cc-pVDZ Basis Set Research Articles

The adaptive shift method in full configuration interaction quantum Monte Carlo: Development and applications.

In a recent paper, we proposed the adaptive shift method for correcting undersampling bias of the initiator-full configuration interaction (FCI) quantum Monte Carlo. The method allows faster convergence with the number of walkers to the FCI limit than the normal initiator method, particularly for large systems. However, in its application to some systems, mostly strongly correlated molecules, the method is prone to overshooting the FCI energy at intermediate walker numbers, with convergence to the FCI limit from below. In this paper, we present a solution to the overshooting problem in such systems, as well as further accelerating convergence to the FCI energy. This is achieved by offsetting the reference energy to a value typically below the Hartree-Fock energy but above the exact energy. This offsetting procedure does not change the exactness property of the algorithm, namely, convergence to the exact FCI solution in the large-walker limit, but at its optimal value, it greatly accelerates convergence. There is no overhead cost associated with this offsetting procedure and is therefore a pure and substantial computational gain. We illustrate the behavior of this offset adaptive shift method by applying it to the N2 molecule, the ozone molecule at three different geometries (an equilibrium open minimum, a hypothetical ring minimum, and a transition state) in three basis sets (cc-pVXZ, X = D, T, Q), and the chromium dimer in the cc-pVDZ basis set, correlating 28 electrons in 76 orbitals. We show that in most cases, the offset adaptive shift method converges much faster than both the normal initiator method and the original adaptive shift method.

Quantum chemical calculation of the primary thermolysis reactions of 1,1-diamino-2,2-dinitroethylene (FOX-7)

The primary thermolysis reactions of 1,1-diamino-2,2-dinitroethylene FOX-7 (1), one of the promising energetic materials, were studied. A number of competing reactions of the primary thermolysis step was calculated: nitro group elimination, rearrangement of the nitro group to the nitrite group, transfer of oxygen and hydrogen atoms to the neighboring carbon atom, and transfer of hydrogen atom to oxygen of the nitro group. The reactions were modeled by the DFT PBE0 method with the cc-pVDZ basis set and by the CCSD(T)/aug-cc-pVDZ method. The activation enthalpies (ΔHa) of several reaction channels range from 200 to 260 kJ mol−1, and they should be taken into account when estimating the thermal stability of the compounds analogous to compound 1. For compound 1, the highest contribution to the overall thermolysis rate is made by the transfer of the hydrogen atom from the amino group to the carbon atom at the nitro groups. This reaction can proceed via four different channels with ΔHa = 200, 206, 235, and 242 kJ mol−1. For the oxygen atom transfer to carbon ΔHa = 244 kJ mol−1, and for the nitro-nitrite isomerization reaction ΔHa = 263 kJ mol−1. The hydrogen atom transfer to oxygen of the nitro group with the formation of nitronic acid (intermediate product) is characterized by the lowest activation energy (130 kJ mol−1), but further transformations via this route occur with higher (more than 300 kJ mol−1) ΔHa values. The checking of the DFT results at the CCSD(T)/aug-cc-pVDZ level showed that the first method only slightly overestimated the energies of various stated over the initial compound 1 and correctly described the ratio of rates of various thermolysis routes.

The performance of phaseless auxiliary-field quantum Monte Carlo on the ground state electronic energy of benzene.

The ground state electronic energy of benzene is the focus of a recent blind test by Eriksen and co-workers [arXiv:2008.02678]. In this note, we report the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) results on the identical problem. We examine trial wavefunctions of the spin-restricted Hartree-Fock (RHF), and complete active space self-consistent field (CASSCF) with an active space of 6-electron and 6-orbital (i.e., CAS(6,6)) form for the cc-pVDZ basis set. ph-AFQMC+RHF deviates from the value where many methods agreed on (i.e., -863 m$E_h$) by -3.1(3) m$E_h$ whereas ph-AFQMC+CAS(6,6) deviates from the same value by -1.3(4) m$E_h$. In addition to this, we report the frozen core correlation energy of ph-AFQMC+RHF in the cc-pVTZ and cc-pVQZ basis sets as well as their complete basis set limit. Our findings highlight the accuracy, flexibility, and scalability of ph-AFQMC with simple trial wavefunctions.

Detailed structural study of cyclic anticancer drug Lorlatinib: spectroscopic and stereostructure investigation (IR, ECD and NMR) using density functional theory approach

Lorlatinib is a third-generation macrocyclic tyrosine kinase inhibitor (TKI) that targets anaplastic lymphoma kinase (ALK) and c-ros oncogene 1 (ROS1) in non-small-cell lung cancer (NSCLC). In this work, an overall structural search of Lorlatinib molecule has been performed by theoretical calculations. The molecular structural optimization, vibrational frequencies, Electronic circular dichroism (ECD) and NMR spectra have been calculated by time-dependence-density functional theory (TD-DFT) using B3LYP method with the 6-311++G(d,p), B3LYP/6-311++G(2d,2p), CAM-B3LYP/TZVP and CAM-ωB97XD/cc-pVDZ basis sets, respectively. IR spectra for Lorlatinib has been recorded in the region of 400–4000 cm−1. 13C and 1H NMR chemical shifts of the molecule was calculated based on the gauge-independent atomic orbital (GIAO) method. All of the calculation results were applied to simulate experimental spectra of the title compound which showed favorable agreement. Furthermore, reliable vibrational assignments which have been made on the basis of potential energy distribution (PED) and characteristic vibrational absorption bands of the title compound in IR spectra have been figured out. Frontier molecular orbitals analysis (FMOs) and the global reactivity descriptors have also been evaluated.

A Systematic Study of DFT Performance for Geometry Optimizations of Ionic Liquid Clusters.

Clusters of two ion pairs of imidazolium-based ionic liquids were optimized with 43 different levels of theory, including DFT functionals and MP2-based methods combined with varying Dunning's basis sets, and added dispersion corrections. Better preforming DFT functionals were then applied to clusters consisting of four ion pairs. Excellent performance of some DFT functionals for the two ion pair clusters did not always match that of the four ion-paired clusters despite interionic distances remaining constant between the optimized two and four ion-paired clusters of the same ionic liquid. Combinations of DFT functional and basis set such as ωB97X-D/cc-pVDZ, M06-2X/aug-cc-pVDZ, B3LYP-D3/cc-pVTZ, and TPSS-D3/cc-pVTZ gave excellent results for geometry optimization of two ion-paired clusters of imidazolium ionic liquids but gave larger deviations when applied to the four ion-paired clusters of varying ionic liquids. Empirical dispersion corrections were seen to be crucial in correctly capturing correlation effects in the studied ionic liquid clusters, becoming more important in larger clusters. Dunning's double-ζ basis set, cc-pVDZ, is associated with the smallest root mean squared deviations for geometries; however, it also produces the largest deviations in total electronic energies. ωB97X-D and M06-2X produced the best performance with the augmented version of this basis set. The triple-ζ basis set, cc-pVTZ, leads to the best performance of most of the DFT functionals (especially the dispersion-corrected ones) used, whereas its augmented version, aug-cc-pVTZ, was not seen to improve results. The combinations of functional and basis set that gave the best geometry and energetics in both two and four ion-paired clusters were PBE-D3/cc-pVTZ, ωB97X-D/aug-cc-pVDZ, and BLYP-D3/cc-pVTZ. All three combinations are recommended for geometry optimizations of larger clusters of ionic liquids. PBE-D3/cc-pVTZ performed the best with an average deviation of 2.3 kJ mol-1 and a standard deviation of 3.4 kJ mol-1 for total electronic energy when applied to four ion-paired clusters. Geometries optimized with FMO2-SRS-MP2/cc-pVTZ produced total energy within 2.0 kJ mol-1 off the benchmark in two ion-paired clusters, with the cc-pVDZ basis set performing unsurprisingly poorly with the same method. The error increased to 4.8 kJ mol-1 on average in four ion-paired clusters, with the smallest RMSD deviations in geometries when compared to the benchmark ones. This study is the first report that investigated the performance of DFT functionals for two and four ion-paired clusters of a wide range of ionic liquids consisting of commonly used cations such as pyrrolidinium, imidazolium, pyridinium, and ammonium. It also identified the importance of assessing the performance of quantum chemical methods for ionic liquids on a variety of cation-anion combinations.

Optimal Orbital Selection for Full Configuration Interaction (OptOrbFCI): Pursuing the Basis Set Limit under a Budget.

Full configuration interaction (FCI) solvers are limited to small basis sets due to their expensive computational costs. An optimal orbital selection for FCI (OptOrbFCI) is proposed to boost the power of existing FCI solvers to pursue the basis set limit under a computational budget. The optimization problem coincides with that of the complete active space SCF method (CASSCF), while OptOrbFCI is algorithmically quite different. OptOrbFCI effectively finds an optimal rotation matrix via solving a constrained optimization problem directly to compress the orbitals of large basis sets to one with a manageable size, conducts FCI calculations only on rotated orbital sets, and produces a variational ground-state energy and its wave function. Coupled with coordinate descent full configuration interaction (CDFCI), we demonstrate the efficiency and accuracy of the method on the carbon dimer and nitrogen dimer under basis sets up to cc-pV5Z. We also benchmark the binding curve of the nitrogen dimer under the cc-pVQZ basis set with 28 selected orbitals, which provide consistently lower ground-state energies than the FCI results under the cc-pVDZ basis set. The dissociation energy in this case is found to be of higher accuracy.

Static- and frequency-dependent NLO properties of dithienothiophene and thienothiophene bridges — A computational investigation

We have explored detailed linear and nonlinear optical properties of push-pull systems bearing thienothiophene and dithienothiophene spacers. By using density functional theory (DFT), frequency-dependent strategies were applied to examine the polarizability ([Formula: see text] and hyperpolarizability ([Formula: see text] and [Formula: see text]. The set of global and range-separated hybrid functionals with different Hartree–Fock (HF) exchange percentage at two basis sets cc-pVDZ and cc-pVTZ were used to evaluate the nonlinear optical (NLO) properties. The observed trends in the absorption maxima supported by perturbation potential analysis; as the absorption maxima increases, the respective amplitude potential decreases. For the investigated compounds, [Formula: see text]-conjugation along with the type of substituted acceptor plays a crucial role in the enhancement of NLO properties. The presence of acceptor group and length of conjugation increase between the D and A group; the first- and second-order intrinsic hyperpolarizability increases, leads to enhanced first- as well as second-order hyperpolarizability. Bond length alternation (BLA)/bond order alteration (BOA) exploration suggested that compounds attain cyanine limit. The trends in NLO properties for investigated compounds are supported by chemical reactivity descriptors, hardness and hyperhardness analysis. The polarizability is linearly correlated with the hyperpolarizability parameters ([Formula: see text] and [Formula: see text] and shows a good regression coefficient by figures of merit analysis.

Study of electronic structure, optoelectronics, linear and nonlinear optical properties and chemical descriptors of dibromodinitrofluorescein isomers in gasphase and solvent media using abinitio and DFT methods

In this work, we have studied the electronic structure, optoelectronics, linear and nonlinear optical properties of dibromodinitrofluorescein isomers in the gas phase and some solvents media using RHF and B3LYP levels of theory with a cc-pVDZ basis set. Our results suggest that solvent media have an effect on certain properties while some are unaffected. We have also determined the energy band gap and some other parameters like ionization potential, electron affinity, and molar refractivity. Finally, we have calculated the reactivity descriptors through some parameters including chemical hardness (η), chemical potential(μ), electrophilicity index(ω), softness (ϑ), electronegativity (EN), Fermi energy (EF), Electro accepting power (ω+), electron-donating power (ω−) and net electrophilicity Δω±, the reflectivity (R), optical frequencyωop, Max of Electron charge (ΔEMAX), Energy change (ΔE) and total Energy minimum(ΔEMIN) of the compounds. Due to the large ⟨α⟩, β, γ, E, P, χ, Ɛ, n, and D of these molecules, we think that these molecules have potential applications in the field of optoelectronics, such as optical communication, optical computing, optical switching, and dynamic image processing.

Effect of Substituents on the Energy Barrier of Internal Rotation in Aminonitroethylenes

Promising energetic materials 1,1-diamino-2,2-dinitroethylene (DADNE) and its derivatives in which one or both hydrogen atoms of the amino group are substituted by the NH2 or OH group were studied by quantum-chemical methods using PBE0 hybrid functional with the cc-pVDZ basis set and the coupled cluster method on the CCSD/aug-cc-pVDZ level. The thermal stability of such substances depends on the energy barrier of internal rotation Er around the C=C bond. The above-indicated substituents decrease Er . The value of Er is mainly determined by the structure of intramolecular hydrogen bonds. Introduction of the amino group leads to a more pronounced decrease in Er than introduction of the hydroxy group does.

Probing the bent bonds in cyclopropane systems for gas storage and separation process: A computational study.

The hydrogen, carbon dioxide, and carbon monoxide gas adsorption and storage capacity of lithium-decorated cyclopropane ring systems were examined with quantum chemical calculations at density functional theory, DFT M06-2X functional using 6-31G(d) and cc-pVDZ basis sets. To examine the reliability of M06-2X DFT functional, a few representative systems are also examined with complete basis set CBS-QB3 method and CCSD-aug-cc-pVTZ level of theory. The cyclopropane systems can bind to one Li+ ion; however, the corresponding the methylated systems can bind with two Li+ ions. The cyclopropane systems can adsorb six hydrogen molecules with an average binding energy of 3.8 kcal/mol. The binding free energy (ΔG) values suggest that the hydrogen adsorption process is feasible at 273.15 K. The calculation of desorption energies indicates the recyclable property of gas adsorbed complexes. The same number of CO2 and CO gas molecules can also be adsorbed with an average binding energy of -14.4 kcal/mol and -10.7 kcal/mol, respectively. The carbon dioxide showed ~3-4 kcal/mol better binding energy as compared to carbon monoxide and hence such designed systems can function as a potential candidate for the separation of these flue gas molecules. The nature of interactions in complexes was examined with atoms in molecules analysis revealed the electrostatic nature for the interaction of Li+ ion with cyclopropane rings. The chemical hardness and electrophilicity calculations showed that the gas adsorbed complexes are rigid and therefore robust as gas storage materials.

Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction

A new method for generating fitting grids for least-squares tensor hypercontraction (LS-THC) is presented. This method draws inspiration from the related interpolative separable density fitting (ISDF) technique, but uses only a pivoted Cholesky decomposition of the metric matrix, S, already computed as a matter of course in LS-THC. The size and quality of the resulting grid is controlled by a user-defined cutoff parameter and the size of the starting grid. Additionally, the Cholesky-based method provides an alternative and possible more numerically stable method for performing the least-squares fit. The quality of the grids produced is evaluated for LS-DF-THC-MP2 calculations on retinal and benzene, the former with a large starting grid and small cc-pVDZ basis set, and the latter with a wide range of grids and basis sets. The error and grid size is found to be well-controlled by either the cutoff parameter (with a large starting grid) or the starting grid size (with a tight cutoff) and highly predictable. The Cholesky-based method is also able to generate unique grids tailored to different charge distributions, for example the (ab|, (ai|, and (ij| distributions that arise in the molecular orbital integrals. While only the (ai| grid directly affects the MP2 energy, the relative sizes of the other grids are examined.

Excited-state photocycodimerization of 6-azauracil to oxazetidine cyclodimer: A mechanism elucidation in water surroundings

The crystal structure of 6-azauracil was proposed by the X-ray powder diffraction pattern of the compound. The packing of the molecules in the unit cell (number of molecules Z = 4) was investigated. A stacked dimer model was chosen from the unit cell for the subsequent theoretical investigation of the mechanism of cyclodimerization to oxazetidine cyclodimer. The mechanism of the transformation of the stacked dimer to oxazetidine cyclodimer through a conical intersection S0/S1 was proposed. The phototransformation occurs along the 1ππ* excited-state reaction path. The calculations were performed at the BLYP theoretical level (Becke-Lee-Yang-Parr functional) and the basis set cc-pVDZ in water surroundings, according to the polarized continuum model (PCM).

Cтруктурные и спектральные свойства хинолизидиновых nалкалоидов: квантово-химические расчеты

Structural and spectroscopic properties of quinolizidine alkaloids lupinine and epilupinine stereoisomers were studied theoretically. The influence of the calculation method and structural change in the molecule on the results of geometry and other properties of compounds was considered. The equilibrium geometry, harmonic vibrational frequencies and infrared intensities were obtained by means of density functional theory (DFT/B3LYP) calculations with the splitvalence medium-sized 6-31G(d) basis and Dunning’s correlation consistent basis set cc-pVDZ. From the optimized structure of the (+)-lupinine and (+)-epilupinine molecules, geometric parameters were compared with the literature X-ray experimental data. Structural and vibrational parameters for the (-)-lupinine and (-)-epilupinine molecules are predicted by theoretical calculations at B3LYP/6-31G(d) and B3LYP/cc-pVDZ levels of theory. Some physical characteristics for the title compounds, such as total electronic energy, zero-point energy, rotational constants and dipole moments were also defined by DFT methods. The thermodynamic functions of the title compounds were performed at the same theory levels. Stationary points are identified by the solution of the oscillatory problem.

Computational investigation on the reaction of dimethyl ether with nitric dioxide. I. Underlying mechanism and accurate energetics

The reaction of dimethyl ether (DME) with nitrogen dioxide (NO2), which plays a critical role in the low-temperature oxidation behavior of DME, is employed as prototype for reactions of heavier clean ether fuels to assess different hybrid density functionals and “double-hybrid” density functionals. The reaction energies and barrier heights for the reaction system were computed with CCSD(T) theory extrapolated to the complete basis set limit using augmented cc-pVDZ and cc-pVTZ basis sets. The involved energetics were also improved by the CCSD(T)/6-311+G(2df,2p), QCISD(T)/6-311+G(2df,2p), G3B3, G3MP2B3, CBS-QB3, G4, and G4MP2 calculations. It is shown that “double-hybrid” density functionals with the TZVP basis set can give accurate geometries and principal moments of inertia of reactants and products and the B2PLYP/TZVP level can achieve results for barrier heights comparable in accuracy to the high-level ab initio results, which is identified as an important potential theoretical level for direct kinetics studies on the rates of these and homologous reaction systems. The calculated results indicate that NO2 preferentially captures an out-of-plane hydrogen atom from the DME molecule by the O or the N end via three distinct channels to produce trans-HONO, cis-HONO, and HNO2, respectively, and each channel involves the formation of a van der Waals post-reaction adducts lying lower in energy than their separate products.

Highly Accurate CCSDT(Q)/CBS Reaction Barrier Heights for a Diverse Set of Transition Structures: Basis Set Convergence and Cost-Effective Approaches for Estimating Post-CCSD(T) Contributions.

The ability to accurately calculate reaction barrier heights is of central importance to many areas of chemistry. We report an extensive study examining the basis set convergence of post-CCSD(T) contributions (up to CCSDT(Q)) for a diverse set of 28 reaction barrier heights. In contrast to previous studies, we focus here on larger transition structures (TSs) involving 4-7 non-hydrogen atoms. The set of reaction barrier heights includes pericyclic, bipolar cycloaddition, cycloreversion, and multiple-proton transfer reactions. We find that in most cases post-CCSD(T) contributions converge rapidly toward the basis set limit, such that even double-ζ and truncated double-ζ basis sets provide useful estimates of the T-(T) and (Q) contributions, respectively. In addition, we find that due to the tendency of these small basis sets to systematically underestimate the T-(T) and (Q) components, scaling is an effective approach for improving performance. For example, scaling the T-(T)/cc-pVDZ contribution by 1.25 results in an RMSD of merely 0.4 kJ mol-1 relative to basis set limit reference values from W3lite-F12 theory. Similarly, calculating the (Q) contribution with a cc-pVDZ basis set without d functions and scaling by 1.6 results in an RMSD of 0.5 kJ mol-1. We also examine the magnitude of post-CCSD(T) contributions for a wide range of TSs. We find that for pericyclic, bipolar cycloaddition, and multiple-proton transfer reactions there is an effective cancellation between the T-(T) and (Q) components (i.e., they have opposite signs and are of similar magnitude), such that overall post-CCSD(T) contributions to the reaction barrier heights are below ∼1 kJ mol-1 (in absolute value). However, for the barrier heights of cycloreversion reactions, the T-(T) and (Q) components are both negative and large and consequentially post-CCSD(T) contributions reduce the reaction barrier heights by significant amounts ranging between 4.1 and 6.7 kJ mol-1.

Photo-Transformation Trajectories of Nitro-Spiropyran in Hybrid Compounds with [60]Fullerene

Photo- and thermo- isomerization trajectories of various conversion pathways between nitro-spiropyran and its trans–trans–cis merocyanine form were produced and the role of nπ* states was investigated along the corresponding potential energy surface calculated using the ωB97XD functional and the cc-pVDZ basis set. The nondissociative nπ* states on the photoisomerization trajectories can switch from/to the dissociative photoactive ππ* state at two intersections between their energy surfaces. The photochromic properties inherited in hybrid compounds of nitro-spiropyran-containing [60]fullerene are interpreted due to a reversible “dual energy bypass” ππ*↔nπ* mechanism in terms of both adiabatic absorption and highly effective nonadiabatic dissipative transitions between the excited states of the photochromic fragment, that prevents energy loss through the [60]fullerene and in this way keeps the photochromic properties intact.

Dependence of the virial exciton model on basis set and exact-exchange fraction.

The exchange-only (uncorrelated) singlet-triplet energy difference in one-electron excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. A nonempirical, virial-theorem argument was presented by Becke [J. Chem. Phys. 148, 044112 (2018)] that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gave HOMO-LUMO singlet excitation energies in small-molecule benchmark sets as good as the popular TD-B3LYP time-dependent approach to excited states. In a subsequent application to long-chain polyenes approaching the polyacetylene limit [A. D. Becke, J. Chem. Phys. 149, 081102 (2018)], we found a dramatic dependence of the optical gap on the amount of exact exchange in the density functionals used to generate the orbitals. Here, we assess the effect of the exact-exchange fraction in standard small-molecule tests. Also, we assess two basis-set extremes: the highly practical cc-pVDZ basis set and the higher-quality aug-cc-pVTZ.

Improving efficiency of semi‐direct møller–plesset second‐order perturbation methods through oversubscription on multiple nodes

The purpose of this work is to evaluate the efficacy of oversubscription, at the 1n, 2n, and 3n levels for n physical cores, on semi-direct MP2 methods within NWChem when using two and three Intel nodes. Semi-direct MP2 energy and gradient calculations were performed on chemical systems ranging from 824 to 1626 basis functions using the cc-pVDZ basis set. Wall times for semi-direct MP2 energies were reduced by as much as 36% using two nodes and 44% using three nodes compared to no oversubscription. Total energy consumed by the CPU and DRAM was also reduced by as much as 12% using two nodes and as much as 20% using three nodes when oversubscribing. MP2 gradient wall times improved by as much as 16% using two nodes and 18% using three nodes compared to execution at the 1n level; however, energy savings were insignificant. Intel performance-counter data show a strong correlation between total wall time saved and less time spent in the idle state, indicating a more efficient use of the processors when oversubscribing. © 2019 Wiley Periodicals, Inc.

Quantum computational study of non-linear optical properties of some phenanthrene derivatives.

Non-linear optical (NLO) behavior of some phenanthrene-based organic molecules is studied using quantum computational MP2 and B3LYP methods with cc-pVDZ basis set. The design of these molecules is based on possible intramolecular charge transfer between electron donor and electron acceptor groups via an aromatic bridge. The -NO2, -CN, -CF3, -C(CF3)C(CF3)2, -SO3H and -C(CN)C(CN)2 acceptors and the -NH2, -N(CH3)2 and pyrrolidinyl donors have been considered. The HOMO and LUMO energies, polarizabilities and first hyperpolarizabilities are calculated for the optimized structures both in the gas phase and in the conductor-like polarizable continuum model (CPCM) of different solvents. Moreover, the energies of the vertical transitions in the UV-Vis range having large oscillator strengths and their corresponding adiabatic transition energies are calculated using TD-DFT-B3LYP/cc-pVDZ method. Also, UV-Vis and infrared spectra are simulated for these designed molecules. Results show that these phenanthrene derivatives have generally very good NLO behavior. Also, NLO properties are enhanced when (-C(CN)C(CN)2 & -NH2) and (-NO2 & pyrrolidinyl) pairs of (acceptor & donor) groups are used. The approach adopted in the present quantum computational study can be used for similar studies for better description and understanding of the NLO responses of the electron donor-bridge-acceptor systems with π-conjugated bridges.

Analytical Energy Gradients for the Cluster-in-Molecule MP2 Method and Its Application to Geometry Optimizations of Large Systems.

An efficient analytical energy gradient algorithm for the cluster-in-molecule (CIM) second order Møller-Plesset perturbation theory (MP2) method is presented. In our algorithm, the gradient contributions from the nonseparable term of the two-body density matrix on a given atom is extracted from calculations on a cluster constructed for this atom. The other terms in the CIM-MP2 energy gradient expression are evaluated by constructing the density matrices of the whole system with the contributions from all clusters constructed. For basis sets with diffuse functions, tight CIM parameters are necessary to obtain accurate gradients. Benchmark calculations show that the CIM-MP2 method can accurately reproduce the conventional MP2 gradients and geometries for larger systems. The optimized structure of a 174-atom oligopeptide using the CIM-MP2 method with the cc-pVDZ basis set is in good agreement with the corresponding crystal structure. The present CIM-MP2 gradient program can be used for optimizing the geometries of large systems with hundreds of atoms on ordinary workstations.