Peter Reinhardt

Basis sets featuring single‐exponent radial functions for each of the nℓ subshells and orthogonality of the radial parts for different values of n within the same ℓ have been generated for elements 1–54 of the periodic table, by minimizing the total energy for different spectroscopic states. The derived basis sets can be fairly dubbed as MAP (minimal atomic parameter/Moscow–Aachen–Paris) basis sets. We show that fundamental properties (total energy, radial expectation values, node positions, etc.) of the generated MAP orbital sets are astonishingly close to those obtained with much larger basis sets known in the literature, without numerical inconsistencies. The obtained exponents follow simple relations with respect to the nuclear charge Z.

The minimum atomic parameters/Moscow–Aachen–Paris (MAP) basis sets—reintroduced in the previous paper—are analyzed with respect to spatial features as orbital shape, possible fits to alternative orbital sets (numerical or quasi‐numerical orbitals, nodeless Slater orbitals), respect of Kato's condition and radial distribution of energy components. For comparing orbital spaces the Frobenius angle between the orbital subspaces they span is introduced as numerical tool. It is shown that the electronic density of the MAP states is depleted around the nucleus with respect to the other orbital sets. Despite this, the similarity between the respective subspaces in all cases (except a unique case of the Pd atom) as measured by the cosine of the Frobenius angle amounts above 0.96 for all atoms. Deviations from the perfect value of Kato's condition amounts systematically to 0.3 and 0.5 for all elements considered. Integrating one‐electron energy contributions from r = ∞ to a finite radius, MAP and Bunge orbitals show about the same values, but for the inner region governed by the polynomial oscillations.

Quantum chemistry is a discipline which relies heavily on very expensive numerical computations. The scaling of correlated wave function methods lies, in their standard implementation, between O(N5) and O(eN), where N is proportional to the system size. Therefore, performing accurate calculations on chemically meaningful systems requires i) approximations that can lower the computational scaling, and ii) efficient implementations that take advantage of modern massively parallel architectures. Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven framework allows the programmer to include any arbitrary set of determinants in the reference space, hence providing greater method- ological freedoms. The sCI method implemented in Quantum Package is based on the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm which complements the variational sCI energy with a PT2 correction. Additional external plugins have been recently added to perform calculations with multireference coupled cluster theory and range-separated density-functional theory. All the programs are developed with the IRPF90 code generator, which simplifies collaborative work and the development of new features. Quantum Package strives to allow easy implementation and experimentation of new methods, while making parallel computation as simple and efficient as possible on modern supercomputer architectures. Currently, the code enables, routinely, to realize runs on roughly 2 000 CPU cores, with tens of millions of determinants in the reference space. Moreover, we have been able to push up to 12 288 cores in order to test its parallel efficiency. In the present manuscript, we also introduce some key new developments: i) a renormalized second-order perturbative correction for efficient extrapolation to the full CI limit, and ii) a stochastic version of the CIPSI selection performed simultaneously to the PT2 calculation at no extra cost.