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The prediction of spectral properties via linear response (LR) theory is an important tool in quantum chemistry for understanding photoinduced processes in molecular systems. With the advances of quantum computing, we recently adapted this method for near-term quantum hardware using a truncated active space approximation with orbital rotation, named quantum linear response (qLR). In an effort to reduce the classic cost of this hybrid approach, we here derive and implement a reduced density matrix (RDM) driven approach of qLR. This allows for the calculation of spectral properties of moderately sized molecules with much larger basis sets than so far possible. We report qLR results for benzene and R-methyloxirane with a cc-pVTZ basis set and study the effect of shot noise on the valence and oxygen K-edge absorption spectra of H2O in the cc-pVTZ basis.
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The interest in mercury radioisotopes, 197mHg (t1/2 = 23.8 h) and 197gHg (t1/2 = 64.14 h), has recently been reignited by the dual diagnostic and therapeutic nature of their nuclear decays. These isotopes emit γ-rays suitable for single photon emission computed tomography imaging and Auger electrons which can be exploited for treating small and metastatic tumors. However, the clinical utilization of 197m/gHg radionuclides is obstructed by the lack of chelators capable of securely binding them to tumor-seeking vectors. This work aims to address this challenge by investigating a series of chemically tailored macrocyclic platforms with sulfur-containing side arms, namely, 1,4,7,10-tetrakis[2-(methylsulfanyl)ethyl]-1,4,7,10-tetraazacyclododecane (DO4S), 1,4,7-tris[2-(methylsulfanyl)ethyl]-1,4,7,10-tetraazacyclododecane (DO3S), and 1,7-bis[2-(methylsulfanyl)ethyl]-1,4,7,10-tetraazacyclododecane-4,10-diacetic acid (DO2A2S). 1,4,7,10-Tetrazacyclododecane-1,4,7,10-tetracetic acid (DOTA), the widest explored chelator in nuclear medicine, and the nonfunctionalized backbone 1,4,7,10-tetrazacyclododecane (cyclen) were considered as well to shed light on the role of the sulfanyl arms in the metal coordination. To this purpose, a comprehensive experimental and theoretical study encompassing aqueous coordination chemistry investigations through potentiometry, nuclear magnetic resonance (NMR) spectroscopy, X-ray crystallography, and density functional theory (DFT) calculations, as well as concentration- and temperature-dependent [197m/gHg]Hg2+ radiolabeling and in vitro stability assays in human serum was conducted. The obtained results reveal that the investigated chelators rapidly complex Hg2+ in aqueous media, forming extremely thermodynamically stable 1:1 metal-to-ligand complexes with superior stabilities compared to those of DOTA or cyclen. These complexes exhibited 6- to 8-fold coordination environments, with donors statically bound to the metal center, as evidenced by the presence of 1H-199Hg spin-spin coupling via NMR. A similar octacoordinated environment was also found for DOTA in both solution and solid state, but in this case, multiple slowly exchanging conformers were detected at ambient temperature. The sulfur-rich ligands quantitatively incorporate cyclotron-produced [197m/gHg]Hg2+ under relatively mild reaction conditions (pH = 7 and T = 50 °C), with the resulting radioactive complexes exhibiting decent stability in human serum (up to 75% after 24 h). By developing viable chelators and understanding the impact of structural modifications, our research addresses the scarcity of suitable chelating agents for 197m/gHg, offering promise for its future in vivo application as a theranostic Auger-emitter radiometal.
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Ciclamas , Compuestos Macrocíclicos , Humanos , Compuestos Macrocíclicos/química , Compuestos Macrocíclicos/síntesis química , Mercurio/química , Azufre/química , Radioisótopos/química , Estructura Molecular , Electrones , Complejos de Coordinación/química , Complejos de Coordinación/síntesis química , Compuestos Heterocíclicos/química , Nanomedicina TeranósticaRESUMEN
We test the performance of the polarizable embedding variational quantum eigensolver self-consistent field (PE-VQE-SCF) model for computing electric field gradients with comparisons to conventional complete active space self-consistent-field (CASSCF) calculations and experimental results. We compute quadrupole coupling constants for ice VIII and ice IX. We find close agreement of the quantum-computing PE-VQE-SCF results with the results from the classical PE-CASSCF calculations and with experiment. Furthermore, we observe that the inclusion of the environment is crucial for obtaining results that match the experimental data. The calculations for ice VIII are within the experimental uncertainty for both CASSCF and VQE-SCF for oxygen and lie close to the experimental value for ice IX as well. With the VQE-SCF, which is based on an adaptive derivative-assembled problem-tailored (ADAPT) ansatz, we find that the inclusion of the environment and the size of the different basis sets do not directly affect the gate counts. However, by including an explicit environment, the wavefunction and therefore the optimization problem become more complicated, which usually results in the need to include more operators from the operator pool, thereby increasing the depth of the circuit.
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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.
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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.
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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.
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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.
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Thiolate containing mercury(II) complexes of the general formula [Hg(SR) 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 ] 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 â¼ 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.
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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".
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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.
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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.
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Timina , Uracilo , Solventes , Adenina , HidrógenoRESUMEN
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.
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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.
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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.
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Guanosina , Hidrógeno , Hidrógeno/química , Uridina , Cinética , Modelos TeóricosRESUMEN
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.
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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).
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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.
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Modelos Teóricos , Fenilendiaminas , Espectroscopía de Resonancia por Spin del Electrón/métodos , CationesRESUMEN
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.
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Adenosina Trifosfato , Magnesio , Adenosina Trifosfato/química , Imidazoles , Espectroscopía de Resonancia Magnética/métodosRESUMEN
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.
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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).