Towards a rational design of laser-coolable molecules: insights from equation-of-motion coupled-cluster calculations.

Access to cold molecules is critical for quantum information science, design of new sensors, ultracold chemistry, and search of new phenomena. These applications depend on the ability to laser-cool molecules. Rigorous theory and qualitative models can play a central role in narrowing down the vast pool of potential candidates amenable to laser cooling. We report a systematic study of structural and optical properties of alkaline earth metal derivatives in the context of their applicability in laser cooling using equation-of-motion coupled-cluster methods. To rationalize and generalize the results from high-level electronic structure calculations, we develop an effective Hamiltonian model. The model explains the observed trends and suggests new principles for the design of laser-coolable molecules.

Analytical Second-Order Properties for the Random Phase Approximation: Nuclear Magnetic Resonance Shieldings.

A method for the analytical computation of nuclear magnetic resonance (NMR) shieldings within the direct random phase approximation (RPA) is presented. As a starting point, we use the RPA ground-state energy expression within the resolution-of-the-identity approximation in the atomic-orbital formalism. As has been shown in a recent benchmark study using numerical second derivatives [Glasbrenner, M. J. Chem. Theory Comput. 2022, 18, 192], RPA based on a Hartree-Fock reference shows accuracies comparable to coupled cluster singles and doubles (CCSD) for NMR chemical shieldings. Together with the much lower computational cost of RPA, it has emerged as an accurate method for the computation of NMR shieldings. Therefore, we aim to extend the applicability of RPA NMR to larger systems by introducing analytical second-order derivatives, making it a viable method for the accurate and efficient computation of NMR chemical shieldings.

Tensor-Hypercontracted MP2 First Derivatives: Runtime and Memory Efficient Computation of Hyperfine Coupling Constants.

We employ our recently introduced tensor-hypercontracted (THC) second-order Møller-Plesset perturbation theory (MP2) method [Bangerter, F. H., Glasbrenner, M., Ochsenfeld, C. J. Chem. Theory Comput. 2021, 17, 211-221] for the computation of hyperfine coupling constants (HFCCs). The implementation leverages the tensor structure of the THC factorized electron repulsion integrals for an efficient formation of the integral-based intermediates. The computational complexity of the most expensive and formally quintic scaling exchange-like contribution is reduced to effectively subquadratic, by making use of the intrinsic, exponentially decaying coupling between tensor indices through screening based on natural blocking. Overall, this yields an effective subquadratic scaling with a low prefactor for the presented THC-based AO-MP2 method for the computation of isotropic HFCCs on DNA fragments with up to 500 atoms and 5000 basis functions. Furthermore, the implementation achieves considerable speedups with up to a factor of roughly 600-1000 compared to previous implementations [Vogler, S., Ludwig, M., Maurer, M., Ochsenfeld, C. J. Chem. Phys. 2017, 147, 024101] for medium-sized organic radicals, while also significantly reducing storage requirements.

Low-Scaling Tensor Hypercontraction in the Cholesky Molecular Orbital Basis Applied to Second-Order Møller-Plesset Perturbation Theory.

We employ various reduced scaling techniques to accelerate the recently developed least-squares tensor hypercontraction (LS-THC) approximation [Parrish, R. M., Hohenstein, E. G., Martínez, T. J., Sherrill, C. D. J. Chem. Phys. 137, 224106 (2012)] for electron repulsion integrals (ERIs) and apply it to second-order Møller-Plesset perturbation theory (MP2). The grid-projected ERI tensors are efficiently constructed using a localized Cholesky molecular orbital basis from density-fitted integrals with an attenuated Coulomb metric. Additionally, rigorous integral screening and the natural blocking matrix format are applied to reduce the complexity of this step. By recasting the equations to form the quantized representation of the 1/r operator Z into the form of a system of linear equations, the bottleneck of inverting the grid metric via pseudoinversion is removed. This leads to a reduced scaling THC algorithm and application to MP2 yields the (sub-)quadratically scaling THC-ω-RI-CDD-SOS-MP2 method. The efficiency of this method is assessed for various systems including DNA fragments with over 8000 basis functions and the subquadratic scaling is illustrated.

Toward Ultracold Organic Chemistry: Prospects of Laser Cooling Large Organic Molecules.

Ultracold organic chemistry enables studies of reaction dynamics and mechanisms in the quantum regime. Access to ultracold molecules hinges on the ability to efficiently scatter multiple photons via quasi-closed cycling transitions. Optical cycling in polyatomic molecules is challenging due to their complex electronic structure. Using equation-of-motion coupled-cluster calculations, we demonstrate that an alkaline earth metal attached to various aromatic ligands (such as benzene, phenol, cyclopentadienyl, and pyrrolide) offers nearly closed cycling transitions with only a few additional repump lasers. We also show that aromatic ligands such as benzene can accommodate multiple cycling centers in various geometrical arrangements, opening new avenues in quantum information science, precision measurements, and ultracold chemistry.