Traditional Basis Sets Research Articles

How the Exchange Energy Can Affect the Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit.

Finite size error is commonly removed from coupled cluster theory calculations by N-1 extrapolations over correlation energy calculations of different system sizes (N), where the N-1 scaling comes from the total energy rather than the correlation energy. However, previous studies in the quantum Monte Carlo community suggest an exchange-energy-like power law of N-2/3 should also be present in the correlation energy when using the conventional Coulomb interaction. The rationale for this is that the total energy goes as N-1 and the exchange energy goes as N-2/3; thus, the correlation energy should be a combination of these two power laws. Further, in coupled cluster theory, these power laws are related to the low G scaling of the transition structure factor, S(G), which is a property of the coupled cluster wave function calculated from the amplitudes. We show here that data from coupled cluster doubles calculations on the uniform electron gas fit a function with a low G behavior of S(G) ∼ G. The prefactor for this linear term is derived from the exchange energy to be consistent with an N-2/3 power law at large N. Incorporating the exchange structure factor into the transition structure factor results in a combined structure factor of S(G) ∼ G2, consistent with an N-1 scaling of the exchange-correlation energy. We then look for the presence of an N-2/3 power law in the energy. To do so, we first develop a plane-wave cutoff scheme with less noise than the traditional basis set used for the uniform electron gas. Then, we collect data from a wide range of electron numbers and densities to systematically test five methods using N-1 scaling, N-2/3 scaling, or combinations of both scaling behaviors. We find that power laws that incorporate both N-1 and N-2/3 scaling perform better than either alone, especially when the prefactor for N-2/3 scaling can be found from exchange energy calculations.

A Comparison of Medium-Sized Basis Sets for the Prediction of Geometries, Vibrational Frequencies, Infrared Intensities and Raman Activities for Water

Optimized geometries, vibrational frequencies, as well as infrared intensities and Raman activities were calculated for water (H2O) utilizing popular quantum mechanical approaches. Here, density functional theory (DFT) calculations were performed using the B3LYP (Becke, three-parameter, Lee-Yang-Parr) functional, as well as ab initio calculations using second-order Møller-Plesset (MP2) perturbation theory and coupled-cluster with single, double and perturbative triple excitations [CCSD(T)] levels of theory were used. We assess and benchmark the performance of 69 different atomic orbital basis sets including various popular families of medium-sized basis sets typically of two to four zeta quality and differing levels of augmentation by polar and diffuse functions. The basis sets range from the commonly adopted Pople-style (6-31G & 6-311G), Dunning’s correlation consistent (cc-pV(n+d)Z & aug-cc-pV(n+d)Z, as well as Truhlar’s calendar variations, Jensen’s polarization consistent (pc-n & aug-pc-n), Ahlrichs (def2-…), Sapporo’s and Karlsruches as well as atomic natural orbitals (ANOs) such as NASA Ames (ANOn), Neese-style, and Roos-style. We also compare several basis sets specifically designed to calculate vibrational and electronic properties, including the Sadlej-pVTZ (and LPol-X families), as well as SNS families of Barone. The results are compared to experimental values where available, or calculations performed with 5 or 6 zeta-level (e.g., cc-pV6Z). The performance of each family of basis sets is discussed in terms of their accuracy (and pitfalls), as well as computational resource scaling and efficiency. The Def2 basis family performs very well overall, yielding more accurate results with lower runtimes than traditional basis sets. ‘May’ basis sets also provide accurate predictions of vibrational frequencies at significantly lower costs. Raman activities can be accurately calculated using MP2 under harmonic approximation with several ‘spectroscopic’ families performing well.

Optimal basis sets for CBS extrapolation of the correlation energy: oV x Z and oV(x+d)Z

We seek correlation consistent double- and triple-zeta basis sets that perform optimally for extrapolating the correlation energy to the one-electron complete basis set limit. Since the methods used are approximate, the novel basis sets become method specific in the sense of performing best for the chosen level of theory. Such basis sets are also shown to perform accurately for tensorial properties and do not significantly alter the Hartree-Fock energy. Quantitatively, the extrapolated correlation energies from (oVdZ, oVtZ) outperform typically by three- to fivefold those obtained from traditional ansatzes with similar flexibility, thus being (VtZ, VqZ) type or even better. They may even outperform explicitly correlated ones. Not surprisingly, the outperformance in relative energies (e.g., atomization and dissociation energies, and ionization potential) is somewhat downscaled, albeit consistently better than with traditional basis sets. As a case study, we also consider the polarizability of p-nitroaniline, a sizeable system for which complete basis set (CBS)(oVdZ, oVtZ) calculations are shown to outperform equally expensive CBS(VdZ, VtZ) results.

Importance of the ligand basis set in ab initio thermochemical calculations of transition metal species

The impact of basis set choice has been considered for a series of transition metal (TM) species. The need for higher level correlation consistent basis sets on both the metal and ligand has been investigated, and permutations in the pairings of basis set used for TM’s and basis set used for ligands can lead to effective routes to complete basis set (CBS) limit extrapolations of thermochemical energetics with little change in thermochemical predictions as compared to those resulting from the use of traditional basis set pairings, while enabling computational cost savings. Basis set superposition errors (BSSE) that can arise have also been considered.

Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved.

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

Laser-induced nuclear magnetic resonance splitting in hydrocarbons

Irradiation of matter with circularly polarized light (CPL) shifts all nuclear magnetic resonance (NMR) lines. The phenomenon arises from the second-order interaction of the electron cloud with the optical field, combined with the orbital hyperfine interaction. The shift occurs in opposite directions for right and left CPL, and rapid switching between them will split the resonance lines into two. We present ab initio and density functional theory predictions of laser-induced NMR splittings for hydrocarbon systems with different sizes: ethene, benzene, coronene, fullerene, and circumcoronene. Due to the computationally challenging nature of the effect, traditional basis sets could not be used for the larger systems. A novel method for generating basis sets, mathematical completeness optimization, was employed. As expected, the magnitude of the spectral splitting increases with the laser beam frequency and polarizability of the system. Massive amplification of the effect is also observed close to the optical excitation energies. A much larger laser-induced splitting is found for the largest of the present molecules than for the previously investigated noble gas atoms or small molecules. The laser intensity required for experimental detection of the effect is discussed.

Basis set approach to the quantum dissipative dynamics: Application of the multiconfiguration time-dependent Hartree method to the spin-boson problem

The feasibility of using a basis set approach to the study of quantum dissipative dynamics is investigated for the spin-boson model, a system of two discrete states linearly coupled to a harmonic bath. The infinite Hamiltonian is discretized to a finite number of degrees of freedom. Traditional basis set approach, in a multiconfiguration time-dependent Hartree context, is used to solve the time-dependent Schrödinger equations by explicitly including all the degrees of freedom (“system”+“bath”). Quantities such as the reduced density matrix are then evaluated via a quadrature summation/Monte Carlo procedure over a certain number of time-dependent wave functions. Numerically exact results are obtained by systematically increasing the number of bath modes used to represent the condensed phase environment, as well as other variational parameters (number of basis functions, configurations, etc.). The potential of the current method is briefly discussed.