The Molecular Sciences Software Institute

Talk given by T. Daniel Crawford at the 2017 NSF SI2 PI meeting on the Molecular Sciences Software Institute (MolSSI)

Basis Set Superposition Errors in the Many-Body Expansion of Molecular Properties

The underlying reasons for the poor convergence of the venerated many-body expansion (MBE) for higher-order response properties are investigated, with a particular focus on the impact of basis set superposition errors. Interaction energies, dipole moments, dynamic polarizabilities, and specific rotations are computed for three chiral solutes in explicit water cages of varying sizes using the MBE including corrections based on the site–site function counterpoise (or “full-cluster” basis) approach. In addition, we consider other possible causes for the observed oscillatory behavior of the MBE, including numerical precision, basis set size, choice of density functional, and snapshot geometry. Our results indicate that counterpoise corrections are necessary for damping oscillations and achieving reasonable convergence of the MBE for higher order properties. However, oscillations in the expansion cannot be completely eliminated for chiroptical properties such as specific rotations due to their inherently nonadditive nature, thus limiting the efficacy of the MBE for studying solvated chiral compounds

Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory

The frozen-virtual natural-orbital (NO) approach, whereby the unoccupied-orbital space is constructed using a correlated density such as that from many-body perturbation theory, has proven to yield compact wave functions for determining ground-state correlation energies and associated properties, with corresponding occupation numbers providing a guide to the truncation of the virtual space. In this work this approach is tested for the first time for the calculation of higher-order response properties, particularly frequency-dependent dipole polarizabilities using coupled-cluster theory. We find that such properties are much more sensitive to the truncation of virtual space in the NO basis than in the original canonical molecular orbital (CMO) basis, with truncation errors increasing linearly with respect to the number of frozen virtual NOs. The reasons behind this poor performance include the more diffuse nature of NOs with low occupation numbers as well as the reduction in sparsity of the perturbed singles amplitudes in the NO basis and the neglect of orbital response. We tested a number of approaches to improve the performance of the NO space, including the use of a field-perturbed density to define the virtual orbitals and various external-space corrections. The truncation of the CMO space, on the other hand, yields errors in coupled-cluster dipole polarizabilities of less than 2% even after removing as much as 50% of the full virtual space. We find that this positive performance of the CMO space results from a cancellation of errors due to the truncation of the unperturbed and perturbed amplitudes, as well as sparsity of the singles amplitudes. We introduce a simple criterion called a dipole amplitude to use as a threshold for truncating the CMO basis for such property calculations

Room-Temperature and Near-Room-Temperature Molecule-Based Magnets

Additional members of the family of high-Tc molecule-based magnets, V[acceptor]2·yCH2Cl2 have been discovered in which the acceptor is a fluorophenyltricyanoethylene. Varying the number and position of the fluorine substitutions around the phenyl ring results in materials with significantly different magnetic ordering temperatures (Tc’s) ranging from 160 to 300 K. Density functional theory calculations were performed on the neutral and anionic forms of the acceptors that reveal modest correlation between Tc and three calculated quantities: the gas-phase electron affinity, the dihedral angle between the phenyl ring and the olefin, and the Mulliken spin densities on the nitrogen atoms. The electrochemistry of the acceptors has also been examined

Protonated 2-Methyl-1,2-epoxypropane: A Challenging Problem for Density Functional Theory

Protonated epoxides feature prominently in organic chemistry as reactive intermediates. Herein, we describe 10 protonated epoxides using B3LYP, MP2, and CCSD/6-311++G** calculations. Relative to CCSD, B3LYP consistently overestimates the C2−O bond length. Protonated 2-methyl-1,2-epoxypropane is the most problematic species studied, where B3LYP overestimates the C2−O bond length by 0.191 Å. Seventeen other density functional methods were applied to this protonated epoxide; on average, they overestimated the CCSD bond length by 0.2 Å. We present a range of data that suggest the difficulty for DFT methods in modeling the structure of the titled protonated epoxide lies in the extremely weak C2−O bond, which is reflected in the highly asymmetric charge distribution between the two ring carbons. Protonated epoxides featuring more symmetrical charge distribution and cyclic homologues featuring less ring strain are treated with greater accuracy by B3LYP. Finally, MP2 performed very well against CCSD, deviating in the C2−O bond length at most by 0.009 Å; it is, therefore, recommended when computational resources prove insufficient for coupled cluster methods

Reduced Scaling Real-Time Coupled Cluster Theory

Real-time coupled cluster (CC) methods have several advantages over their frequency-domain counterparts, namely, response and equation of motion CC theories. Broadband spectra, strong fields, and pulse manipulation allow for the simulation of complex spectroscopies that are unreachable using frequency-domain approaches. Due to the high-order polynomial scaling, the required numerical time propagation of the CC residual expressions is a computationally demanding process. This scaling may be reduced by local correlation schemes, which aim to reduce the size of the (virtual) orbital space by truncation according to user-defined parameters. We present the first application of local correlation to real-time CC. As in previous studies of locally correlated frequency-domain CC, traditional local correlation schemes are of limited utility for field-dependent properties; however, a perturbation-aware scheme proves promising. A detailed analysis of the amplitude dynamics suggests that the main challenge is a strong time dependence of the wave function sparsity

Structure of [18]Annulene Revisited: Challenges for Computing Benzenoid Systems

For cyclic conjugated structures, erratic computational results have been obtained with Hartree–Fock (HF) molecular orbital (MO) methods as well as density functional theory (DFT) with large HF-exchange contributions. In this work, the reasons for this unreliability are explored. Extensive computations on [18]annulene and related compounds highlight the pitfalls to be avoided and the due diligence required for such computational investigations. In particular, a careful examination of the MO singlet-stability eigenvalues is recommended. The appearance of negative eigenvalues is not (necessarily) problematic, but near-zero (positive or negative) eigenvalues can lead to dramatic errors in vibrational frequencies and related properties. DFT approaches with a lower HF admixture generally appear more robust in this regard for the description of benzenoid structures, although they may exaggerate the tendency toward planarity and C–C bond-equalization. For the iconic [18]annulene, the results support a nonplanar equilibrium structure. The density-fitted frozen natural orbital coupled-cluster singles and doubles with perturbative triples [DF-FNO CCSD(T)] method of electron correlation with an aug-pVQZ/aug-pVTZ basis set places the C2 global minimum 1.1 kcal mol–1 below the D6h stationary point

On the use of property-oriented basis sets for the simulation of vibrational chiroptical spectroscopies

We computed vibrational circular dichroism (VCD) and Raman optical activity (ROA) spectra for a test set of six chiral compounds using two standard density-functionals and an array of basis sets. We analysed the performance of property-oriented basis sets using a quadruple-zeta basis as a reference against four key metrics. We find little qualitative difference between the spectra produced by the larger basis sets (ORP, LPolX, aug-cc-pVTZ, and aug-cc-pVQZ), though their quantitative metrics exhibit wide variations. The smaller basis sets (rDPS, augD-3-21G, augT3-3-21G, Sadlej-pVTZ, and aug-cc-pVDZ) performed better for VCD rotatory strengths than for the corresponding ROA circular intensity differences (CIDs). However, this trend diminishes as the basis-set size is increased, lending validity to the conclusion that more robust property-oriented basis sets are required for ROA spectral generation than that of VCD. We observed improved performance in the mid-infrared region compared to the high-frequency regime, as well as overestimation of VCD rotatory strengths in the latter region as compared to the reference. We conclude that the ORP and LPol-ds basis sets are the most efficient and effective choices of basis set for the prediction of VCD and ROA spectra, as they provide both highly accurate results at reduced computational expense.</p

Challenges in the Use of Quantum Computing Hardware-Efficient Ansätze in Electronic Structure Theory

Advances in quantum computation for electronic structure, and particularly heuristic quantum algorithms, create an ongoing need to characterize the performance and limitations of these methods. Here we discuss some potential pitfalls connected with the use of hardware-efficient Ansätze in variational quantum simulations of electronic structure. We illustrate that hardware-efficient Ansätze may break Hamiltonian symmetries and yield nondifferentiable potential energy curves, in addition to the well-known difficulty of optimizing variational parameters. We discuss the interplay between these limitations by carrying out a comparative analysis of hardware-efficient Ansätze versus unitary coupled cluster and full configuration interaction, and of second- and first-quantization strategies to encode Fermionic degrees of freedom to qubits. Our analysis should be useful in understanding potential limitations and in identifying possible areas of improvement in hardware-efficient Ansätze