The variational quantum eigensolver self-consistent field method within a polarizable embedded framework

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.

On the performance of HRPA(D) for NMR spin-spin coupling constants: Smaller molecules, aromatic and fluoroaromatic compounds

In this study, the performance of the doubles-corrected higher random-phase approximation [HRPA(D)] has been investigated in calculations of nuclear magnetic resonance spin-spin coupling constants (SSCCs) for 58 molecules with the experimental values used as the reference values. HRPA(D) is an approximation to the second-order polarization propagator approximation (SOPPA) and is, therefore, computationally less expensive than SOPPA. HRPA(D) performs comparable and sometimes even better than SOPPA, and therefore, when calculating SSCCs, it should be considered as an alternative to SOPPA. Furthermore, it was investigated whether a coupled-cluster singles, doubles and perturbative triples [CCSD(T)] or Møller-Plesset second order (MP2) geometry optimization was optimal for a SOPPA and a HRPA(D) SSCC calculation for eight smaller molecules. CCSD(T) is the optimal geometry optimization for the SOPPA calculation, and MP2 was optimal for HRPA(D) SSCC calculations.

Exploring Alternate Methods for the Calculation of High-Level Vibrational Corrections of NMR Spin-Spin Coupling Constants

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wave function that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wave function and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarization propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available (i.e., CC3//CCSD(T) + CCSD//CCSD(T)). CCSD//CCSD(T) statistics showed favorable statistics in comparison to experimental values, albeit at an unfavorably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all of the other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational-corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis set or lack of solvation effects for the CC3 equilibrium calculations.

A Theoretical Study of Hydrogen Abstraction Reactions in Guanosine and Uridine

All practically possible hydrogen abstraction reactions for guanosine and uridine have been investigated through quantum chemical calculations of energy barriers and rate constants. This was done at the level of density functional theory (DFT) with the ωB97X-D functional and the 6-311++G(2df,2pd) Pople basis set. Transition state theory with the Eckart tunneling correction was used to calculate the rate constants. The results show that the reaction involving the hydrogen labelled C4' in the ribofuranose part has the largest rate constant for guanosine with the value 5.097×1010 L mol-1s-1 and the largest for uridine with the value 1.62×1010 L mol-1s-1. Based on the results for these two nucleosides, there is a noticeable similarity between the rate constants in the ribofuranose part of the molecule, even though they are bound to two entirely different nucleobases.

Calculation of electric field gradients in Cd(II) model complexes of the CueR protein metal site

With this work we first test various DFT functionals against CCSD(T) for calculation of EFGs at the position of Cd(II) in a very small model system, Cd(SCH₃)₂. Moreover, the available basis sets in ADF are tested in terms of basis set convergence, and the effect of including relativistic effects using the scalar relativistic and spin orbit ZORA Hamiltonians is explored. The results indicate that an error of up to around 10% on the calculated EFG may be expected using spin-orbit ZORA and the BHandHLYP functional with a locally dense basis set. Next, this method was applied to model systems of the CueR protein, aiming to interpret ¹¹¹Ag-PAC spectroscopic data. Note that ¹¹¹Ag decays to ¹¹¹Cd on which the PAC data are recorded. Surprisingly, model systems truncated - as is often done - at the first C-C bond from the central Cd(II) are inadequate in size, and larger model systems must be employed to achieve reliable EFG calculations. The calculated EFGs agree well with experimental PAC data, and indicate that shortly after the nuclear decay the structure relaxes from linear two-coordinate AgS₂ in the native protein, to a structure (or structures) where Cd(II) recruits additional ligands such as backbone carbonyl oxygens to achieve higher coordination number(s).

Indirect nuclear spin-spin couplings with third order contributions added to the SOPPA method

In this article, a modification of the second order polarization propagator approximation (SOPPA) method is introduced and illustrated for the calculation of the indirect nuclear spin-spin couplings. The standard SOPPA method, although cheaper in terms of computational cost, offers less accurate results than the ones obtained with coupled cluster methods. A new method, named SOPPA+A3-3, was therefore developed by adding the terms of the third order A matrix that rely on the second order double amplitudes. The performance of this third order contribution was studied using the CCSD method as a reference, calculating the spin-spin couplings of molecules of diverse sizes and compositions, and comparing them to the SOPPA method. The results show that inclusion of this third order contribution gives more accurate results than the standard SOPPA method with a level of accuracy close to that of the coupled cluster method with only small increase of computational cost of the response calculation that dominates the computational cost for small to medium sized molecules. The implementation of the first contributions to the third order polarization propagator approximation (TOPPA) in the Dalton program thus already shows a significant change in these molecular properties over those obtained with the standard SOPPA method.

A Combined Experimental and Theoretical Study of ESR Hyperfine Coupling Constants for N,N,N',N'-Tetrasubstituted p-Phenylenediamine Radical Cations

A test set of N,N,N',N'-tetrasubstituted p-phenylenediamines are experimentally explored using ESR (electron spin resonance) spectroscopy and analysed from a computational standpoint thereafter. This computational study aims to further aid structural characterisation by comparing experimental ESR hyperfine coupling constants (hfccs) with computed values calculated using ESR-optimised "J-style" basis sets (6-31G(d,p)-J, 6-31G(d,p)-J, 6-311++G(d,p)-J, pcJ-1, pcJ-2 and cc-pVTZ-J) and hybrid-DFT functionals (B3LYP, PBE0, TPSSh, ωB97XD) as well as MP2. PBE0/6-31g(d,p)-J with a polarised continuum solvation model (PCM) correlated best with the experiment, giving an R2 value of 0.8926. A total of 98% of couplings were deemed satisfactory, with five couplings observed as outlier results, thus degrading correlation values significantly. A higher-level electronic structure method, namely MP2, was sought to improve outlier couplings, but only a minority of couples showed improvement, whilst the remaining majority of couplings were negatively degraded.

Magnesium(II)‐ATP Complexes in 1‐Ethyl‐3‐Methylimidazolium Acetate Solutions Characterized by 31 Mg β‐Radiation‐Detected NMR Spectroscopy

The complexation of Mg^II with adenosine 5′‐triphosphate (ATP) is omnipresent in biochemical energy conversion, but is difficult to interrogate directly. Here we use the spin‐1/2 β‐emitter ³¹Mg to study Mg^II‐ATP complexation in 1‐ethyl‐3‐methylimidazolium acetate (EMIM‐Ac) solutions using β‐radiation‐detected nuclear magnetic resonance (β‐NMR). We demonstrate that (nuclear) spin‐polarized ³¹Mg, following ion‐implantation from an accelerator beamline into EMIM‐Ac, binds to ATP within its radioactive lifetime before depolarizing. The evolution of the spectra with solute concentration indicates that the implanted ³¹Mg initially bind to the solvent acetate anions, whereafter they undergo dynamic exchange and form either a mono‐ (³¹Mg‐ATP) or di‐nuclear (³¹MgMg‐ATP) complex. The chemical shift of ³¹Mg‐ATP is observed up‐field of ³¹MgMg‐ATP, in accord with quantum chemical calculations. These observations constitute a crucial advance towards using β‐NMR to probe chemistry and biochemistry in solution.

A tale of two vectors: A Lanczos algorithm for calculating RPA mean excitation energies

The experimental and theoretical determination of the mean excitation energy, I(0), and the stopping power, S(v), of a material is of great interest in particle and material physics and radiation therapy. For calculations of I(0), the complete set of electronic transitions in a given basis set is required, effectively limiting such calculations to systems with a small number of electrons, even at the random-phase approximation (RPA)/time-dependent Hartree-Fock (TDHF) or time-dependent density-functional theory level. To overcome such limitations, we present here the implementation of a Lanczos algorithm adapted for the paired RPA/TDHF eigenvalue problem in the Dalton program and show that it provides good approximation of the entire RPA eigenspectra in a reduced space. We observe rapid convergence of I(0) with the number of Lanczos vectors as the algorithm favors the transitions with large contributions. In most cases, the algorithm recovers RPA I(0) values of up to 0.5% accuracy at less than a quarter of the full space size. The algorithm not only exploits the RPA paired structure to save computational resources but also preserves certain sum-over-states properties, as first demonstrated by Johnson et al. [Comput. Phys. Commun. 120, 155 (1999)]. The block Lanczos RPA solver, as presented here, thus shows promise for computing mean excitation energies for systems larger than what was computationally feasible before.

On the Unexpected Accuracy of the M06L Functional in the Calculation of 1JFC Spin-Spin Coupling Constants

One-bond spin-spin coupling constants (SSCCs) between F and C are computed with density functional theory (DFT). Surprisingly, M06L stands out for its striking accuracy, outperforming any other investigated functional, including PBE0, otherwise considered one of the most reliable for couplings involving F. Although the computation of nuclear magnetic resonance (NMR) parameters involving F is known to be a challenging task, even with a rather small basis set as pcJ-1, M06L provides results with a MAD = 11.7 Hz, whereas the average deviation gets as much as 5 times larger for PBE0 (MAD = 60.0 Hz). In the context of SSCCs on the order of 300 Hz, this is particularly remarkable. We find that the accuracy of M06L/pcJ-1 in predicting ¹J_FC constants does not stem from a well-suited exchange or correlation part of the functional. Instead, it is believed to arise from a fortuitous cancellation of errors, as revealed by investigating the convergence of the basis set. Our findings also indicate that ¹J_FC constants are highly dependent on the amount of exact exchange included in the expression of the functional, with large fractions being critically important to achieving satisfactory results. Studying the effects of the geometry on ¹J_FC, we find that optimizing the geometry at the level of theory used to calculate SSCCs generally improves the quality of the results, although the combination of a M06-2X/aug-cc-pVTZ geometry with M06L/pcJ-1 ¹J_FC constants best reproduces the experimental data for organofluorine compounds (with the exception of fluoroalkenes).

Azo-hydrazone molecular switches: Synthesis and NMR conformational investigation

A series of five intramolecularly hydrogen-bonded arylhydrazone (aryl = phenol, p-nitrophenol, anisole, quinoline) derived molecular switches have been synthesized and characterized by NMR and HRMS techniques. It was found that the compounds exist as different isomers in solution. An investigation of both conformational and/or configurational changes of the azo-hydrazone compounds was carried out by 1D ¹ H- and ¹³ C- spectra, 2D NOESY, COSY, HSQC, and HMBC techniques. It was found that these stimuli-responsive molecular switches exist mainly in the E form by intramolecularly hydrogen bonded between NH and the pyridine nitrogen at equilibrium. Deprotonation of the neutral E form yields the E' deprotonated isomer. Prediction of ¹³ C-NMR chemical shifts was achieved by DFT quantum mechanical calculations. Anions have traditionally been difficult to calculate correctly, so calculations of the anion using different functionals, basis sets, and solvent effects are also included. Deuterium isotope effects on the ¹³ C-NMR chemical shifts were employed in the assignments and furthermore utilized as indicators of intramolecular hydrogen bonding. Studies in various organic solvents including CDCl₃ , CD₃ CN, and DMSO-d₆ were also performed aiming to monitor dynamic changes over several days. The effect of the hydrogen bonded solvents leads to Z forms.

The aug-cc-pVTZ-J basis set for the p-block fourth-row elements Ga, Ge, As, Se, and Br

The aug-cc-pVTZ-J basis set family is extended to include the fourth-row p-block elements Ga, Ge, As, Se, and Br. We use the established approach outlined by Sauer and coworkers (J. Chem. Phys. 115, 1324 [2001], J. Chem. Phys. 133, 054308 [2010], J. Chem. Theory Comput. 7, 4070 [2011], and J. Chem. Theory Comput. 7, 4077 [2011]) where the completely uncontracted aug-cc-pVTZ basis set is saturated with tight s-, p-, d-, and f-functions to form the aug-cc-pVTZ-Juc basis set for the tested elements. The saturation is carried out on the simplest hydrides possible for the tested elements GaH, GeH₄ , AsH₃ , H₂ Se, and HBr until an improvement is less than 0.01% for all s-, p-, and d-functions added. f-Functions are added to an improvement less than or equal to 1.0% due to the computational expense these functions add. The saturated aug-cc-pVTZ-Juc (26s16p12d5f) is then recontracted using the molecular orbital coefficients from self-consistent field calculations on the simple hydrides to improve computational efficiency. During contraction of the basis set, we observe that the linear hydrogen bromide molecule has a slower convergence than the other tested molecules which sets a limit on the accuracy obtained. All calculations with the contracted aug-cc-pVTZ-J [17s10p7d5f] gives results that are within 1.0% of the uncontracted results at considerable computational savings.

Prediction of the standard potentials for one-electron oxidation of N,N,N',N' tetrasubstituted p-phenylenediamines by calculation

The formal potentials for the reversible one-electron oxidation of N,N,N',N' tetrasubstituted p-phenylenediamines in acetonitrile have been applied as a test set for benchmarking computational methods for a series of compounds with only small structural differences. The aim of the study is to propose a simple method for calculating the standard oxidation potentials, and therefore, the protocol is progressively developed by adding more terms in the energy expression. In addition, the effect of including implicit solvation models (IEFPCM, CPCM, and SMD), larger basis sets, and correlation methods are investigated. The oxidation potentials calculated using the G3MP2B3 approach with IEFPCM resulted in the best fit (R² = 0.9624), but the slope of the correlation line, 0.74, is far from the optimal value, 1.00. B3LYP/6-311++G(d,p) and TPSSh/6-311++G(2d,p) yielded only slightly less consistent data (R² = 0.9388 and R² = 0.9425), but with much better slopes, 1.00 and 0.94, respectively. We conclude that it is important to investigate the basis set size and treatment of electron correlation when calculating oxidation potentials for N,N,N',N' tetrasubstituted p-phenylenediamines.

The best density functional theory functional for the prediction of 1 H and 13 C chemical shifts of protonated alkylpyrroles

The prediction of ¹³ C chemical shifts can be challenging with density functional theory (DFT). In this study 39 different functionals and three different basis sets were tested on three neutral alkylpyrroles and their corresponding protonated species. The calculated shielding constants were compared to experimental data and results from previous calculations at the MP2. We find that the meta-hybrid functional TPSSh with either the Pople style basis set 6-311++G(2d,p) or the polarization consistent basis set pcSseg-1 gives the best results for the ¹³ C chemical shifts, whereas for the ¹ H chemical shifts it is the TPSSh functional with either the 6-311++G(2d,p) or pcSseg-2 basis set. Including an explicit solvent molecule hydrogen bonded to NH in the alkylpyrroles improves the results slightly for the ¹³ C chemical shifts. On the other hand, for ¹ H chemical shifts the opposite is true. Compared to calculations at the MP2 level none of the DFT functionals can compete with MP2 for the ¹³ C chemical shifts but for the ¹ H chemical shifts the investigated DFT functionals are shown to give better agreement with experiment than MP2 calculations.

Benchmarking Correlated Methods for Static and Dynamic Polarizabilities: The T145 Data Set Evaluated with RPA, RPA(D), HRPA, HRPA(D), SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, and CCSD

Due to the importance of predicting static and dynamic polarizabilities, the performance of various correlated linear response methods including random phase approximation (RPA), RPA(D), higher-order random phase approximation (HRPA), HRPA(D), second-order polarization propagator approximation (SOPPA), SOPPA(CC2), SOPPA(CCSD), CC2, and CCSD has been evaluated against CCSD(T) (static case) and CCSD (dynamic cases) for the T145 set of 145 organic molecules. The benchmark reveals that the HRPA(D) method has the best performance for both static and dynamic polarizabilities apart from CCSD. RPA(D) ranks second for the dynamic cases and third for the static case. Using coupled-cluster amplitudes in SOPPA(CCSD) and SOPPA(CC2), the SOPPA results are significantly improved. The HRPA method has the largest deviations from the reference values for both cases. In general, according to the performance and computational cost of the methods, the HRPA(D) and RPA(D) methods are proposed for calculations of static and dynamic polarizabilities of this and similar sets of molecules.

A Density Functional Theory Study of Optical Rotation in Some Aziridine and Oxirane Derivatives

We present time-dependent density functional theory (TDDFT) calculations of the electronic optical rotation (ORP) for seven oxirane and two aziridine derivatives in the gas phase and in solution and compare the results with the available experimental values. For seven of the studied molecules it is the first time that their optical rotation was studied theoretically and we have therefore investigated the influence of several settings in the TDDFT calculations on the results. This includes the choice of the one-electron basis set, the exchange-correlation functional or the particular polarizable continuum model (PCM). We can confirm that polarized quadruple zeta basis sets augmented with diffuse functions are necessary for converged results and find that the aug-pc-3 basis set is a viable alternative to the frequently employed aug-cc-pVQZ basis set. Based on our study, we cannot recommend the generalized gradient functional KT3 for calculations of the ORP in these compounds, whereas the hybrid functional PBE0 gives results quite similar to the long-range correct CAM-B3LYP functional. Finally, we observe large differences in the solvent effects predicted by the integral equation formalism of PCM and the SMD variant of PCM. For the majority of solute/solvent combinations in this study, we find that the SMD model in combination with the PBE0 functional and the aug-pc-3 basis set gives the best agreement with the experimental values.

A QM/MM study of the conformation stability and electronic structure of the photochromic switches derivatives of DHA/VHF in acetonitrile solution

We present a detailed theoretical study of the electronic absorption spectra and thermochemistry of molecular photoswitches composed of one and two photochromic units of dihydroazulene (DHA)/vinylheptafulvene (VHF) molecules. Six different isomers are considered depending on the ring opening/closure forms of the DHA units. The solvent effect of acetonitrile is investigated using a sequential Molecular Mechanics/Quantum Mechanics approach. The thermochemical investigations of these photochromic molecules were performed using the Free Energy Perturbation method, and the simulations were performed using Configurational Bias Monte Carlo. We show that to open the 5-member ring of the DHA, there is no significant gain in thermal release of energy for the back reaction when a unit or two DHA units are considered. Overall, we found agreement between the solvation free energy based on Monte Carlo simulations and the continuum solvent model. However, the cavitation term in the continuum model is shown to be a source of disagreement when the non-electrostatic terms are compared. The electronic absorption spectra are calculated using TDDFT CAM-B3LYP/cc-pVDZ. Agreement with experiment is obtained within 0.1 eV, considering statistically uncorrelated configurations from the simulations. Inhomogeneous broadening is also considered and found to be well described in all cases.

Free Molecule Studies by Perturbed γ-γ Angular Correlation: A New Path to Accurate Nuclear Quadrupole Moments

Accurate nuclear quadrupole moment values are essential as benchmarks for nuclear structure models and for the interpretation of experimentally determined nuclear quadrupole interactions in terms of electronic and molecular structure. Here, we present a novel route to such data by combining perturbed γ-γ angular correlation measurements on free small linear molecules, realized for the first time within this work, with state-of-the-art ab initio electronic structure calculations of the electric field gradient at the probe site. This approach, also feasible for a series of other cases, is applied to Hg and Cd halides, resulting in Q(^{199}Hg,5/2^{-})=+0.674(17)  b and Q(^{111}Cd,5/2^{+})=+0.664(7)  b.

NMR parameters of FNNF as a test for coupled-cluster methods: CCSDT shielding and CC3 spin-spin coupling

NMR shielding and spin-spin coupling constants of cis and trans isomers of FNNF have been determined to near-quantitative accuracy from ab initio calculations. The FNNF system, containing multiple N-F bonds and fluorine atoms, provides a severe test of computational methods. Coupled-cluster methods were used with large basis sets and complete basis set (CBS) extrapolations of the equilibrium geometry results, with vibrational and relativistic corrections. Shielding constants were calculated with basis sets as large as aug-cc-pCV7Z, together with coupled-cluster expansions up to CCSDT, at the all-electron CCSD(T)/aug-cc-pCVQZ optimized geometries. Spin-spin coupling constants have been determined with specialized versions of the correlation consistent basis sets ccJ-pVXZ, further augmented with diffuse functions. All-electron coupled-cluster methods up to CC3 were applied in these calculations. The results of this work highlight the application of state-of-the-art theoretical techniques, and provide the most accurate NMR properties of FNNF to date, which can serve to guide and supplement NMR experimentation.

Enhancing NMR Quantum Computation by Exploring Heavy Metal Complexes as Multiqubit Systems: A Theoretical Investigation

Assembled together with the most common qubits used in nuclear resonance magnetic (NMR) quantum computation experiments, spin-1/2 nuclei, such as ¹¹³Cd, ¹⁹⁹Hg, ¹²⁵Te, and ⁷⁷Se, could leverage the prospective scalable quantum computer architectures, enabling many and heteronuclear qubits for NMR quantum information processing (QIP) implementations. A computational design strategy for prescreening recently synthesized complexes of cadmium, mercury, tellurium, selenium, and phosphorus (called MRE complexes) as suitable qubit molecules for NMR QIP is reported. Chemical shifts and spin-spin coupling constants (SSCCs) in five MRE complexes were examined using the spin-orbit zeroth order regular approximation (ZORA) at the density functional theory level and the four-component relativistic Dirac-Kohn-Sham approach. In particular, the influence of different conformers, basis sets, exchange-correlation functionals, and methods to treat the relativistic as well as solvent effects were studied. The differences in the chemical shifts and SSCCs between different low energy conformers of the studied complexes were found to be very small. The TZ2P basis set was found to be the optimum choice for the studied chemical shifts, while the TZ2P-J basis set was the best for the couplings studied in this work. The PBE0 exchange-correlation functional exhibited the best performance for the studied MRE complexes. The addition of solvent effects has not improved on the gas phase results in comparison to the experiment, with the exception of the phosphorus chemical shift. The use of MRE complexes as qubit molecules for NMR QIP could face the challenges in single qubit control and multiqubit operations. They exhibit chemical shifts appropriately dispersed, allowing qubit addressability and exceptionally large spin-spin couplings, which could reduce the time of quantum gate operations and likely preserve the coherence.

Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

Noniterative Doubles Corrections to the Random Phase and Higher Random Phase Approximations: Singlet and Triplet Excitation Energies

The second‐order noniterative doubles‐corrected random phase approximation (RPA) method has been extended to triplet excitation energies and the doubles‐corrected higher RPA method as well as a shifted version for calculating singlet and triplet excitation energies are presented here for the first time. A benchmark set consisting of 20 molecules with a total of 117 singlet and 71 triplet excited states has been used to test the performance of the new methods by comparison with previous results obtained with the second‐order polarization propagator approximation (SOPPA) and the third order approximate coupled cluster singles, doubles and triples model CC3. In general, the second‐order doubles corrections to RPA and HRPA significantly reduce both the mean deviation as well as the standard deviation of the errors compared to the CC3 results. The accuracy of the new methods approaches the accuracy of the SOPPA method while using only 10–60% of the calculation time. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

RPA(D) and HRPA(D): Two new models for calculations of NMR indirect nuclear spin-spin coupling constants

In this article, the RPA(D) and HRPA(D) models for the calculation of linear response functions are presented. The performance of the new RPA(D) and HRPA(D) models is compared to the performance of the established RPA, HRPA, and SOPPA models in calculations of indirect nuclear spin-spin coupling constants using the CCSD model as a reference. The doubles correction offers a significant improvement on both the RPA and HRPA models; however, the improvement is more dramatic in the case of the RPA model. For all coupling types investigated in this study, the results obtained using the HRPA(D) model are comparable in accuracy to those given by the SOPPA model, while requiring between 30% and 90% of the calculation time needed for SOPPA. The RPA(D) model, while of slightly lower accuracy compared to the CCSD model than HRPA(D), offered calculation times of only approximately 25% of those required for SOPPA for all the investigated molecules. © 2018 Wiley Periodicals, Inc.

Determining short-lived solid forms during phase transformations using molecular dynamics

We demonstrate that elusive high-energy metastable crystal structures can be determined from molecular dynamics simulations.

Computational Prediction of 1 H and 13 C NMR Chemical Shifts for Protonated Alkylpyrroles: Electron Correlation and Not Solvation is the Salvation

Prediction of chemical shifts in organic cations is known to be a challenge. In this article we meet this challenge for α-protonated alkylpyrroles, a class of compounds not yet studied in this context, and present a combined experimental and theoretical study of the ¹³ C and ¹ H chemical shifts in three selected pyrroles. We have investigated the importance of the solvation model, basis set, and quantum chemical method with the goal of developing a simple computational protocol, which allows prediction of ¹³ C and ¹ H chemical shifts with sufficient accuracy for identifying such compounds in mixtures. We find that density functional theory with the B3LYP functional is not sufficient for reproducing all ¹³ C chemical shifts, whereas already the simplest correlated wave function model, Møller-Plesset perturbation theory (MP2), leads to almost perfect agreement with the experimental data. Treatment of solvent effects generally improves the agreement with experiment to some extent and can in most cases be accomplished by a simple polarizable continuum model. The only exception is the NH proton, which requires inclusion of explicit solvent molecules in the calculation.

Direct observation of Mg2+ complexes in ionic liquid solutions by 31Mg β-NMR spectroscopy

NMR spectra of Mg2+ ions in ionic liquids were recorded using a highly sensitive variant of NMR spectroscopy known as β-NMR. The β-NMR spectra of MgCl2 in EMIM-Ac and EMIM-DCA compare favourably with conventional NMR, and exhibit linewidths of ∼3 ppm, allowing for discrimination of species with oxygen and nitrogen coordination.

Development of polarization consistent basis sets for spin-spin coupling constant calculations for the atoms Li, Be, Na, and Mg

The pcJ-n basis set, optimized for spin-spin coupling constant calculations using density functional theory methods, are expanded to also include the s-block elements Li, Be, Na, and Mg, by studying several small molecules containing these elements. This is done by decontracting the underlying pc-n basis sets, followed by augmentation with additional tight functions. As was the case for the p-block elements, the convergence of the results can be significantly improved by augmentation with tight s-functions. For the p-block elements, additional tight functions of higher angular momentum were also needed, but this is not the case for the s-block elements. A search for the optimum contraction scheme is carried out using the criterion that the contraction error should be lower than the inherent error of the uncontracted pcJ-n relative to the uncontracted pcJ-4 basis set. A large search over possible contraction schemes is done for the Li₂ and Na₂ molecules, and based on this search contracted pcJ-n basis sets for the four atoms are recommended. This work shows that it is more difficult to contract the pcJ-n basis sets, than the underlying pc-n basis sets. However, it also shows that the pcJ-n basis sets for Li and Be can be more strongly contracted than the pcJ-n basis sets for the p-block elements. For Na and Mg, the contractions are to the same degree as for the p-block elements.

Z-dependence of mean excitation energies for second and third row atoms and their ions

All mean excitation energies for second and third row atoms and their ions are calculated in the random-phase approximation using large basis sets. To a very good approximation, it turns out that mean excitation energies within an isoelectronic series are a quadratic function of the nuclear charge. It is demonstrated that this behavior is linked to the fact that the contributions from continuum electronic states give the dominate contributions to the mean excitation energies and that these contributions for atomic ions appear hydrogen-like. We argue that this finding may present a method to get a first estimate of mean excitation energies also for other non-relativistic atomic ions.

Relativistic DFT Calculations of Hyperfine Coupling Constants in 5d Hexafluorido Complexes: [ReF6 ]2- and [IrF6 ]2

The performance of relativistic density functional theory (DFT) methods has been investigated for the calculation of the recently measured hyperfine coupling constants of hexafluorido complexes [ReF6 ]2- and [IrF6 ]2- . Three relativistic methods were employed at the DFT level of theory: the 2-component zeroth-order regular approximation (ZORA) method, in which the spin-orbit coupling was treated either variationally (EV ZORA) or as a perturbation (LR ZORA), and the 4-component Dirac-Kohn-Sham (DKS) method. The dependence of the results on the basis set and the choice of exchange-correlation functional was studied. Furthermore, the effect of varying the amount of Hartree-Fock exchange in the hybrid functionals was investigated. The LR ZORA and DKS methods combined with DFT led to very similar deviations (about 20 %) from the experimental values for the coupling constant of complex [ReF6 ]2- by using hybrid functionals. However, none of the methods were able to reproduce the large anisotropy of the hyperfine coupling tensor of complex [ReF6 ]2- . For [IrF6 ]2- , the EV ZORA and DKS methods reproduced the experimental tensor components with deviations of ≈10 and ≈5 % for the hybrid functionals, whereas the LR ZORA method predicted the coupling constant to be around one order of magnitude too large owing to the combination of large spin-orbit coupling and very low excitation energies.

Theoretical study of the NMR chemical shift of Xe in supercritical condition

In this work we investigate the level of theory necessary for reproducing the non-linear variation of the ¹²⁹Xe nuclear magnetic resonance (NMR) chemical shift with the density of Xe in supercritical conditions. In detail we study how the ¹²⁹Xe chemical shift depends under supercritical conditions on electron correlation, relativistic and many-body effects. The latter are included using a sequential-QM/MM methodology, in which a classical MD simulation is performed first and the chemical shift is then obtained as an average of quantum calculations of 250 MD snapshots conformations carried out for Xe _n clusters (n = 2 - 8 depending on the density). The analysis of the relativistic effects is made at the level of 4-component Hartree-Fock calculations (4c-HF) and electron correlation effects are considered using second order Møller-Plesset perturbation theory (MP2). To simplify the calculations of the relativistic and electron correlation effects we adopted an additive scheme, where the calculations on the Xe _n clusters are carried out at the non-relativistic Hartree-Fock (HF) level, while electron correlation and relativistic corrections are added for all the pairs of Xe atoms in the clusters. Using this approach we obtain very good agreement with the experimental data, showing that the chemical shift of ¹²⁹Xe in supercritical conditions is very well described by cluster calculations at the HF level, with small contributions from relativistic and electron correlation effects.

Molecular Switching in Confined Spaces: Effects of Encapsulating the DHA/VHF Photo-Switch in Cucurbiturils

Confinement of reactive chemical species uniquely affects chemical reactivity by restricting the physical space available and by restricting access to interactions with the solvent. In Nature, for example, confined protein binding pockets govern processes following photoisomerization reactions and the isomerizations themselves. Here we describe the first example of a dihydroazulene/vinylheptafulvene (DHA/VHF) photo-switch functioning in water, and we show how its switching behavior is strongly influenced by supramolecular interactions with a series of cucurbit[n]uril (CB) host molecules. In CB7 inclusion complexes, the kinetics of the thermal VHF-to-DHA back-reaction is accelerated, while in CB8 inclusion complexes, the kinetics is slowed down as compared to the free photo-switch. The effect of the CB encapsulation of the photo-switch can be effectively canceled by introducing a guest that binds the CB more strongly. According to DFT calculations, a stabilization of the reactive s-cis VHF conformer relative to the s-trans VHF appears to be a contributing factor responsible for the accelerated back-reaction when encapsulated in CB7.

Azadioxatriangulenium and Diazaoxatriangulenium: Quantum Yields and Fundamental Photophysical Properties

Over the last decade, we have investigated and exploited the photophysical properties of triangulenium dyes. Azadioxatriangulenium (ADOTA) and diazaoxatriangulenium (DAOTA), in particular, have features that make them useful in various fluorescence-based technologies (e.g., bioimaging). Through our work with ADOTA and DAOTA, we became aware that the reported fluorescence quantum yields (ϕ_fl) for these dyes are lower than their actual values. We thus set out to further investigate the fundamental structure-property relationships in these unique conjugated cationic systems. The nonradiative processes in the systems were explored using transient absorption spectroscopy and time-resolved emission spectroscopy in combination with computational chemistry. The influence of molecular oxygen on the fluorescence properties was explored, and the singlet oxygen sensitization efficiencies of ADOTA and DAOTA were determined. We conclude that, for these dyes, the amount of nonradiative deactivation of the first excited singlet state (S₁) of the azaoxa-triangulenium fluorophores is low, that the rate of such deactivation is slower than what is observed in common cationic dyes, that there are no observable radiative transitions occurring from the first excited triplet state (T₁) of these dyes, and that the efficiency of sensitized singlet oxygen production is low (ϕ_Δ ≤ 10%). These photophysical results provide a solid base upon which technological applications of these fluorescent dyes can be built.

Importance of Triples Contributions to NMR Spin-Spin Coupling Constants Computed at the CC3 and CCSDT Levels

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin-spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1-3%, but much higher corrections were found for ¹J_CN in FCN, 15.7%, and ¹J_OF in OF₂, 6.4%. The changes vary significantly in the case of multibond couplings, with differences of up to 10%, and even 13.6% for ³J_FH in fluoroacetylene. Calculations at the coupled cluster singles, doubles, and triples (CCSDT) level indicate that the most important contributions arising from connected triple excitations in the coupled cluster expansion are accounted for at the CC3 level. Thus, we believe that the CC3 method will become the standard approach for the calculation of reference values of nuclear spin-spin coupling constants.