Complete Active Space Methods for NISQ Devices: The Importance of Canonical Orbital Optimization for Accuracy and Noise Resilience

To avoid the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive regions, which is also known as complete active space methods. However, selecting the active space alone is not enough to accurately describe quantum mechanical effects such as correlation. This study emphasizes the importance of optimizing the active space orbitals to describe correlation and improve the basis-dependent Hartree-Fock energies. We will explore classical and quantum computation methods for orbital optimization and compare the chemically inspired ansatz, UCCSD, with the classical full CI approach for describing the active space in both weakly and strongly correlated molecules. Finally, we will investigate the practical implementation of a quantum CASSCF, where hardware-efficient circuits must be used and noise can interfere with accuracy and convergence. Additionally, we will examine the impact of using canonical and noncanonical active orbitals on the convergence of the quantum CASSCF routine in the presence of noise

Complex Linear Response Functions for a Multiconfigurational Self-Consistent Field Wave Function in a High Performance Computing Environment

We present novel developments for the highly efficient evaluation of complex linear response functions of a multiconfigurational self-consistent field (MCSCF) wave function as implemented in MultiPsi. Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved. Two bottlenecks of large scale MC-CPP calculations, namely, the memory footprint and computational time, are addressed. The former is addressed by limiting the size of the subspace of trial vectors by using singular value decomposition (SVD) on either orbital or CI subspaces. The latter is addressed using an efficient parallel implementation as well as the strategy of dynamically adding linear response equations at near-convergence to neighboring roots. Furthermore, a novel methodology for decomposing MC-CPP spectra in terms of intuitive orbital excitations in an approximate fashion is presented. The performance of the code is illustrated with several numerical examples, including the X-ray spectrum of a molecule with nearly one hundred atoms. Additionally, for X-ray spectroscopy, the effect of including or excluding the core orbital in the active space on small covalent metal complexes is discussed

Complex Linear Response Functions for a Multiconfigurational Self-Consistent Field Wave Function in a High Performance Computing Environment

We present novel developments for the highly efficient evaluation of complex linear response functions of a multiconfigurational self-consistent field (MCSCF) wave function as implemented in MultiPsi. Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved. Two bottlenecks of large scale MC-CPP calculations, namely, the memory footprint and computational time, are addressed. The former is addressed by limiting the size of the subspace of trial vectors by using singular value decomposition (SVD) on either orbital or CI subspaces. The latter is addressed using an efficient parallel implementation as well as the strategy of dynamically adding linear response equations at near-convergence to neighboring roots. Furthermore, a novel methodology for decomposing MC-CPP spectra in terms of intuitive orbital excitations in an approximate fashion is presented. The performance of the code is illustrated with several numerical examples, including the X-ray spectrum of a molecule with nearly one hundred atoms. Additionally, for X-ray spectroscopy, the effect of including or excluding the core orbital in the active space on small covalent metal complexes is discussed

Unravelling the mechanism of pH-regulation in dinoflagellate luciferase

Dinoflagellates are the dominant source of bioluminescence in coastal waters. The luminescence reaction involves the oxidation of luciferin by a luciferase enzyme, which only takes place at low pH. The pH-dependence has previously been linked to four conserved histidines. It has been suggested that their protonation might induce a conformational change in the enzyme, thereby allowing substrate access to the binding pocket. Yet, the precise mechanism of luciferase activation has remained elusive. Here, we use computational tools to predict the open structure of the luciferase in Lingulodinium polyedra and to decipher the nature of the opening mechanism. Through accelerated molecular dynamics simulations, we demonstrate that the closed-open conformational change likely takes place via a tilt of the pH-regulatory helix-loop-helix domain. Moreover, we propose that the molecular basis for the transition is electrostatic repulsion between histidine-cation pairs, which destabilizes the closed conformation at low pH. Finally, by simulating truncated mutants, we show that eliminating the C-terminus alters the shape of the active site, effectively inactivating the luciferase

Complete active space methods for NISQ devices: The importance of canonical orbital optimization for accuracy and noise resilience

To break the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive, also known as complete active space methods. Nevertheless, more than the active space selection is needed for accuracy and effectively describing quantum mechanical effects as correlation. This study highlights the importance of optimizing the active space orbitals to describe correlation and improve the Hartree-Fock energies. We will explore orbital optimization classically and through quantum computation and how, theoretically, a chemically inspired ansatz as the UCCSD compares with a classical full CI (FCI) description of the active space in weakly and strongly correlated molecules. Finally, we will explore the practical implementation of a quantum CASSCF where hardware-efficient circuits need to be used, and noise hinders its accuracy and convergence. Moreover, we explore canonical and non-canonical active orbitals and how those influence the convergence of the quantum CASSCF routine in the presence of noise

Quantifying similarity for spectra with a large number of overlapping transitions : Examples from soft X-ray spectroscopy

Theoretical simulations are frequently used to assign electronic and geometric structure from spectral fingerprints. However, such assignments are prone to expectation bias. Bias can be reduced by using numerical measures of the similarity between calculated and experimental spectra. However, the commonly used pointwise comparisons cannot handle larger deviations in peak position. Here a weighted cross-correlation function is used to evaluate similarity scores for soft X-ray spectra of first-row transition metals. These spectra consist of hundreds of overlapping resonances, which makes spectral decomposition difficult. They are also challenging to model, leading to significant errors in both peak position and intensity. It is first shown how the choice of weight-function width can be related to the modeling errors. The method is then applied to evaluate the sensitivity of multiconfigurational wavefunction and charge-transfer multiplet simulations to model choices. The approach makes it possible to assess the reliability of assignments from spectral fingerprinting

Origin of core-to-core x-ray emission spectroscopy sensitivity to structural dynamics

Recently, coherent structural dynamics in the excited state of an iron photosensitizer was observed through oscillations in the intensity of K alpha x-ray emission spectroscopy (XES). Understanding the origin of the unexpected sensitivity of core-to-core transitions to structural dynamics is important for further development of femtosecond time-resolved XES methods and, we believe, generally necessary for interpretation of XES signals from highly non-equilibrium structures that are ubiquitous in photophysics and photochemistry. Here, we use multiconfigurational wavefunction calculations combined with atomic theory to analyze the emission process in detail. The sensitivity of core-to-core transitions to structural dynamics is due to a shift of the minimum energy metal-ligand bond distance between 1s and 2p core-hole states. A key effect is the additional contraction of the non-bonding 3s and 3p orbitals in 1s core-hole states, which decreases electron-electron repulsion and increases overlap in the metal-ligand bonds. The effect is believed to be general and especially pronounced for systems with strong bonds. The important role of 3s and 3p orbitals is consistent with the analysis of radial charge and spin densities and can be connected to the negative chemical shift observed for many transition metal complexes. The XES sensitivity to structural dynamics can be optimized by tuning the emission energy spectrometer, with oscillations up to +/- 4% of the maximum intensity for the current system. The theoretical predictions can be used to design experiments that separate electronic and nuclear degrees of freedom in ultrafast excited state dynamics.QC 20210215</p

Efficient calculations of a large number of highly excited states for multiconfigurational wavefunctions

Electronically excited states play important roles in many chemical reactions and spectroscopic techniques. In quantum chemistry, a common technique to solve excited states is the multiroot Davidson algorithm, but it is not designed for processes like X-ray spectroscopy that involves hundreds of highly excited states. We show how the use of a restricted active space wavefunction together with a projection operator to remove low-lying electronic states offers an efficient way to reach single and double-core-hole states. Additionally, several improvements to the stability and efficiency of the configuration interaction (CI) algorithm for a large number of states are suggested. When applied to a series of transition metal complexes the new CI algorithm does not only resolve divergence issues but also leads to typical reduction in computational time by 70%, with the largest savings for small molecules and large active spaces. Together, the projection operator and the improved CI algorithm now make it possible to simulate a wide range of single- and two-photon spectroscopies

Accurate calculations of geometries and singlet-triplet energy differences for active-site models of [NiFe] hydrogenase

We have studied the geometry and singlet-triplet energy difference of two mono-nuclear Ni(2+) models related to the active site in [NiFe] hydrogenase. Multiconfigurational second-order perturbation theory based on a complete active-space wavefunction with an active space of 12 electrons in 12 orbitals, CASPT2(12,12), reproduces experimental bond lengths to within 1 pm. Calculated singlet-triplet energy differences agree with those obtained from coupled-cluster calculations with single, double and (perturbatively treated) triple excitations (CCSD(T)) to within 12 kJ mol(-1). For a bimetallic model of the active site of [NiFe] hydrogenase, the CASPT2(12,12) results were compared with the results obtained with an extended active space of 22 electrons in 22 orbitals. This is so large that we need to use restricted active-space theory (RASPT2). The calculations predict that the singlet state is 48-57 kJ mol(-1) more stable than the triplet state for this model of the Ni-SIa state. However, in the [NiFe] hydrogenase protein, the structure around the Ni ion is far from the square-planar structure preferred by the singlet state. This destabilises the singlet state so that it is only ∼24 kJ mol(-1) more stable than the triplet state. Finally, we have studied how various density functional theory methods compare to the experimental, CCSD(T), CASPT2, and RASPT2 results. Semi-local functionals predict the best singlet-triplet energy differences, with BP86, TPSS, and PBE giving mean unsigned errors of 12-13 kJ mol(-1) (maximum errors of 25-31 kJ mol(-1)) compared to CCSD(T). For bond lengths, several methods give good results, e.g. TPSS, BP86, and M06, with mean unsigned errors of 2 pm for the bond lengths if relativistic effects are considered.status: publishe

Benzophenone Ultrafast Triplet Population : Revisiting the Kinetic Model by Surface-Hopping Dynamics

The photochemistry of benzophenone, a paradigmatic organic molecule for photosensitization, was investigated by means of surface-hopping ab initio molecular dynamics. Different mechanisms were found to be relevant within the first 600 fs after excitation; the long debated direct (S-1 -&gt; T-1) and indirect (S-1 -&gt; T-2 -&gt; T-1) mechanisms for population of the low-lying triplet state are both possible, with the latter being prevalent. Moreover, we established the existence of a kinetic equilibrium between the two triplet states, never observed before. This fact implies that a significant fraction of the overall population resides in T-2, eventually allowing one to revisit the usual spectroscopic assignment proposed by transient absorption spectroscopy. This finding is of particular interest for photocatalysis as well as for DNA damages studies because both T-1 and T-2 channels are, in principle, available for benzophenone-mediated photoinduced energy transfer toward DNA