Basis Set Size Research Articles

Prediction of the standard potentials for one-electron oxidation of N,N,N',N' tetrasubstituted p-phenylenediamines by calculation.

The formal potentials for the reversible one-electron oxidation of N,N,N',N' tetrasubstituted p-phenylenediamines in acetonitrile have been applied as a test set for benchmarking computational methods for a series of compounds with only small structural differences. The aim of the study is to propose a simple method for calculating the standard oxidation potentials, and therefore, the protocol is progressively developed by adding more terms in the energy expression. In addition, the effect of including implicit solvation models (IEFPCM, CPCM, and SMD), larger basis sets, and correlation methods are investigated. The oxidation potentials calculated using the G3MP2B3 approach with IEFPCM resulted in the best fit (R2 = 0.9624), but the slope of the correlation line, 0.74, is far from the optimal value, 1.00. B3LYP/6-311++G(d,p) and TPSSh/6-311++G(2d,p) yielded only slightly less consistent data (R2 = 0.9388 and R2 = 0.9425), but with much better slopes, 1.00 and 0.94, respectively. We conclude that it is important to investigate the basis set size and treatment of electron correlation when calculating oxidation potentials for N,N,N',N' tetrasubstituted p-phenylenediamines.

Equation of state of atomic solid hydrogen by stochastic many-body wave function methods.

We report a numerical study of the equation of state of crystalline body-centered-cubic (BCC) hydrogen, tackled with a variety of complementary many-body wave function methods. These include continuum stochastic techniques of fixed-node diffusion and variational quantum Monte Carlo and the Hilbert space stochastic method of full configuration-interaction quantum Monte Carlo. In addition, periodic coupled-cluster methods were also employed. Each of these methods is underpinned with different strengths and approximations, but their combination in order to perform reliable extrapolation to complete basis set and supercell size limits gives confidence in the final results. The methods were found to be in good agreement for equilibrium cell volumes for the system in the BCC phase.

Gas-Phase Thermochemistry of MX3 and M2X6 (M = Sc, Y; X = F, Cl, Br, I) from a Composite Reaction-Based Approach: Homolytic versus Heterolytic Cleavage.

A domain-based local-pair natural-orbital coupled-cluster approach with single, double, and improved linear-scaling perturbative triple correction via an iterative algorithm, DLPNO-CCSD(T1), was applied within the framework of the Feller-Peterson-Dixon approach to derive gas-phase heats of formation of scandium and yttrium trihalides and their dimers via a set of homolytic and heterolytic dissociation reactions. All predicted heats of formation moderately depend on the reaction type with the most and least negative values obtained for homolytic and heterolytic dissociation, respectively. The basis set size dependence, as well as the influence of static correlation effects not covered by the standard (DLPNO-)CCSD(T) approach, suggests that exploitation of the heterolytic dissociation reactions with the formation of M3+ and X- ions leads to the most robust heats of formation. The gas-phase formation enthalpies ΔHf°(0 K)/ΔHf°(298.15 K) and absolute entropies S°(298.15 K) were obtained for the first time for the Sc2F6, Sc2Br6, and Sc2I6 species. For ScBr3, ScI3, Sc2Cl6, and Y2Cl6, we suggest a reexamination of the experimental heats of formation available in the literature. For other compounds, the predicted values were found to be in good agreement with the experimental estimates. Extracted MX3 (M = Sc, Y; X = F, Cl, Br, and I) 0 K atomization enthalpies indicate weaker bonding when moving from fluorine to iodine and from yttrium to scandium. Likewise, the stability of yttrium trihalide dimers degrades when going from fluorine to iodine. Respective scandium trihalide dimers are less stable, with 0 K dimer dissociation energy decreasing in the row fluorine - chlorine - bromine ≈ iodine. Correlation of the (n - 1)s2p6 electrons on bromine and iodine, inclusion of zero-point energy, relativistic effects, and the effective-core-potential correction as well as amelioration of the DLPNO localization inaccuracy are shown to be of similar magnitude, which is critical if accurate heats of formation are a goal.

Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets.

We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller-Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn-Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn-Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.

Eight-Dimensional Wave Packet Dynamics Within the Quantum Transition-State Framework: State-to-State Reactive Scattering for H2 + CH3 ⇆ H + CH4.

The present work investigates the calculation of S-matrix elements for six-atom reactions combining reduced-dimensional wave packet dynamics and the quantum transition-state framework. We employ the eight-dimensional (8D) model Hamiltonian developed by Palma and Clary [J. Chem. Phys. 2000, 112, 1859-1867] and reduce basis set sizes as well as the number of wave packets by exploiting space inversion and permutation symmetry. Mode-specific chemistry in the H2 + CH3 ⇆ H + CH4 reaction is studied with full quantum-state resolution. Results for the H + CH4 reaction are compared to full-dimensional benchmark results. Detailed state-to-state results for the H2 + CH3 reaction are presented for the first time. Although the "loss of memory" effect dominates for total energies up to 0.6 eV, more complex patterns emerge at higher energies. The agreement between the present reduced-dimensional and the accurate full-dimensional results is generally good. However, shortcomings in the reduced-dimensional model can also be noted. They are related to the description of the symmetric and asymmetric C-H stretch motion in the CH4 molecule.

Atomic and ionic polarizabilities of B, C, N, O, and F

AbstractAccurate polarizabilities of atoms and molecules are critical in the treatment of optical and dielectric properties, in the modeling and interpretation of intermolecular interactions, in scattering processes, and in chemical reactivity. In this work we provide a systematic study of the atomic/ionic static dipole polarizabilities of the first‐row elements: B+, B, B−, C2+, C+, C, C−, N2+, N+, N, O2+, O+, O, O−, F2+, F+, F, and F−. We used the CCSD(T) method with a range of large correlation‐consistent basis sets augmented with a series of diffusion functions (x‐aug‐cc‐pVXZ). We discuss the trends in the dependence of dipole polarizability from the basis set size and/or number of diffuse functions and report the recommended values of average dipole polarizabilities for this series. The systematic survey of dipole polarizabilities for ions from boron to fluorine, including the extrapolation to complete basis set limit, is presented for the first time.

Extended Second-Order Multireference Algebraic Diagrammatic Construction Theory for Charged Excitations.

We report a new implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulations of electron attachment and ionization in strongly correlated molecular systems (EA/IP-MR-ADC). Following our recent work on IP-MR-ADC [J. Chem. Theory Comput. 2019, 15, 5908], we present the first implementation of the second-order MR-ADC method for electron attachment (EA-MR-ADC(2)) and two extended second-order approximations (EA- and IP-MR-ADC(2)-X) that incorporate a partial treatment of third-order electron correlation effects. Introducing a small approximation for the second-order amplitudes of the effective Hamiltonian, our implementation of EA- and IP-MR-ADC(2)-X has a low computational scaling with the basis set size M. Additionally, we describe an efficient algorithm for solving the first-order amplitude equations in MR-ADC and partially contracted second-order N-electron valence perturbation theory (NEVPT2) which completely avoids computation of the four-particle reduced density matrices without introducing any approximations or imaginary-time propagation. For a benchmark set of eight small molecules, a carbon dimer, and a twisted ethylene, we demonstrate that EA- and IP-MR-ADC(2)-X achieve an accuracy similar to that of strongly contracted NEVPT2 while having a lower computational scaling with the active space size and providing efficient access to transition properties.

Experimentally Established Benchmark Calculations of 31P NMR Quantities

AbstractThe accuracy of different density function theory functionals and the MP2 approximation in 31P NMR calculations has been evaluated for ten phosphorous containing molecules in which the phosphorous atoms are not involved in intermolecular interactions. The obtained absolute chemical shielding tensors are compared to experimental ones. The dependence of the numerical values on the size of basis sets has been inspected from the 6‐311G(2d,p) to the pcSseg‐3 basis sets. General recommendations on the most reliable functionals and the smallest possible size of a basis set have been reported. For example, the use of the M06 L functional should be avoided. For five polycrystalline samples, the conformation of molecules has been identified with a high precision. These structures have been used to determine the reference values of the absolute chemical shielding for the TPSSh, B3LYP, and ωB97XD functionals and different basis sets. As reported in the supporting information, these structures can be used to determine the reference value of the absolute chemical shielding for any approximation of interest.

Diagrammatic Monte Carlo method for impurity models with general interactions and hybridizations

We present a diagrammatic Monte Carlo method for quantum impurity problems with general interactions and general hybridization functions. Our method uses a recursive determinant scheme to sample diagrams for the scattering amplitude. Unlike in other methods for general impurity problems, an approximation of the continuous hybridization function by a finite number of bath states is not needed, and accessing low temperature does not incur an exponential cost. We test the method for the example of molecular systems, where we systematically vary temperature, interatomic distance, and basis set size. We further apply the method to an impurity problem generated by a self-energy embedding calculation of correlated antiferromagnetic NiO. We find that the method is ideal for quantum impurity problems with a large number of orbitals but only moderate correlations.

Crystal and geometry-optimized structure of an anthracene-based Diels-Alder adduct.

Computational calculations of an anthracene-based Diels-Alder adduct, namely, 17-ethyl-1-hydroxymethyl-17-azapentacyclo[6.6.5.02,7.09,14.015,19]nonadeca-2,4,6,9,11,13-hexaene-16,18-dione, C21H19NO3, predicting density functional theory (DFT) optimized geometries in the gas phase are compared in terms of accuracy relative to the solid-state crystal structure and computational cost. Crystal structure determination and Hirshfeld surface analysis of the racemic product reveal that the molecules are linked by O-H...O=C hydrogen bonds between the hydroxy and carbonyl groups, accounting for 9.5% of the intermolecular contacts, while H...H contacts represent 56.9% of the total. Boltzmann population analysis of computed relative rotamer abundances in the gas phase are based on lower-level geometry optimization and thermochemical corrections coupled with higher-level electronic energy calculations using the B2PLYP double-hybrid functional. As expected, the choice of density functional has a greater effect than the basis set on accuracy for all levels of theory. For any given functional, increasing the basis set size did not always correlate with increasingly accurate structures. The hybrid functional B3LYP without dispersion correction routinely gave the closest approximations to the crystal structure where the B3LYP/aug-cc-pVDZ combination afforded the best structure (r.m.s. deviation= 0.1314 Å). However, the B3LYP/6-31+G(d,p) level of theory represents the best compromise between accuracy (r.m.s. deviation = 0.1388 Å) and cost as it yielded appreciably accurate results in a fraction of the time compared to other method combinations.

Local energy decomposition of coupled‐cluster interaction energies: Interpretation, benchmarks, and comparison with symmetry‐adapted perturbation theory

AbstractLocal energy decomposition analysis provides a breakdown of the domain‐based local pair natural orbital CCSD(T) [DLPNO‐CCSD(T)] energy into additive contributions representing the interaction between pairs of user‐defined fragments. Each of these fragment‐pairwise components can be further decomposed into a sum of physically meaningful terms, such as electrostatics, dispersion, and exchange. In this study, the dependence of such energy terms on the basis set size, the approximations used for the two‐electron integrals, and the localization scheme used for the virtual orbitals have been carefully evaluated on the interaction energies of the S66 benchmark set. A comparison with the energy components obtained at the SAPT2 + (3)δMP2 level of Symmetry‐Adapted Perturbation Theory is also provided.

Exciton g factors of van der Waals heterostructures from first-principles calculations

External fields are a powerful tool to probe optical excitations in a material. The linear energy shift of an excitation in a magnetic field is quantified by its effective g-factor. Here we show how exciton g-factors and their sign can be determined by converged first principles calculations. We apply the method to monolayer excitons in semiconducting transition metal dichalcogenides and to interlayer excitons in MoSe$_2$/WSe$_2$ heterobilayers and obtain good agreement with recent experimental data. The precision of our method allows to assign measured g-factors of optical peaks to specific transitions in the band structure and also to specific regions of the samples. This revealed the nature of various, previously measured interlayer exciton peaks. We further show that, due to specific optical selection rules, g-factors in van der Waals heterostructures are strongly spin- and stacking-dependent. The calculation of orbital angular momenta requires the summation over hundreds of bands, indicating that for the considered two-dimensional materials the basis set size is a critical numerical issue. The presented approach can potentially be applied to a wide variety of semiconductors.

The pseudoatomic orbital basis: electronic accuracy and soft-mode distortions in ABO3 perovskites

The perovskite oxides are known to be susceptible to structural distortions over a long wavelength when compared to their parent cubic structures. From an ab initio simulation perspective, this requires accurate calculations including many thousands of atoms; a task well beyond the remit of traditional plane wave-based density functional theory (DFT). We suggest that this void can be filled using the methodology implemented in the large-scale DFT code, CONQUEST, using a local pseudoatomic orbital (PAO) basis. Whilst this basis has been tested before for some structural and energetic properties, none have treated the most fundamental quantity to the theory, the charge density n(r) itself. An accurate description of n(r) is vital to the perovskite oxides due to the crucial role played by short-range restoring forces (characterised by bond covalency) and long range Coulomb forces as suggested by the soft-mode theory of Cochran and Anderson. We find that modestly sized basis sets of PAOs can reproduce the plane-wave charge density to a total integrated error of better than 0.5% and provide Bader partitioned ionic charges, volumes and average charge densities to similar degree of accuracy. Further, the multi-mode antiferroelectric distortion of PbZrO3 and its associated energetics are reproduced by better than 99% when compared to plane-waves. This work suggests that electronic structure calculations using efficient and compact basis sets of pseudoatomic orbitals can achieve the same accuracy as high cutoff energy plane-wave calculations. When paired with the CONQUEST code, calculations with high electronic and structural accuracy can now be performed on many thousands of atoms, even on systems as delicate as the perovskite oxides.

First-principles study on the structure and optical spectroscopy of the redox-active center of blue copper proteins

We present first-principles calculations on the geometrical structures and optical absorption properties of redox-active centers in two types of blue copper proteins, plastocyanin (Pc) and pseudoazurin (PAz). Two four-coordination (4C) cluster models consisting 111-atom were constructed based on the crystal structures of the two proteins. The optimized configurations of the proposed models took on highly identical geometry as the crystal structures and the calculated absorption spectra of both models acceptably reproduced the corresponding experimental spectra. Based on spectral simulations, we were able to confirm the indispensable role of axial ligand methionine (Met) in both proteins. The difference in the absorption spectroscopy of the two types of proteins was caused by the changes to the ground state wave functions which originate mainly from the different coordination structures of the redox-active center, especially the different Cu-SMet bond lengths. The effects of density functionals and the size of basis sets were also tested.

Accelerating Auxiliary-Field Quantum Monte Carlo Simulations of Solids with Graphical Processing Units.

We outline how auxiliary-field quantum Monte Carlo (AFQMC) can leverage graphical processing units (GPUs) to accelerate the simulation of solid state systems. By exploiting conservation of crystal momentum in the one- and two-electron integrals, we show how to efficiently formulate the algorithm to best utilize current GPU architectures. We provide a detailed description of different optimization strategies and profile our implementation relative to standard approaches, demonstrating a factor of 40 speedup over a CPU implementation. With this increase in computational power, we demonstrate the ability of AFQMC to systematically converge solid state calculations with respect to basis set and system size by computing the cohesive energy of carbon in the diamond structure to within 0.02 eV of the experimental result.

Efficient two-electron ansatz for benchmarking quantum chemistry on a quantum computer

Quantum chemistry provides key applications for near-term quantum computing, but these are greatly complicated by the presence of noise. In this work we present an efficient ansatz for the computation of two-electron atoms and molecules within a hybrid quantum-classical algorithm. The ansatz exploits the fundamental structure of the two-electron system, and treating the nonlocal and local degrees of freedom on the quantum and classical computers, respectively. Here the nonlocal degrees of freedom scale linearly with respect to basis-set size, giving a linear ansatz with only $\mathcal{O}(1)$ circuit preparations required for reduced state tomography. We implement this benchmark with error mitigation on two publicly available quantum computers, calculating accurate dissociation curves for 4- and 6- qubit calculations of ${\rm H}_\textrm{2}^{}$ and ${\rm H}_\textrm{3}^+$.

Plane wave basis set correction methods for RPA correlation energies.

Electronic correlation energies from the random-phase approximation converge slowly with respect to the plane wave basis set size. We study the conditions under which a short-range local density functional can be used to account for the basis set incompleteness error. Furthermore, we propose a one-shot extrapolation scheme based on the Lindhard response function of the homogeneous electron gas. The different basis set correction methods are used to calculate equilibrium lattice constants for prototypical solids of different bonding types.

Performance of TDDFT Vertical Excitation Energies of Core-Substituted Naphthalene Diimides.

We have evaluated the performance of various density functionals, covering generalized gradient approximation (GGA), global hybrid (GH) and range‐separated hybrid (RSH), using time dependent density functional theory (TDDFT) for computing vertical excitation energies against experimental absorption maximum (λmax) for a set of 10 different core‐substituted naphthalene diimides (cNDI) recorded in dichloromethane. The computed excitation in case of GH PBE0 is most accurate while the trend is most systematic with RSH LCY‐BLYP compared to λmax. We highlight the importance of including solvent effects for optimal agreement with the λmax. Increasing the basis set size from TZ2P to QZ4P has a negligible influence on the computed excitation energies. Notably, RSH CAMY‐B3LYP gave the least error for charge‐transfer excitation. The poorest agreement with λmax is obtained with semi‐local GGA functionals. Use of the optimally‐tuned RSH LCY‐BLYP* is not recommended because of the high computational cost and marginal improvement in results.

Noncovalent interactions in crowded olefinic radical cations

Aim. To study the effect of electronic (α- and β-hyperconjugations) and steric (noncovalent interactions) factors on the structures of olefinic radical cations.Results and discussion. The effect of intramolecular dispersion interactions on the structures of crowded alkenes in the neutral and ionized forms has been studied at the density functional theory (DFT) level with and without dispersion corrections included, as well as at the MP2 theory level with medium size basis sets. The results obtained are compared to the available experimental data. An excellent agreement has been found between the experimental and MP2/DFT-computed geometries of sesquihomoadamantene, adamantylidene adamantane, bis-2,2,5,5-tetramethylcyclopentylidene, bis-D3-homocub-4-ylidene, and bis-CS-homocub-8-ylidene in the neutral and ionized forms. The experimental ionization potentials are better reproduced with the DFT-methods.Experimental part. The structure and composition of compounds were proved by the methods of 1H and 13C NMR-spectroscopy, and GC-MS-analysis. Elemental analysis was performed for the compounds obtained.Conclusions. The twisting of the olefinic moieties in the sesquihomoadamantene and adamantylidene adamantane radical cations is determined by the balance between the σ-π-hyperconjugation and residual one-electron π-bonding and is close to that of the prototypical ethylene radical cation (29°). The twisting reaches 55° for the bis-2,2,5,5-tetramethylcyclopentylidene radical cation due to substantial steric repulsions between methyl groups. At the same time, the ionized states of bis-D3-homocub-4-ylidene and bis-CS-homocub-8-ylidene retain their planarity due to β-CC-hyperconjugation and intramolecular dispersion attractions. Received: 26.12.2019Revised: 17.01.2020Accepted: 27.02.2020

Hierarchical equations of motion method based on Fano spectrum decomposition for low temperature environments.

The hierarchical equations of motion (HEOM) method has become one of the most popular methods for the studies of the open quantum system. However, its applicability to systems at ultra-low temperatures is largely restrained by the enormous computational cost, which is caused by the numerous exponential functions required to accurately characterize the non-Markovian memory of the reservoir environment. To overcome this problem, a Fano spectrum decomposition (FSD) scheme has been proposed recently [Cui et al., J. Chem. Phys. 151, 024110 (2019)], which expands the reservoir correlation functions using polynomial-exponential functions and hence greatly reduces the size of the memory basis set. In this work, we explicitly establish the FSD-based HEOM formalisms for both bosonic and fermionic environments. The accuracy and efficiency of the FSD-based HEOM are exemplified by the calculated low-temperature dissipative dynamics of a spin-boson model and the dynamic and static properties of a single-orbital Anderson impurity model in the Kondo regime. The encouraging numerical results highlight the practicality and usefulness of the FSD-based HEOM method for general open systems at ultra-low temperatures.