Improved CPS and CBS Extrapolation of PNO-CCSD(T) Energies: The MOBH35 and ISOL24 Data Sets.

Computation of heats of reaction of large molecules is now feasible using the domain-based pair natural orbital (PNO)-coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] theory. However, to obtain agreement within 1 kcal/mol of experiment, it is necessary to eliminate basis set incompleteness error, which comprises both the AO basis set error and the PNO truncation error. Our investigation into the convergence to the canonical limit of PNO-CCSD(T) energies with the PNO truncation threshold T shows that errors follow the model E(T)=E+AT1/2. Therefore, PNO truncation errors can be eliminated using a simple two-point CPS extrapolation to the canonical limit so that subsequent CBS extrapolation is not limited by the residual PNO truncation error. Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are larger for molecules with significant static correlation and that it is necessary to use very tight thresholds of T=10-8 to ensure that errors do not exceed 1 kcal/mol. We present a lower-cost extrapolation scheme that uses information from small basis sets to estimate the PNO truncation errors for larger basis sets. In this way, the canonical limit of CCSD(T) calculations on sizable molecules with large basis sets can be reliably estimated in a practical way. Using this approach, we report near complete basis set (CBS)-CCSD(T) reaction energies for the full ISOL24 and MOBH35 data sets.

Continuous-wave cavity ringdown for high-sensitivity polarimetry and magnetometry measurements.

We report the development of a novel variant of cavity ringdown polarimetry using a continuous-wave laser operating at 532 nm for highly precise chiroptical activity and magnetometry measurements. The key methodology of the apparatus relies upon the external modulation of the laser frequency at the frequency splitting between non-degenerate left- and right-circularly polarized cavity modes. The method is demonstrated by the evaluation of the Verdet constants of crystalline CeF3 and fused silica, in addition to the observation of gas- and solution-phase optical rotations of selected chiral molecules. Specifically, optical rotations of (i) vapors of α-pinene and R-(+)-limonene, (ii) mutarotating D-glucose in water, and (iii) acidified L-histidine solutions are determined. The detection sensitivities for the gas- and solution-phase chiral activity measurements are ∼30 and ∼120µdeg over a 30 s detection period per cavity round trip pass, respectively. Furthermore, the measured optical rotations for R-(+)-limonene are compared with computations performed using the TURBOMOLE quantum chemistry package. The experimentally observed optically rotatory dispersion of this cyclic monoterpene was thus rationalized via a consideration of its room temperature conformer distribution as determined by the aforementioned single-point energy calculations.

TURBOMOLE: Today and Tomorrow.

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

A Regularized Second-Order Correlation Method from Green's Function Theory.

We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.

Grid-based methods for chemistry simulations on a quantum computer.

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.

Molecular excited state calculations with adaptive wavefunctions on a quantum eigensolver emulation: reducing circuit depth and separating spin states.

Ab initio electronic excited state calculations are necessary for the quantitative study of photochemical reactions, but their accurate computation on classical computers is plagued by prohibitive resource scaling. The Variational Quantum Deflation (VQD) is an extension of the quantum-classical Variational Quantum Eigensolver (VQE) algorithm for calculating electronic excited state energies, and has the potential to address some of these scaling challenges using quantum computers. However, quantum computers available in the near term can only support a limited number of quantum circuit operations, so reducing the quantum computational cost in VQD methods is critical to their realisation. In this work, we investigate the use of adaptive quantum circuit growth (ADAPT-VQE) in excited state VQD calculations, a strategy that has been successful previously in reducing the resources required for ground state energy VQE calculations. We also invoke spin restrictions to separate the recovery of eigenstates with different spin symmetry to reduce the number of calculations and accumulation of errors in computing excited states. We created a quantum eigensolver emulation package - Quantum Eigensolver Building on Achievements of Both quantum computing and quantum chemistry (QEBAB) - for testing the proposed adaptive procedure against two existing VQD methods that use fixed-length quantum circuits: UCCGSD-VQD and k-UpCCGSD-VQD. For a lithium hydride test case we found that the spin-restricted adaptive growth variant of VQD uses the most compact circuits out of the tested methods by far, consistently recovers adequate electron correlation energy for different nuclear geometries and eigenstates while isolating the singlet and triplet manifold. This work is a further step towards developing techniques which improve the efficiency of hybrid quantum algorithms for excited state quantum chemistry, opening up the possibility of exploiting real quantum computers for electronic excited state calculations sooner than previously anticipated.

The rotational spectrum of H2S⋯HI and an investigation by ab initio calculations of the origins of the observed doubling of rotational transitions in both H2S⋯HI and H2S⋯F2.

The rotational spectrum of the complex H2S⋯HI observed with a pulsed-jet, Fourier-transform microwave spectrometer shows that each rotational transition is split into a closely spaced doublet, a pattern similar to that observed earlier for the halogen-bonded complex H2S⋯F2. The origin of the doubling has been investigated by means of ab initio calculations conducted at the CCSD(T)(F12*)/cc-pVDZ-F12 level. Two paths were examined by calculating the corresponding energy as a function of two angles. One path involved inversion of the configuration at S through a planar transition state of C2v symmetry via changes in the angle ϕ between the C2 axis of H2S and the line joining the H and I nuclei [the potential energy function V(ϕ)]. The other was a torsional oscillation θ about the local C2 axis of H2S that also exchanges the equivalent H nuclei [the potential energy function V(θ)]. The inversion path is slightly lower in energy and much shorter in arc length and is therefore the favored tunneling pathway. In addition, calculation of V(ϕ) for the series of hydrogen- and halogen-bonded complexes H2S⋯HX (X = F, Cl, or Br) and H2S⋯XY (XY = Cl2, Br2, ClF, BrCl, or ICl) at the same level of theory revealed that doubling is unlikely to be resolved in these, in agreement with experimental observations. The barrier heights of the V(ϕ) of all ten complexes examined were found to be almost directly proportional to the dissociation energies De.

Basis set extrapolation in pair natural orbital theories.

We present the results of a benchmark study of the effect of Pair Natural Orbital (PNO) truncation errors on the performance of basis set extrapolation. We find that reliable conclusions from the application of Helgaker's extrapolation method are only obtained when using tight PNO thresholds of at least 10-7. The use of looser thresholds introduces a significant risk of observing a false basis set convergence and underestimating the residual basis set errors. We propose an alternative extrapolation approach based on the PNO truncation level that only requires a single basis set and show that it is a viable alternative to hierarchical basis set extrapolation methods.

Hydrogen-Atom Tunneling in Metaphosphorous Acid.

Invited for the cover of this issue is X. Zeng and co-workers at Soochow University, University of Stuttgart, and Max-Planck Institute for Solid State Research. The image depicts the fast tunneling transformation of the highly elusive metaphosphorous acid (HOPO). Read the full text of the article at 10.1002/chem.202000844.

Ab initio calculation of rovibrational states for non-degenerate double-well potentials: cis-trans isomerization of HOPO.

The rovibrational spectra of metaphosphorous acid, HOPO, and its deuterated isotopologue have been studied by vibrational configuration interaction calculations, relying on the internal coordinate path Hamiltonian and the Watson Hamiltonian. Tunneling effects for the overtones of the torsional mode, which gives rise to the cis-trans isomerization, and its rovibrational transitions have been investigated in detail. Due to strong matrix effects, comparison with experimental data is hindered, and thus, the calculations provide accurate estimates for the fundamental modes of these species.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Hydrogen-Atom Tunneling in Metaphosphorous Acid.

Metaphosphorous acid (HOPO), a key intermediate in phosphorus chemistry, has been generated in syn- and anti-conformations in the gas phase by high-vacuum flash pyrolysis (HVFP) of a molecular precursor ethoxyphosphinidene oxide (EtOPO→C2 H4 +HOPO) at ca. 1000 K and subsequently trapped in an N2 -matrix at 2.8 K. Unlike the two conformers of the nitrogen analogue HONO, the anti-conformer of HOPO undergoes spontaneous rotamerization at 2.8 K via hydrogen-atom tunneling (HAT) with noticeable kinetic isotope effects for H/D (>104 for DOPO) and 16 O/18 O (1.19 for H18 OPO and 1.06 for HOP18 O) in N2 -matrices.

Efficient and accurate description of adsorption in zeolites.

Accurate theoretical methods are needed to correctly describe adsorption on solid surfaces or in porous materials. The random phase approximation (RPA) with singles corrections scheme and the second order Møller-Plesset perturbation theory (MP2) are two schemes, which offer high accuracy at affordable computational cost. However, there is little knowledge about their applicability and reliability for different adsorbates and surfaces. Here, we calculate adsorption energies of seven different molecules in zeolite chabazite to show that RPA with singles corrections is superior to MP2, not only in terms of accuracy but also in terms of computer time. Therefore, RPA with singles is a suitable scheme for obtaining highly accurate adsorption energies in porous materials and similar systems.

Principal Domains in Local Correlation Theory.

The computational efficiency of local correlation methods is strongly dependent on the size of the domain of functions used to expand local correlating orbitals such as orbital specific or pair natural orbitals. Here, we define a principal domain of order m as the subset of m one-particle functions that provides the best support for a given n-electron wave function by maximizing the partial trace of the one-body reduced density matrix. Principal domains maximize the overlap between the wave function and its approximant for two-electron systems and are the domain selection equivalent of Löwdin's natural orbitals. We present an efficient linear scaling greedy algorithm for obtaining principal domains of projected atomic orbitals and demonstrate its utility in the context of the pair natural orbital local correlation theory. We numerically determine thresholds such that the projected atomic orbital domain error is an order of magnitude smaller than the pair natural orbital truncation error.

Role of Valence and Semicore Electron Correlation on Spin Gaps in Fe(II)-Porphyrins.

The role of valence and semicore correlation in differentially stabilizing the intermediate spin state of Fe(II)-porphyrins is analyzed. For CASSCF treatments of valence correlation, a (32,34) active space containing metal 3 d, d' orbitals and the entire π system of the porphyrin is necessary to stabilize the intermediate spin state. Semicore correlation provides a minor (-1.6 kcal/mol) but quantitatively significant correction. Accounting for valence, semicore, and correlation beyond the active space enlarges the (3 E g-5 A1 g) spin gap to -5.7 kcal/mol.

Anharmonic excited state frequencies of para-difluorobenzene, toluene and catechol using analytic RI-CC2 second derivatives.

Analytic second nuclear derivatives for excited electronic state energies have been implemented for the resolution-of-the-identity accelerated CC2, CIS(D∞) and ADC(2) models. Our efficient implementation with O(N2) memory demands enables the treatment of medium sized molecules with large basis sets and high numerical precision and thereby paves the way for semi-numerical evaluation of the higher-order derivatives required for anharmonic corrections to excited state vibrational frequencies. We compare CC2 harmonic and anharmonic excited state frequencies with experimental values for para-difluorobenzene, toluene and catechol. Basis set problems occur for out-of-plane bending vibrations due to intramolecular basis set superposition error. For non-planar molecules and in plane modes of planar molecules, the agreement between theory and experiment is better than 30 cm-1 on average and we reassign a number of experimental bands on the basis of the ab initio predictions.

Experimental and computational studies of Criegee intermediate reactions with NH3 and CH3NH2.

Ammonia and amines are emitted into the troposphere by various natural and anthropogenic sources, where they have a significant role in aerosol formation. Here, we explore the significance of their removal by reaction with Criegee intermediates, which are produced in the troposphere by ozonolysis of alkenes. Rate coefficients for the reactions of two representative Criegee intermediates, formaldehyde oxide (CH2OO) and acetone oxide ((CH3)2COO) with NH3 and CH3NH2 were measured using cavity ring-down spectroscopy. Temperature-dependent rate coefficients, k(CH2OO + NH3) = (3.1 ± 0.5) × 10-20T2 exp(1011 ± 48/T) cm3 s-1 and k(CH2OO + CH3NH2) = (5 ± 2) × 10-19T2 exp(1384 ± 96/T) cm3 s-1 were obtained in the 240 to 320 K range. Both the reactions of CH2OO were found to be independent of pressure in the 10 to 100 Torr (N2) range, and average rate coefficients k(CH2OO + NH3) = (8.4 ± 1.2) × 10-14 cm3 s-1 and k(CH2OO + CH3NH2) = (5.6 ± 0.4) × 10-12 cm3 s-1 were deduced at 293 K. An upper limit of ≤2.7 × 10-15 cm3 s-1 was estimated for the rate coefficient of the (CH3)2COO + NH3 reaction. Complementary measurements were performed with mass spectrometry using synchrotron radiation photoionization giving k(CH2OO + CH3NH2) = (4.3 ± 0.5) × 10-12 cm3 s-1 at 298 K and 4 Torr (He). Photoionization mass spectra indicated production of NH2CH2OOH and CH3N(H)CH2OOH functionalized organic hydroperoxide adducts from CH2OO + NH3 and CH2OO + CH3NH2 reactions, respectively. Ab initio calculations performed at the CCSD(T)(F12*)/cc-pVQZ-F12//CCSD(T)(F12*)/cc-pVDZ-F12 level of theory predicted pre-reactive complex formation, consistent with previous studies. Master equation simulations of the experimental data using the ab initio computed structures identified submerged barrier heights of -2.1 ± 0.1 kJ mol-1 and -22.4 ± 0.2 kJ mol-1 for the CH2OO + NH3 and CH2OO + CH3NH2 reactions, respectively. The reactions of NH3 and CH3NH2 with CH2OO are not expected to compete with its removal by reaction with (H2O)2 in the troposphere. Similarly, losses of NH3 and CH3NH2 by reaction with Criegee intermediates will be insignificant compared with reactions with OH radicals.

Orbital-Optimized Distinguishable Cluster Theory with Explicit Correlation.

A combination of orbital-optimized methods with explicit correlation is discussed for the example of the orbital-optimized distinguishable cluster approach. It is shown that the perturbative approach is applicable even in strongly correlated situations, and it is important in these cases to use Lagrange multipliers together with the amplitudes. The partial amplitude relaxation can be applied to relax the amplitudes and makes absolute energies closer to complete basis set results.

Relaxing Constrained Amplitudes: Improved F12 Treatments of Orbital Optimization and Core-Valence Correlation Energies.

We present a Lagrangian correction for the energy change upon releasing constraints imposed on coupled cluster amplitudes. We demonstrate that our correction (i) eliminates the systematic basis set error of the posthoc F12 treatment in orbital optimized methods and (ii) can be used to relax the F12 amplitudes and significantly reduce the sensitivity of the core-valence correlation energies to the exponent of the correlation factor, while retaining the low cost of the fixed amplitude approach.