Coupled Cluster Theory Research Articles

A theoretical study of propynal under interstellar conditions and beyond, covering low-frequency infrared spectra, spectroscopic constants, and hot bands

ABSTRACTFrom an astrochemical point of view, propynal is a complex organic molecule. Moreover, it is a potential candidate for the formation of prebiotic propanal and propenal. Therefore, this molecule is of particular interest for astrochemical investigations. As it has been detected in the interstellar medium, it is of high relevance in this field of research. Although experimental data are available for the vibrational fundamental bands and rotational constants, experimental data for vibrational overtones and combination bands are scarce and fairly old. Additionally, high-level ab initio calculations are also not reported. In this work, we provide accurate quantum chemical calculations as well as a detailed analysis of vibrational and rovibrational properties for this molecule. The low-frequency spectrum up to $350\, \,\,\text{cm}^{-1}$ has been studied for temperatures between 10 and $300\, \text{K}$. For the same temperature range, partition functions are provided. Furthermore, the impact of hot bands up to room temperature has been investigated. A comparison of our results with experimental data is provided for the rotational constants, geometrical parameters, and a rovibrational spectrum. The underlying potential energy surface within these calculations is based on explicitly correlated coupled-cluster theory and includes up to four-mode coupling terms within an n-mode expansion. The vibrational and rovibrational calculations rely on vibrational and rovibrational configuration interaction theories, respectively.

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles.

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion MonteCarlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Redox Potentials with COSMO-RS: Systematic Benchmarking with Different Databases.

Recent techniques of computational electrochemistry can yield redox potentials with accuracy as good as 0.1 V. Yet, many such methods are not universal, easy to use, or computationally efficient. Herein, we provide a systematic benchmarking of a relatively cheap and straightforward computational approach for fairly accurate computations of redox potentials. It is based on a combination of the conductor-like screening model for real solvents (COSMO-RS) and the density functional theory (DFT). The benchmarking is done with databases covering diverse redox systems, including transition-metal aquacomplexes and various organic and inorganic compounds. In addition, we also present our own test set aiming at maximum chemical diversity and maximum range of redox potential values. We assess the performance of the fairly efficient computational protocol combining the COSMO-RS with the BP86 DFT functional. This is done by calibrating it against different high-level state-of-the-art techniques, in particular, polarizable continuum model (PCM) connected to composite G3(MP2,CC)(+) method, domain-based pair natural orbital implementation of coupled cluster theory, or complete basis set CBS-QB3 method. We also elaborate on the absolute reduction potential value of standard hydrogen electrode to be used with COSMO-RS, and we propose the value of approx. 4.4 V. The COSMO-RS/BP86-D3(BJ) combination outperforms other methods on a wide range of redox systems. However, we show that its accuracy is based on a balanced error cancelation and, therefore, it cannot be further systematically improved. As a result, the proposed procedure represents a pragmatic choice for large-scale screening, yet it could be combined with more advanced methods for detailed studies.

A DZ white dwarf with a 30 MG magnetic field

ABSTRACTMagnetic white dwarfs with field strengths below 10 MG are easy to recognize since the Zeeman splitting of spectral lines appears proportional to the magnetic field strength. For fields ≳100 MG, however, transition wavelengths become chaotic, requiring quantum-chemical predictions of wavelengths and oscillator strengths with a non-perturbative treatment of the magnetic field. While highly accurate calculations have previously been performed for hydrogen and helium, the variational techniques employed become computationally intractable for systems with more than three to four electrons. Modern computational techniques, such as finite-field coupled-cluster theory, allow the calculation of many-electron systems in arbitrarily strong magnetic fields. Because around 25 per cent of white dwarfs have metal lines in their spectra, and some of those are also magnetic, the possibility arises for some metals to be observed in very strong magnetic fields, resulting in unrecognizable spectra. We have identified SDSS J114333.48+661531.83 as a magnetic DZ white dwarf, with a spectrum exhibiting many unusually shaped lines at unknown wavelengths. Using atomic data calculated from computational finite-field coupled-cluster methods, we have identified some of these lines arising from Na, Mg, and Ca. Surprisingly, we find a relatively low field strength of 30 MG, where the large number of overlapping lines from different elements make the spectrum challenging to interpret at a much lower field strength than for DAs and DBs. Finally, we model the field structure of SDSS J1143+6615 finding the data are consistent with an offset dipole.

Intermolecular interactions in clusters of ethylammonium nitrate and 1-amino-1,2,3-triazole.

The intermolecular interaction energies, including hydrogen bonds (H-bonds), of clusters of the ionic liquid ethylammonium nitrate (EAN) and 1-amino-1,2,3-triazole (1-AT) based deep eutectic propellants (DeEP) are examined. 1-AT is introduced as a neutral hydrogen bond donor (HBD) to EAN in order to form a eutectic mixture. The effective fragment potential (EFP) is used to examine the bonding interactions in the DeEP clusters. The resolution of the Identity (RI) approximated second order Møller-Plesset perturbation theory (RI-MP2) and coupled cluster theory (RI-CCSD(T)) are used to validate the EFP results. The EFP method predicts that there are significant polarization and charge transfer effects in the EAN:1-AT complexes, along with Coulombic, dispersion and exchange repulsion interactions. The EFP interaction energies are in good agreement with the RI-MP2 and RI-CCSD(T) results. The quasi-atomic orbital (QUAO) bonding and kinetic bond order (KBO) analyses are additionally used to develop a conceptual and semi-quantitative understanding of the H-bonding interactions as a function of the size of the system. The QUAO and KBO analyses suggest that the H-bonds in the examined clusters follow the characteristic hydrogen bonding three-center four electron interactions. The strongest H-bonding interactions between the (EAN)1:(1-AT)n and (EAN)2:(1-AT)n (n = 1-5) complexes are observed internally within EAN; that is, between the ethylammonium cation [EA]+ and the nitrate anion ([NO3]-). The weakest H-bonding interactions occur between [NO3]- and 1-AT. Consequently, the average strengths of the H-bonds within a given (EAN)x:(1-AT)n complex decrease as more 1-AT molecules are introduced into the EAN monomer and EAN dimer. The QUAO bonding analysis suggests that 1-AT in (EAN)x:(1-AT)n can act as both a HBD and a hydrogen bond acceptor simultaneously. It is observed that two 1-AT molecules can form H-bonds to each other. Although the KBOs that correspond to H-bonding interactions in [EA]+:1-AT, [NO3]-:1-AT and between two 1-AT molecules are weaker than the H-bonds in EAN, those weak H-bond networks with 1-AT could be important to form a stable DeEP.

Accurate calculation of the interaction of a barium monofluoride molecule with an argon atom: A step towards using matrix isolation of BaF for determining the electron electric dipole moment

Calculations of the BaF–Ar triatomic system are performed with a relativistic Hamiltonian and coupled cluster theory at the CCSD(T) level for 1386 positions of the Ar atom relative to the BaF molecule. Calculations are repeated with increasing basis sets (double-, triple-, quadruple- and quintuple-zeta), and these are extrapolated to estimate the complete-basis-set limit. The resulting energies provide a potential energy for the interaction of an Ar atom with a BaF molecule. A fit is presented that parametrizes this potential. This work is needed for an understanding of the position, modes of motion and energy shifts of BaF isolated in an Ar matrix. This understanding will guide the EDM3 collaboration in its pursuit of a precision measurement of the electron electric dipole moment using BaF isolated in a cryogenic Ar matrix.

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects.

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born-Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6 bohr - a geometry close to the minimum of the total potential energy surface - our three-body potential amounts to -90.6 mK, with an estimated uncertainty of 0.5 mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides r12, r23, and r31, the potential takes correctly into account all angular terms decaying as r-l12 r-m23 r-n21 with l + m + n ≤ 14 for the nonrelativistic Born-Oppenheimer energy and l + m + n ≤ 9 for the post-Born-Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous works.

Barrier heights, reaction energies and bond dissociation energies for RH + HO2 reactions with coupled-cluster theory, density functional theory and diffusion quantum Monte Carlo methods.

Hydrogen abstraction reactions by the HO2 radical from hydrocarbon molecules are an important class of reactions in the autoignition of hydrocarbon fuels. Performance of DLPNO-CC and DFT methods using three hybrids and four double hybrids as well as FN-DMC with the single-Slater-Jastrow trial wavefunction on barrier heights and reaction energies of RH + HO2 reactions as well as bond dissociation energies of the involved X-H molecules is evaluated by comparison with the highly accurate CCSD(T)-F12b/CBS results in this study. Our results show that the DLPNO-CCSD(T)-F12 method can achieve highly accurate barrier heights, reaction energies and X-H bond energies for RH + HO2 reactions at a relatively low computational cost, and it is applicable to the H-abstraction reactions of larger molecules. Among all DFAs, MN15 and the employed double hybrids can achieve accurate barrier heights and reaction energies with MADs of less than or around 2 kJ mol-1, but their error on X-H bond energies is more pronounced. Only DSD-BLYP and DSD-PBEB95 can provide X-H bond energies with MADs less than 4 kJ mol-1. Considering dispersion correction in DFT calculations does not improve these barrier heights and reaction energies. The error of FN-DMC on barrier heights and reaction energies is slightly larger than that of MN15 and those of double hybrids, but it can achieve results within chemical accuracy for these reactions and the X-H bond energies.

An intramolecular vibrationally excited intermolecular potential energy surface and predicted 2OH overtone spectroscopy of H2O-Kr.

A new five-dimensional potential energy surface (PES) for H2O-Kr which explicitly includes the intramolecular 2OH overtone state of the H2O monomer is presented. The intermolecular potential energies were evaluated using explicitly correlated coupled cluster theory [CCSD(T)-F12] with a large basis set. Four vibrationally averaged analytical intermolecular PESs for H2O-Kr with H2O molecules in its |00+〉, |02+〉, |02-〉, and |11+〉 states are obtained by fitting to the multi-dimensional Morse/Long-Range potential function form. Each vibrationally averaged PES fitted to 578 points has root-mean-square (RMS) deviations smaller than 0.14 cm-1 and requires only 58 parameters. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels for |00+〉, |02+〉, |02-〉, and |11+〉 states of the H2O-Kr complexes. The calculated |02-〉Πf/e(101) ← |00+〉Σe(000) and |02+〉Πf/e(110) ← |00+〉Σe(101) infrared transitions are in excellent agreement with the experimental values with RMS discrepancies being only 0.007 and 0.016 cm-1, respectively. These analytical PESs can be used to provide reliable theoretical guidance for future infrared overtone spectroscopy of H2O-Kr.

Benchmarking ionization potentials using the simple pCCD model.

The electron-detachment energy is measured by the ionization potential (IP). As a result, it is a fundamental, observable and important molecular electronic signature in photoelectron spectroscopy. A precise theoretical prediction of electron-detachment energies or ionization potentials is essential for organic optoelectronic systems like transistors, solar cells, or light-emitting diodes. In this work, we benchmark the performance of the recently presented IP variant of the equation-of-motion pair coupled cluster doubles (IP-EOM-pCCD) model to determine IPs. Specifically, the predicted ionization energies are compared to experimental results and higher-order coupled cluster theories based on statistically assessing 201 electron-detached states of 41 organic molecules for three different molecular orbital basis sets and two sets of particle-hole operators. While IP-EOM-pCCD features a reasonable spread and skewness of ionization energies, its mean error and standard deviation differ by up to 1.5 eV from reference data. Our study, thus, highlights the importance of dynamical correlation to reliably predict IPs from a pCCD reference function in small organic molecules.

Incinerability of PFOA and HFPO-DA: Mechanisms, kinetics, and thermal stability ranking

Thermal treatment is currently the only full-scale technology for the destruction of per- and polyfluoroalkyl substances (PFAS) in wastes. However, concerns exist about the emission of incomplete combustion products from incinerators. To address critical knowledge gaps around the incinerability of PFAS, highest-level coupled cluster theory was applied to elucidate the primary thermal destruction pathways, mechanisms, and kinetics for perfluorooctanoic acid (PFOA) and hexafluoropropylene oxide dimer acid (HFPO-DA, sometimes referred to as “GenX”). These PFAS were then ranked based on U.S. EPA's Thermal Stability Index, which ranges from Class 1 for the most thermally stable chemicals to Class 7 for the most thermally labile chemicals. Initial decomposition of both carboxylic acids proceeds through HF elimination at the α-carbon, but for PFOA surprisingly shifts towards C-COOH bond dissociation in the presence of ammonia due to ammonium stabilization of the variational transition state. Branching substantially reduces the required incineration temperatures, while chain length has no impact on perfluoroalkyl carboxylic acid (PFCA) decomposition rates. Bimolecular reactions with secondary species such as counterions and radicals have lower activation barriers than unimolecular decomposition, but their second-order kinetics depend on concentration and thus waste stream composition, which varies in practice. Simulating radical concentrations under typical incineration conditions, the determined free energies of activation suggest an incinerability ranking for linear PFOA in Class 3, for branched PFOA in Class 4, and for HFPO-DA as well as both PFOA and HFPO-DA ammonium salts in Class 5. Collectively, the temperatures needed to destroy 99.99% of PFOA, HFPO-DA, and other PFCAs in 2 seconds gas residence time are well below those of other commonly incinerated organic compounds such as chlorobenzene (Class 1). Ultimately, sufficient supply of radical donors is critical to ensure safe, efficient, and complete destruction of PFAS during thermal treatment.

A transferable recommender approach for selecting the best density functional approximations in chemical discovery.

Approximate density functional theory has become indispensable owing to its balanced cost-accuracy trade-off, including in large-scale screening. To date, however, no density functional approximation (DFA) with universal accuracy has been identified, leading to uncertainty in the quality of data generated from density functional theory. With electron density fitting and Δ-learning, we build a DFA recommender that selects the DFA with the lowest expected error with respect to the gold standard (but cost-prohibitive) coupled cluster theory in a system-specific manner. We demonstrate this recommender approach on the evaluation of vertical spin splitting energies of transition metal complexes. Our recommender predicts top-performing DFAs and yields excellent accuracy (about 2 kcal mol-1) for chemical discovery, outperforming both individual Δ-learning models and the best conventional single-functional approach from a set of 48 DFAs. By demonstrating transferability to diverse synthesized compounds, our recommender potentially addresses the accuracy versus scope dilemma broadly encountered in computational chemistry.

Relativistic ab initio study on the spectroscopic and radiative properties of the lowest states and modeling of the optical cycles for the LiFr molecule

The LiFr diatomic represents a promising candidate for indirect laser cooling that has not yet been investigated not theoretically or experimentally. The potential energy curves of the ground and low-lying excited states of the LiFr heteronuclear alkali metal dimer are calculated using the Fock-space relativistic coupled cluster theory for the first time. A number of properties such as the electronic term energies, equilibrium internuclear distances, transition and permanent dipole moments, sequences of vibrational energies, harmonic vibrational frequencies, Franck–Condon factors, and radiative lifetimes (including bound and free transitions) are predicted. The probabilities of the two-step schemes (optical cycles) for the transfer process of the LiFr molecules from high excited vibrational states to the ground vibronic state are also predicted. The data obtained would be useful for laser cooling and spectral experiments with LiFr molecules.

Connections between many-body perturbation and coupled-cluster theories.

Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.

A Cost Effective Scheme for the Highly Accurate Description of Intermolecular Binding in Large Complexes.

There has been a growing interest in quantitative predictions of the intermolecular binding energy of large complexes. One of the most important quantum chemical techniques capable of such predictions is the domain-based local pair natural orbital (DLPNO) scheme for the coupled cluster theory with singles, doubles, and iterative triples [CCSD(T)], whose results are extrapolated to the complete basis set (CBS) limit. Here, the DLPNO-based focal-point method is devised with the aim of obtaining CBS-extrapolated values that are very close to their canonical CCSD(T)/CBS counterparts, and thus may serve for routinely checking a performance of less expensive computational methods, for example, those based on the density-functional theory (DFT). The efficacy of this method is demonstrated for several sets of noncovalent complexes with varying amounts of the electrostatics, induction, and dispersion contributions to binding (as revealed by accurate DFT-based symmetry-adapted perturbation theory (SAPT) calculations). It is shown that when applied to dimeric models of poly(3-hydroxybutyrate) chains in its two polymorphic forms, the DLPNO-CCSD(T) and DFT-SAPT computational schemes agree to within about 2 kJ/mol of an absolute value of the interaction energy. These computational schemes thus should be useful for a reliable description of factors leading to the enthalpic stabilization of extended systems.

The subsystem quantum chemistry program Serenity

AbstractSERENITY [J Comput Chem. 2018;39:788–798] is an open‐source quantum chemistry software that provides an extensive development platform focused on quantum‐mechanical multilevel and embedding approaches. In this study, we give an overview over the developments done in Serenity since its original publication in 2018. This includes efficient electronic‐structure methods for ground states such as multilevel domain‐based local pair natural orbital coupled cluster and Møller–Plesset perturbation theory as well as the multistate frozen‐density embedding quasi‐diabatization method. For the description of excited states, SERENITY features various subsystem‐based methods such as embedding variants of coupled time‐dependent density‐functional theory, approximate second‐order coupled cluster theory and the second‐order algebraic diagrammatic construction technique as well as GW/Bethe–Salpeter equation approaches. SERENITY's modular structure allows combining these methods with density‐functional theory (DFT)‐based embedding through various practical realizations and variants of subsystem DFT including frozen‐density embedding, potential‐reconstruction techniques and projection‐based embedding.This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

How to renormalize coupled cluster theory

Coupled cluster theory is an attractive tool to solve the quantum many-body problem because its singles and doubles (CCSD) approximation is computationally affordable and yields about 90% of the correlation energy. Capturing the remaining 10%, e.g., via including triples, is numerically expensive. Here, we assume that short-range three-body correlations dominate and---following Lepage (arXiv:nucl-th/9706029)---that their effects can be included within CCSD by renormalizing the three-body contact interaction. We renormalize this contact in $^{16}\mathrm{O}$ and obtain systematically improved CCSD results for $^{24}\mathrm{O}, ^{20--34}\mathrm{Ne}, ^{40,48}\mathrm{Ca}, ^{78}\mathrm{Ni}, ^{90}\mathrm{Zr}$, and $^{100}\mathrm{Sn}$.

Cluster Amplitudes and Their Interplay with Self-Consistency in Density Functional Methods.

Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic density, ground state energy, and related properties. However, for dissociation of molecular systems into open-shell fragments, due to the self-interaction error present in a large number of density functional approximations, the self-consistent procedure based on the this type of transformation gives rise to the well-known charge delocalization problem. To avoid this issue, we showed previously that the cluster operator of coupled-cluster theory can be utilized within the context of DFT to solve in an alternative and approximate fashion the ground-state self-consistent problem. This work further examines the application of the singles cluster operator to molecular ground state calculations. Two approximations are derived and explored: i) A linearized scheme of the quadratic equation used to determine the cluster amplitudes. ii) The effect of carrying the calculations in a non-self-consistent field fashion. These approaches are found to be capable of improving the energy and density of the system and are quite stable in either case. The theoretical framework discussed in this work could be used to describe, with an added flexibility, quantum systems that display challenging features and require expanded theoretical methods.

Core spectroscopy of oxazole.

We have measured, analyzed, and simulated the ground state valence photoelectron spectrum, x-ray absorption (XA) spectrum, x-ray photoelectron (XP) spectrum as well as normal and resonant Auger-Meitner electron (AE) spectrum of oxazole at the carbon, oxygen, and nitrogen K-edge in order to understand its electronic structure. Experimental data are compared to theoretical calculations performed at the coupled cluster, restricted active space perturbation theory to second-order and time-dependent density functional levels of theory. We demonstrate (1) that both N and O K-edge XA spectra are sensitive to the amount of dynamical electron correlation included in the theoretical description and (2) that for a complete description of XP spectra, additional orbital correlation and orbital relaxation effects need to be considered. The normal AE spectra are dominated by a singlet excitation channel and well described by theory. The resonant AE spectra, however, are more complicated. While the participator decay channels, dominating at higher kinetic energies, are well described by coupled cluster theory, spectator channels can only be described satisfactorily using a method that combines restricted active space perturbation theory to second order for the bound part and a one-center approximation for the continuum.

Isotope shifts in cadmium as a sensitive probe for physics beyond the standard model

Isotope shifts (ISs) of atomic energy levels are sensitive probes of nuclear structure and new physics beyond the standard model. We present an analysis of the ISs of the cadmium atom (Cd I) and singly charged cadmium ion (Cd II). ISs of the 229 nm, 326 nm, 361 nm and 480 nm lines of Cd I are measured with a variety of techniques; buffer–gas-cooled beam spectroscopy, capturing atoms in a magneto-optic-trap, and optical pumping. IS constants for the D1 and D2 lines of Cd II are calculated with high accuracy by employing analytical response relativistic coupled-cluster theory in the singles, doubles and triples approximations. Combining the calculations for Cd II with experiments, we infer IS constants for all low-lying transitions in Cd I. We benchmark existing calculations via different many-body methods against these constants. Our calculations for Cd II enable nuclear charge radii of Cd isotopes to be extracted with unprecedented accuracy. The combination of our precise calculations and measurements shows that King plots for Cd I can improve the state-of-the-art sensitivity to a new heavy boson by up to two orders of magnitude.