute energies change significantly the relative energies of the protonated and deprotonated states of His291 remain close to the previously reported ones and therefore do not change significantly the pK(a) values reported earlier. Therefore, our new improved calculations support for the proposed His291 model of the CcO pump.     

Diastereomer configurations from joint experimental-computational analysis

The potential of the approach combining nuclear magnetic resonance (NMR) spectroscopy, relaxed grid search (RGS), molecular dynamics (MD) simulations, and quantum mechanical (QM) calculations for the determination of diastereomer configurations is demonstrated using four diastereomers of a trisubstituted epoxide. Since the change in configuration of the chiral center is expected to change the distribution of conformer populations (including those of side-chain rotamers), changes in NMR parameters [chemical shifts, J couplings, and nuclear Overhauser effects (NOEs)] are expected. The method therefore relies on (1) identification of possible conformations in each diastereomer using relaxed grid search analysis and MD simulations; (2) geometry optimizations of conformers selected from step (1), followed by calculations of their relative energies (populations) using QM methods; (3) calculations of averaged NMR parameters using QM methods; (4) matching calculated and experimental values of NMR parameters of diastereomers. The diastereomer configurations are considered resolved, if three NMR parameters different in nature, chemical shifts, J couplings, and NOEs, are in agreement. A further advantage of this method is that full structural and dynamics characterization of each of the diastereomers is achieved based on the joint analysis of experimental and computational data.     

Long-range corrected density functional calculations of chemical reactions: redetermination of parameter

Chemical reaction calculations were carried out using the long-range correction (LC) scheme, which improves long-range exchange effects in density functional theory (DFT) [J. Chem. Phys. 115, 3540 (2001); 120, 8425 (2004)]. A new determination of the LC scheme parameter mu was made by a root mean square fit of the percent error in calculated atomization energies. As a result, the parameter mu was optimized as 0.47, which is higher than the previous one (mu=0.33). Using this new parameter mu, LC-DFT was firstly applied to geometry optimizations of the G2 benchmark set molecules. Consequently, this new LC-DFT gave more accurate bond lengths and bond angles than previous LC-DFT and hybrid B3LYP results. Following this result, the authors calculated reaction barrier height energies of benchmark reaction sets, which have been underestimated in conventional DFT calculations. Calculated results showed that LC-DFT provided much more accurate barrier height energies with errors less than half those of previous LC-DFT and B3LYP studies. To test the general validity of the new LC-DFT, the authors finally calculated reaction enthalpies. As a result, they found that the LC scheme using the new mu clearly improved the accuracy of calculated enthalpies. The authors therefore conclude that the insufficient inclusion of long-range exchange effects is responsible for the underestimation of reaction barriers in DFT calculations and that LC-DFT using the new parameter is a powerful tool for theoretically investigating chemical reactions.     

Comparison of Some Computational Methods for Geometry Optimisation of Phosphorus Acid Derivatives

Several economical methods for geometry optimization, that should be applicable to larger molecules, have been evaluated for 19 phosphorus acid derivatives. MP2/cc-pVDZ geometry optimizations are used as reference points and the geometries obtained from the other methods are evaluated with respect to deviations in bond lengths and angles, from the reference geometries. The geometry optimization methods are also compared to the much used B3LYP/6-31G(d) method. Single point energies obtained by subsequent EDF1/6-31+G(d) or B3LYP/6-31+G(d,p) calculations on the respective equilibrium geometries are also reported relative to the energies obtained from the reference geometries. The geometries from HF/MIDI! optimizations were closer to those of the references than the geometries of the HF/3-21G(d), HF/6-31G(d), and B3LYP/MIDI! optimizations. The EDF1/6-31+G(d) or B3LYP/6-31+G(d,p) single point energies obtained from the HF/3-21G(d), HF/6-31G(d), and B3LYP/MIDI! geometries gave a mean absolute deviation (MAD) from that of the reference geometries of 1.4-3.9 kcal mol m 1 . The HF/MIDI! geometries, however, gave EDF1/6-31+G(d) and B3LYP/6-31+G(d,p) energies with a MAD of only about 0.5 and 0.55 kcal mol m 1 respectively from the energies obtained with the reference geometries. Thus, use of HF/MIDI! for geometry optimization of phosphorus acids is a method that gives geometries of near-MP2 quality, resulting in a fair accuracy of energies in subsequent single point calculations, at a much lower computational cost other methods that give similar accuracies.