Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification.

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is based on an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of challenging molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods─including heat-bath CI, the density matrix renormalization group approach, and FCIQMC─to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.

Near-exact nuclear gradients of complete active space self-consistent field wave functions.

In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules. We show that HCISCF nuclear gradients are fairly insensitive to the size of the "selected" variational space, which allows us to reduce the computational cost without introducing significant errors. The ability of the HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems, which require a larger active space than possible with a complete active space self-consistent field. Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT). We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional. We also use the HCISCF gradients to optimize geometries for this species and study the adiabatic singlet-triplet gap. During geometry optimization, we find that multiple near-degenerate local minima exist on the triplet potential energy surface.

Intrinsic electronic spectra of cryogenically prepared protoporphyrin IX ions in vacuo - deprotonation-induced Stark shifts.

We present electronic spectra containing the Qx and Qy absorption bands of singly and doubly deprotonated protoporphyrin IX, prepared as mass selected ions in vacuo at cryogenic temperatures, revealing vibronic structure in both bands. We assign the vibronic progression of the Qx band using a Frank-Condon-Herzberg-Teller simulation based on time-dependent density functional theory, comparing the observed bands with those calculated for porphine. A comparison of the electronic spectra of the two charge states allows investigation of the electronic Stark effect with an electric field strength beyond the capabilities of typical laboratory setups. We analyze the differences in the electronic spectra of the two charge states using n-electron valence perturbation theory (NEVPT2) and simulated charge distributions.

Recent developments in the PySCF program package.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.

Intrinsic photophysics of nitrophenolate ions studied by cryogenic ion spectroscopy.

The intrinsic photophysics of nitrophenolate isomers (meta, para, and ortho) was studied at low temperature using photodissociation mass spectrometry in a cryogenic ion trap instrument. Each isomer has distinct photophysics that affects the excited state lifetimes, as observed experimentally in their spectroscopic linewidths. Visible-light-induced excitation of m-nitrophenolate gives rise to well-resolved vibronic features in the spectrum of the S1 state. The para and ortho isomers have broad spectra - even at cryogenic temperatures - due to their shorter excited state lifetimes and spectral congestion. We present computational evidence for mixing of the first and second excited states of o-nitrophenolate, leading to significant additional broadening in the experimental spectrum.

Cheap and Near Exact CASSCF with Large Active Spaces.

We use the recently developed Heat-bath Configuration Interaction (HCI) algorithm as an efficient active space solver to perform multiconfiguration self-consistent field calculations (HCISCF) with large active spaces. We give a detailed derivation of the theory and show that difficulties associated with non-variationality of the HCI procedure can be overcome by making use of the Lagrangian formulation to calculate the HCI relaxed two-body reduced density matrix. HCISCF is then used to study the electronic structure of butadiene, pentacene, and Fe-porphyrin. One of the most striking results of our work is that the converged active space orbitals obtained from HCISCF are relatively insensitive to the accuracy of the HCI calculation. This allows us to obtain nearly converged CASSCF energies with an estimated error of less than 1 mHa using the orbitals obtained from the HCISCF procedure in which the integral transformation is the dominant cost. For example, an HCISCF calculation on the Fe-porphyrin model complex with an active space of (44e, 44o) took only 412 s per iteration on a single node containing 28 cores, out of which 185 s was spent in the HCI calculation and the remaining 227 s was used mainly for integral transformation. Finally, we also show that active space orbitals can be optimized using HCISCF to substantially speed up the convergence of the HCI energy to the Full CI limit because HCI is not invariant to unitary transformations within the active space.

Electronic Spectra of Tris(2,2'-bipyridine)-M(II) Complex Ions in Vacuo (M = Fe and Os).

We measured the electronic spectra of mass-selected [M(bpy)3]2+ (M = Fe and Os, bpy = 2,2'-bipyridine) ions in vacuo by photodissociation spectroscopy of their N2 adducts, [M(bpy)3]2+·N2. Extensive band systems in the visible (predominantly charge transfer) and near-ultraviolet (ππ*) spectral regions are reported. The [M(bpy)3]2+·N2 target ions were prepared by condensing N2 onto electrosprayed ions in a cryogenic ion trap at ca. 25 K and then mass-selected by time-of-flight mass spectrometry. The electronic photodissociation spectra of the cold, gas-phase ions closely reflect their intrinsic properties, i.e., without perturbation by solvent effects. The spectra are interpreted using time-dependent density functional theory calculations both with and without accounting for relativistic effects.

UV Spectra of Tris(2,2'-bipyridine)-M(II) Complex Ions in Vacuo (M = Mn, Fe, Co, Ni, Cu, Zn).

We present electronic spectra in the π-π* region of a series of tris(bpy)-M(II) complex ions (bpy = 2,2'-bipyridine; M = Mn, Fe, Co, Ni, Cu, Zn) in vacuo for the first time. By applying photodissociation spectroscopy to cryogenically cooled and mass selected [MII(bpy)3]2+ ions, we obtain the intrinsic spectra of these ions at low temperature without perturbation by solvent interaction or crystal lattice shifts. This allows spectroscopic analysis of these complex ions in greater detail than possible in the condensed phase. We interpret our experimental data by comparison with time-dependent density functional theory.

Hydration of a Binding Site with Restricted Solvent Access: Solvatochromic Shift of the Electronic Spectrum of a Ruthenium Polypyridine Complex, One Molecule at a Time.

We report the electronic spectra of mass selected [(bpy)(tpy)Ru-OH2]2+·(H2O)n clusters (bpy = 2,2'-bipyridine, tpy =2,2':6'2″-terpyridine, n = 0-4) in the spectral region of their metal-to-ligand charge transfer bands. The spectra of the mono- and dihydrate clusters exhibit partially resolved individual electronic transitions. The water network forming at the aqua ligand leads to a rapid solvatochromic shift of the peak of the band envelope: addition of only four solvent water molecules can recover 78% of the solvatochromic shift in bulk solution. The sequential shift of the band shows a clear change in behavior with the closing of the first hydration shell. We compare our experimental data to density function theory (DFT) calculations for the ground and excited states.

The electronic spectrum of cryogenic ruthenium-tris-bipyridine dications in vacuo.

We report the electronic spectrum of the prototypical ruthenium coordination complex Ru(bpy)3 (2+) (bpy = 2, 2'-bipyridine) by messenger tagging with N2 in a cryogenic ion trap and photodissociation spectroscopy of mass selected Ru(bpy)3 (2+) ⋅ N2 ions. We observe individual electronic bands and groups of bands with unprecedented detail, particularly in the usually unresolved metal-to-ligand charge transfer region of the spectrum. By comparing our experimental results with time-dependent density functional theory, both with and without spin-orbit interaction [Heully et al., J. Chem. Phys. 131, 184308 (2009)], we are able to assign the spectrum of the isolated ion.

Ligand Influence on the Electronic Spectra of Dicationic Ruthenium-Bipyridine-Terpyridine Complexes.

We report electronic spectra of a series of ruthenium polypyridine complexes of the form [(trpy)(bipy)Ru(II)-L](2+) (bipy = 2,2'-bipyridine and trpy = 2,2':6',2″-terpyridine), where L represents a small molecular ligand that occupies the last coordination site. Species with L = H2O, CO2, CH3CN, and N2 were investigated in vacuo using photodissociation spectroscopy. All species exhibit bright metal-to-ligand charger transfer (MLCT) bands in the visible and near UV, but with different spectral envelopes and peak energies, encoding the influence of the ligand L on the electronic structure of the complex. Several individual electronic bands can be resolved for L = H2O and CO2, while the spectra for L = N2 and CH3CN are more congested, even at low ion temperatures. The experimental results are discussed in the framework of time-dependent density functional theory.