A comparative study of single reference correlation methods of the coupled-pair type

Actinide-Actinide Bonding: Electron Delocalisation and σ-Aromaticity in the Tri-Thorium Cluster [{Th(η8 -C8 H8 )(μ-Cl)2 }3 K2 ]

The tri-thorium cluster [{Th(η8 -C8 H8 )(μ3 -Cl)2 }3 {K(THF)2 }2 ]∞ (Nature 2021, 598, 72-75) was reported to feature intriguing σ-aromatic bonding between the thorium atoms, a mode of metal-metal bonding unique in the actinide series. However, the presence of this bonding motif has since been challenged by others. Here, we computationally explore electron delocalisation in a molecular cluster fragment of [{Th(η8 -C8 H8 )(μ3 -Cl)2 }3 {K(THF)2 }2 ]∞ and examine its responses to an applied magnetic field using a variety of methods. We also discuss the importance of the choice of basis set for the Th atoms and issues regarding locating QTAIM bond critical points. When taken together, the computed data consistently suggest the presence of delocalised Th-Th bonding and Th3 σ-aromaticity.

New Local Explorations of the Unitary Coupled Cluster Energy Landscape

The recent quantum information boom has effected a resurgence of interest in the unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ansätze prompted us to investigate the classical approach of truncating the Taylor series expansion (instead of a perturbative expansion) of the UCC with singles and doubles (UCCSD) energy at the second order. This amounts to an approach where the electron correlation energy is estimated by taking a single Newton-Raphson step from Hartree-Fock toward UCCSD. Such an approach has been explored previously, but the accuracy was not extensively studied. In this paper, we investigate the performance and observe similar pathologies to the linearized coupled cluster with singles and doubles. We introduce the use of derivatives of order three or greater to help partially recover the variational lower bound of true UCCSD, restricting these derivatives to those of the "unmixed" category in order to simplify the model. By testing the approach on several potential energy surfaces and reaction energies, we find this "diagonal" approximation to higher order terms to be effective at reducing sensitivity near singularities for strongly correlated regimes, while not significantly diminishing the accuracy of weakly correlated systems.

Molecules of life: studying the interaction between water and phosphine in argon matrices

The interaction between water and phosphine isolated in solid argon matrices has been investigated. Infrared spectra of matrices containing water and phosphine, as well as their deuterium and ¹⁸O isotopologues, revealed that a weak hydrogen bonded complex is formed, with an O-H⋯P bonding motif. This was supported by high level ab initio calculations, which predict a binding energy of only 5.1 kJ mol^-1 (430 cm^-1).

Accurate Property Prediction by Second Order Perturbation Theory: The REMP and OO-REMP Hybrids

The prediction of molecular properties such as equilibrium structures or vibrationalwavenumbers is a routine task in computational chemistry. If very high accuracy is required, however, the use of computationally demanding ab initio wavefunction methods is mandatory. We present property calculations utilizing the REMP and OO-REMP hybrid perturbation theories showing that with the latter approach, very accurate results are obtained at second order in perturbation theory. Specifically, equilibrium structures and harmonic vibrational wavenumbers as well as dipole moments of closed and open shell molecules were calculated and compared to the best available experimental results or very accurate calculations.OO-REMP is capable of predicting bond lengths of small closed and open shell molecules with an accuracy of 0.2 pm and 0.5 pm, respectively, often within the range of experimental uncertainty. Equilibrium harmonic vibrational wavenumbers are predicted with an accuracy better than 20 cm−1 . Dipole moments of small closed and open shell molecules are reproduced with a relative error of less than 3 %. Across all investigated properties it turns out that a 20 %:80 % MP:RE mixing ratio consistently provides the best results. This is in line with our previous findings featuring closed and open shell reaction energies.

Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions

Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH₄ and F₂ where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

57Fe Mössbauer parameters from domain based local pair-natural orbital coupled-cluster theory

We report on applications of the domain based local pair-natural orbital (PNO) coupled-cluster method within the singles and doubles approximation (DLPNO-CCSD) to the calculation of ⁵⁷Fe isomer shifts and quadrupole splittings in a small training set of iron complexes consisting of large molecular ligands and iron atoms in varying charge, spin, and oxidation states. The electron densities and electric field gradients needed for these calculations were obtained within the recently implemented analytic derivative scheme. A method for the direct treatment of scalar relativistic effects in the calculation of effective electron densities is described by using the first-order Douglas-Kroll-Hess Hamiltonian and a Gaussian charge distribution model for the nucleus. The performance of DLPNO-CCSD is compared with four modern-day density functionals, namely, RPBE, TPSS, B3LYP, and B2PLYP, as well as with the second-order Møller-Plesset perturbation theory. An excellent correlation between the calculated electron densities and the experimental isomer shifts is attained with the DLPNO-CCSD method. The correlation constant a obtained from the slope of the linear correlation plot is found to be ≈-0.31 a.u.³ mm s^-1, which agrees very well with the experimental calibration constant α = -0.31 ± 0.04 a.u.³ mm s^-1. This value of a is obtained consistently using both nonrelativistic and scalar relativistic DLPNO-CCSD electron densities. While the B3LYP and B2PLYP functionals achieve equally good correlation between theory and experiment, the correlation constant a is found to deviate from the experimental value. Similar trends are observed also for quadrupole splittings. The value of the nuclear quadrupole moment for ⁵⁷Fe is estimated to be 0.15 b at the DLPNO-CCSD level. This is consistent with previous results and is here supported by a higher level of theory. The DLPNO-CCSD results are found to be insensitive to the intrinsic approximations in the method, in particular the PNO occupation number truncation error, while the results obtained with density functional theory (DFT) are found to depend on the choice of the functional. In a statistical sense, i.e., on the basis of the linear regression analysis, however, the accuracies of the DFT and DLPNO-CCSD results can be considered comparable.

Nucleophilic Fluorination with KF Catalyzed by 18-Crown-6 and Bulky Diols: A Theoretical and Experimental Study

The activation of potassium fluoride for nucleophilic fluorination of alkyl halides is an important challenge because of the high lattice energy of this salt and its low solubility in many polar aprotic solvents. Crown ethers have been used for increasing the solubilization of KF during several decades. Nevertheless, these macrocycles are not enough to produce a high reaction rate. In this work, theoretical methods were used for designing a synergic combination of bulky diols with crown ethers able to accelerate this kind of reaction. The calculations have predicted that the bulky diol 1,4-Bis(2-hydroxy-2-propyl)benzene, which has distant hydroxyl groups, is able to catalyze nucleophilic fluorination in combination with 18-crown-6 via two hydrogen bonds to the S_N2 transition state. Experimental studies following the theoretical predictions have confirmed the catalytic effect and the estimated kinetic data point out that the bulky diol at 1 mol L^-1 in combination with 18-crown-6 is able to produce an 18-fold increase in the reaction rate in relation to crown ether catalysis only. The reaction produces 46% yield of fluorination after 24 h at moderate temperature of 82 °C, with minimal formation of the side elimination product. Thus, this work presents an improved method for fluorination with KF salt.

Benchmarking the inversion barriers in σ3λ3-phosphorus compounds: a computational study

Benchmark study of three mechanisms for inversion at phosphorus, including parametric criteria for classification and analysis of factors affecting barriers.

REMP: A hybrid perturbation theory providing improved electronic wavefunctions and properties

We propose a new perturbation theoretical approach to the electron correlation energy by choosing the zeroth order Hamiltonian as a linear combination of the corresponding "Retaining the Excitation degree" (RE) and the Møller-Plesset (MP) operators. In order to fulfill Kato cusp conditions, the RE and MP contributions are chosen to sum up to one. 15% ± 5% MP contribution is deduced to be in an optimal range from a fit of the first order REMP wavefunction to near full configuration interaction reference data. For closed shell systems, the same range of MP weights shows best performance for equilibrium bond distances and vibrational wavenumbers of diatomic molecules, the reaction energies in the spin component scaled MP2 fit set, the transition energies of the BHPERI test set, and the parameterized coupled cluster with singles and doubles (pCCSD) fit set. For these properties, REMP outperforms all other tested perturbation theories at second order and shows equal performance as the best coupled pair approaches or pCCSD methods as well as the best double hybrid density functionals. Furthermore, REMP is shown to fulfill all required fundamental boundary conditions of proper wavefunction based quantum chemical methods (unitary invariance and size consistency).

Quantum Chemical Calculations on CHOP Derivatives-Spanning the Chemical Space of Phosphinidenes, Phosphaketenes, Oxaphosphirenes, and COP- Isomers

After many decades of intense research in low-coordinate phosphorus chemistry, the advent of Na[OCP] brought new stimuli to the field of CHOP isomers and derivatives thereof. The present theoretical study at the CCSD(T)/def2-TZVPP level describes the chemical space of CHOP isomers in terms of structures and potential energy surfaces, using oxaphosphirene as the starting point, but also covering substituted derivatives and COP- isomers. Bonding properties of the P⁻C, P⁻O, and C⁻O bonds in all neutral and anionic isomeric species are discussed on the basis of theoretical calculations using various bond strengths descriptors such as WBI and MBO, but also the Lagrangian kinetic energy density per electron as well as relaxed force constants. Ring strain energies of the superstrained 1H-oxaphosphirene and its barely strained oxaphosphirane-3-ylidene isomer were comparatively evaluated with homodesmotic and hyperhomodesmotic reactions. Furthermore, first time calculation of the ring strain energy of an anionic ring is described for the case of oxaphosphirenide.

Can density cumulant functional theory describe static correlation effects?

We evaluate the performance of density cumulant functional theory (DCT) for capturing static correlation effects. In particular, we examine systems with significant multideterminant character of the electronic wave function, such as the beryllium dimer, diatomic carbon, m-benzyne, 2,6-pyridyne, twisted ethylene, as well as the barrier for double-bond migration in cyclobutadiene. We compute molecular properties of these systems using the ODC-12 and DC-12 variants of DCT and compare these results to multireference configuration interaction and multireference coupled-cluster theories, as well as single-reference coupled-cluster theory with single, double (CCSD), and perturbative triple excitations [CCSD(T)]. For all systems the DCT methods show intermediate performance between that of CCSD and CCSD(T), with significant improvement over the former method. In particular, for the beryllium dimer, m-benzyne, and 2,6-pyridyne, the ODC-12 method along with CCSD(T) correctly predict the global minimum structures, while CCSD predictions fail qualitatively, underestimating the multireference effects. Our results suggest that the DC-12 and ODC-12 methods are capable of describing emerging static correlation effects but should be used cautiously when highly accurate results are required. Conveniently, the appearance of multireference effects in DCT can be diagnosed by analyzing the DCT natural orbital occupations, which are readily available at the end of the energy computation.

CPh3 as a functional group in P-heterocyclic chemistry: elimination of HCPh3 in the reaction of P-CPh3 substituted Li/Cl phosphinidenoid complexes with Ph2CO

Li/Cl phosphinidenoid complexes 2a–c react with benzaldehyde to give 3a–c, but with benzophenone formation of complexes 4 and 5 was observed, the latter revealing the elimination of HCPh₃.

Mechanism and free energy profile of base-catalyzed Knoevenagel condensation reaction

A reliable theoretical calculation of the free energy profile of a base-catalyzed Knoevenagel reaction shows that hydroxide ion elimination step is rate determining.

Rearrangement and deoxygenation of 3,3-bis(2-pyridyl)oxaphosphirane complexes

The reaction of Li/Cl phosphinidenoid pentacarbonylmetal(0) complexes with bis(2-pyridyl)ketone led to overcrowded oxaphosphirane derivatives. They can undergo deoxygenation by Ti(iii) reagents or ring expansion via P–C cleavage followed by P–N cyclization.

Benchmark Study of Density Cumulant Functional Theory: Thermochemistry and Kinetics

We present an extensive benchmark study of density cumulant functional theory (DCFT) for thermochemistry and kinetics of closed- and open-shell molecules. The performance of DCFT methods (DC-06, DC-12, ODC-06, and ODC-12) is compared to that of coupled-electron pair methods (CEPA0 and OCEPA0) and coupled-cluster theory (CCSD and CCSD(T)) for the description of noncovalent interactions (A24 database), barrier heights of hydrogen-transfer reactions (HTBH38), radical stabilization energies (RSE30), adiabatic ionization energies (AIE), and covalent bond stretching in diatomic molecules. Our results indicate that out of four DCFT methods the ODC-12 method is the most reliable and accurate DCFT formulation to date. Compared to CCSD, ODC-12 shows superior results for all benchmark tests employed in our study. With respect to coupled-pair theories, ODC-12 outperforms CEPA0 and shows similar accuracy to the orbital-optimized CEPA0 variant (OCEPA0) for systems at equilibrium geometries. For covalent bond stretching, ODC-12 is found to be more reliable than OCEPA0. For the RSE30 and AIE data sets, ODC-12 shows competitive performance with CCSD(T). In addition to benchmark results, we report new reference values for the RSE30 data set computed using coupled cluster theory with up to perturbative quadruple excitations.

Density cumulant functional theory from a unitary transformation: N-representability, three-particle correlation effects, and application to O4(+)

A new approach to density cumulant functional theory is developed that derives density cumulant N-representability conditions from an approximate Fock space unitary transformation. We present explicit equations for the third- and fourth-order two-particle cumulant N-representability, as well as the second-order contributions that depend on the connected three-particle density cumulant. These conditions are used to formulate the ODC-13 method and the non-iterative (λ3) correction that employ an incomplete description of the fourth-order two-particle cumulant N-representability and the second-order three-particle correlation effects, respectively. We perform an analysis of the ODC-13 N-representability description for the dissociation of H2 and apply the ODC-13 method and the (λ3) correction to diatomic molecules with multiple bond character and the symmetry-breaking tetraoxygen cation (O4(+)). For the O4(+) molecule, the vibrational frequencies of the ODC-13(λ3) method do not exhibit spatial symmetry breaking and are in a good agreement with the recent infrared photodissociation experiment. We report the O4(+) equilibrium structure, harmonic frequencies, and dissociation energy computed using ODC-13(λ3) with a diffuse, core-correlated aug-cc-pCVTZ basis set.

Multifunctional Benzothiadiazole-Based Small Molecules Displaying Solvatochromism and Sensing Properties toward Nitroarenes, Anions, and Cations

Aryl or heteroaryl 5-substituted imidazo-benzothiadiazole derivatives were synthesized and shown to display remarkable solvatofluorochromism and selectively sense mercury(II) cations, acetate anions, and nitroaromatic derivatives, with discrimination between p-nitrophenol and picric acid. These novel sensors are of importance these days, as the detection of explosives is a high priority in issues of national security and environmental protection. To determine the ion binding properties of the sensors, their absorption and fluorescence emission spectra upon binding different cations and anions were compared. Significant shifts in the spectra were only observed for mercury(II) and acetate. The binding of these two ions was further studied using (1)H NMR. The binding properties of different nitroaromatic compounds were also determined, and the results showed the importance of the presence of a phenol group in the guest molecule. Specifically, the two sensors were shown to discriminate between p-nitrophenol and picric acid. Finally, the mechanism of fluorescence quenching upon addition of nitrophenols was determined by computational methods.

Orbital-optimized density cumulant functional theory

In density cumulant functional theory (DCFT) the electronic energy is evaluated from the one-particle density matrix and two-particle density cumulant, circumventing the computation of the wavefunction. To achieve this, the one-particle density matrix is decomposed exactly into the mean-field (idempotent) and correlation components. While the latter can be entirely derived from the density cumulant, the former must be obtained by choosing a specific set of orbitals. In the original DCFT formulation [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] the orbitals were determined by diagonalizing the effective Fock operator, which introduces partial orbital relaxation. Here we present a new orbital-optimized formulation of DCFT where the energy is variationally minimized with respect to orbital rotations. This introduces important energy contributions and significantly improves the description of the dynamic correlation. In addition, it greatly simplifies the computation of analytic gradients, for which expressions are also presented. We offer a perturbative analysis of the new orbital stationarity conditions and benchmark their performance for a variety of chemical systems.