On the geometry dependence of the nuclear magnetic resonance chemical shift of mercury in thiolate complexes: A relativistic density functional theory study.

Thiolate containing mercury(II) complexes of the general formula [Hg(SR) n $$ {}_n $$ ] 2 - n $$ {}^{2-n} $$ have been of great interest since the toxicity of mercury was recognized. 199Hg nuclear magnetic resonance spectroscopy (NMR) is a powerful tool for characterization of mercury complexes. In this work, the Hg shielding constants in a series of [Hg(SR) n $$ {}_n $$ ] 2 - n $$ {}^{2-n} $$ complexes are therefore investigated computationally with particular emphasis on their geometry dependence. Geometry optimizations and NMR chemical shift calculations are performed at the density functional theory (DFT) level with both the zeroth-order regular approximation (ZORA) and four-component relativistic methods. The four exchange-correlation (XC) functionals PBE0, PBE, B3LYP, and BLYP are used in combination with either Dyall's Gaussian-type (GTO) or Slater-type orbitals (STOs) basis sets. Comparing ZORA and four-component calculations, one observes that the calculated shielding constants for a given molecular geometry have a constant difference of ∼ $$ \sim $$ 1070 ppm. This confirms that ZORA is an acceptable relativistic method to compute NMR chemical shifts. The combinations of four-component/PBE0/v3z and ZORA/PBE0/QZ4P are applied to explore the geometry dependence of the isotropic shielding. For a given coordination number, the distance between mercury and sulfur is the key factor affecting the shielding constant, while changes in bond and dihedral angles and even different side groups have relatively little impact.

Performance of range-separated long-range SOPPA short-range density functional theory method for vertical excitation energies.

In this paper, benchmark results are presented on the calculation of vertical electronic excitation energies using a long-range second-order polarization propagator approximation (SOPPA) description with a short-range density functional theory description based on the Perdew-Burke-Ernzerhof (PBE) functional. The excitation energies are investigated for 132 singlet states and 71 triplet states across 28 medium-sized organic molecules. The results show that overall SOPPA-srPBE always performs better than PBE and that SOPPA-srPBE performs better than SOPPA for singlet states, but slightly worse than SOPPA for triplet states when CC3 results are the reference values.

Extensive folding variability between homologous chromosomes in mammalian cells.

Genetic variation and 3D chromatin structure have major roles in gene regulation. Due to challenges in mapping chromatin conformation with haplotype-specific resolution, the effects of genetic sequence variation on 3D genome structure and gene expression imbalance remain understudied. Here, we applied Genome Architecture Mapping (GAM) to a hybrid mouse embryonic stem cell (mESC) line with high density of single nucleotide polymorphisms (SNPs). GAM resolved haplotype-specific 3D genome structures with high sensitivity, revealing extensive allelic differences in chromatin compartments, topologically associating domains (TADs), long-range enhancer-promoter contacts, and CTCF loops. Architectural differences often coincide with allele-specific differences in gene expression, mediated by Polycomb repression. We show that histone genes are expressed with allelic imbalance in mESCs, are involved in haplotype-specific chromatin contact marked by H3K27me3, and are targets of Polycomb repression through conditional knockouts of Ezh2 or Ring1b. Our work reveals highly distinct 3D folding structures between homologous chromosomes, and highlights their intricate connections with allelic gene expression.

Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer.

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets and of H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

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.

The Importance of Anharmonicity and Solvent Effects on the OH Radical Attack on Nucleobases.

Previous theoretical investigations of the reactions between an OH radical and a nucleobase have stated the most important pathways to be the C5-C6 addition for pyrimidines and the C8 addition for purines. Furthermore, the abstraction of a methyl hydrogen from thymine has also been proven an important pathway. The conclusions were based solely on gas-phase calculations and harmonic vibrational frequencies. In this paper, we supplement the calculations by applying solvent corrections through the polarizable continuum model (PCM) solvent model and applying anharmonicity in order to determine the importance of anharmonicity and solvent effects. Density functional theory (DFT) at the ωB97-D/6-311++G(2df,2pd) level with the Eckart tunneling correction is used. The total reaction rate constants are found to be 1.48 ×10-13 cm3 molecules-1s-1 for adenine, 1.02 ×10-11 cm3 molecules-1s-1 for guanine, 5.52 ×10-13 cm3 molecules-1s-1 for thymine, 1.47 ×10-13 cm3 molecules-1s-1 for cytosine and 7.59 ×10-14 cm3 molecules-1s-1 for uracil. These rates are found to be approximately two orders of magnitude larger than experimental values. We find that the tendencies observed for preferred pathways for reactions calculated in a solvent are comparable to the preferred pathways for reactions calculated in gas phase. We conclude that applying a solvent has a larger impact on more parameters compared to the inclusion of anharmonicity. For some reactions the inclusion of anharmonicity has no effect, whereas for others it does impact the energetics.

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.

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 coupled cluster singles and doubles 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 a small increase in the 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 in the Dalton program, thus, already shows a significant change in these molecular properties over those obtained with the standard SOPPA method.

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).

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 ß-Radiation-Detected NMR Spectroscopy.

The complexation of MgII with adenosine 5'-triphosphate (ATP) is omnipresent in biochemical energy conversion, but is difficult to interrogate directly. Here we use the spin- 1/2 ß-emitter 31 Mg to study MgII -ATP complexation in 1-ethyl-3-methylimidazolium acetate (EMIM-Ac) solutions using ß-radiation-detected nuclear magnetic resonance (ß-NMR). We demonstrate that (nuclear) spin-polarized 31 Mg, 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 31 Mg initially bind to the solvent acetate anions, whereafter they undergo dynamic exchange and form either a mono- (31 Mg-ATP) or di-nuclear (31 MgMg-ATP) complex. The chemical shift of 31 Mg-ATP is observed up-field of 31 MgMg-ATP, in accord with quantum chemical calculations. These observations constitute a crucial advance towards using ß-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 1JFC 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 1JFC 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 1JFC, 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 1JFC constants best reproduces the experimental data for organofluorine compounds (with the exception of fluoroalkenes).

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.

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.