Basis Set Limit of CCSD(T) Energies: Explicit Correlation Versus Density-Based Basis-Set Correction.

A thorough comparison is carried out for explicitly correlated and density-based basis-set correction approaches, which were primarily developed to mitigate the basis-set incompleteness error of wave function methods. An efficient implementation of the density-based scheme is also presented, utilizing the density-fitting approximation. The performance of these approaches is comprehensively tested for the second-order Møller-Plesset (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] methods with respect to the corresponding complete basis set references. It is demonstrated that the density-based correction together with complementary auxiliary basis set (CABS)-corrected Hartree-Fock energies is highly robust and effectively reduces the error of the standard approaches; however, it does not outperform the corresponding explicitly correlated methods. Nevertheless, what still makes the density-corrected CCSD and CCSD(T) methods competitive is that their computational costs are roughly half of those of the corresponding explicitly correlated variants. Additionally, an incremental approach for standard CCSD and CCSD(T) is introduced. In this simple scheme, the total energies are corrected with the CABS correction and explicitly correlated MP2 contributions. As demonstrated, the resulting methods yield surprisingly good results, below 1 kcal/mol for thermochemical properties even with a double-ζ basis, while their computational expenses are practically identical to those of the density-based basis-set correction approaches.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level.

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

Reduced-Cost Second-Order Algebraic-Diagrammatic Construction Method for Core Excitations.

Our reduced-cost scheme [J. Chem. Phys. 2018, 148, 094111] based on the frozen virtual natural orbital and natural auxiliary function approaches is extended to core excitations. The efficiency of the approximation is presented for the second-order algebraic-diagrammatic construction [ADC(2)] method invoking the core-valence separation (CVS) and density fitting approaches. The errors introduced by the present scheme are comprehensively analyzed for more than 200 excitation energies and 80 oscillator strengths, including C, N, and O K-edge excitations, as well as 1s → π* and Rydberg transitions. Our results show that significant savings can be gained in computational requirements at the expense of a moderate error. That is, the mean absolute error for the excitation energies, being lower than 0.20 eV, is an order of magnitude smaller than the intrinsic error of CVS-ADC(2), while the mean relative error for the oscillator strengths is between 0.06 and 0.08, which is still acceptable. As significant differences for different types of excitations cannot be observed, the robustness of the approximation is also demonstrated. The improvements in the computational requirements are measured for extended molecules. In this case, an overall 7-fold speedup is obtained in the wall-clock times, while dramatic reductions in the memory requirements are also achieved. In addition, it is also proved that the new approach enables us to perform CVS-ADC(2) calculations within reasonable runtime for systems of 100 atoms using reliable basis sets.

Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations.

The double-hybrid (DH) time-dependent density functional theory is extended to core excitations. Two different DH formalisms are presented utilizing the core-valence separation (CVS) approximation. First, a CVS-DH variant is introduced relying on the genuine perturbative second-order correction, while an iterative analogue is also presented using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH ansatz. The performance of the new approaches is tested for the most popular DH functionals using the recently proposed XABOOM [J. Chem. Theory Comput.2021, 17, 1618] benchmark set. In order to make a careful comparison, the accuracy and precision of the methods are also inspected. Our results show that the genuine approaches are highly competitive with the more advanced CVS-ADC(2)-based methods if only excitation energies are required. In contrast, as expected, significant differences are observed in oscillator strengths; however, the precision is acceptable for the genuine functionals as well. Concerning the performance of the CVS-DH approaches, the PBE0-2/CVS-ADC(2) functional is superior, while its spin-opposite-scaled variant is also recommended as a cost-effective alternative. For these approaches, significant improvements are realized in the error measures compared with the popular CVS-ADC(2) method.

Performance of Multilevel Methods for Excited States.

The performance of multilevel quantum chemical approaches, which utilize an atom-based system partitioning scheme to model various electronic excited states, is studied. The considered techniques include the mechanical-embedding (ME) of "our own N-layered integrated molecular orbital and molecular mechanics" (ONIOM) method, the point charge embedding (PCE), the electronic-embedding (EE) of ONIOM, the frozen density-embedding (FDE), the projector-based embedding (PbE), and our local domain-based correlation method. For the investigated multilevel approaches, the second-order algebraic-diagrammatic construction [ADC(2)] approach was utilized as the high-level method, which was embedded in either Hartree-Fock or a density functional environment. The XH-27 test set of Zech et al. [ J. Chem. Theory Comput., 2018, 14, 4028] was used for the assessment, where organic dyes interact with several solvent molecules. With the selection of the chromophores as active subsystems, we conclude that the most reliable approach is local domain-based ADC(2) [L-ADC(2)], and the least robust schemes are ONIOM-ME and ONIOM-EE. The PbE, FDE, and PCE techniques often approach the accuracy of the L-ADC(2) scheme, but their precision is far behind. The results suggest that a more conservative subsystem selection algorithm or the inclusion of subsystem charge-transfers is required for the atom-based cost-efficient methods to produce high-accuracy excitation energies.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange-correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach.

Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States.

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput. 17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States.

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

The MRCC program system: Accurate quantum chemistry from water to proteins.

MRCC is a package of ab initio and density functional quantum chemistry programs for accurate electronic structure calculations. The suite has efficient implementations of both low- and high-level correlation methods, such as second-order Møller-Plesset (MP2), random-phase approximation (RPA), second-order algebraic-diagrammatic construction [ADC(2)], coupled-cluster (CC), configuration interaction (CI), and related techniques. It has a state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)] code, and its specialties, the arbitrary-order iterative and perturbative CC methods developed by automated programming tools, enable achieving convergence with regard to the level of correlation. The package also offers a collection of multi-reference CC and CI approaches. Efficient implementations of density functional theory (DFT) and more advanced combined DFT-wave function approaches are also available. Its other special features, the highly competitive linear-scaling local correlation schemes, allow for MP2, RPA, ADC(2), CCSD(T), and higher-order CC calculations for extended systems. Local correlation calculations can be considerably accelerated by multi-level approximations and DFT-embedding techniques, and an interface to molecular dynamics software is provided for quantum mechanics/molecular mechanics calculations. All components of MRCC support shared-memory parallelism, and multi-node parallelization is also available for various methods. For academic purposes, the package is available free of charge.

Reduced-Scaling Correlation Methods for the Excited States of Large Molecules: Implementation and Benchmarks for the Second-Order Algebraic-Diagrammatic Construction Approach.

A framework for reduced-scaling implementation of excited-state correlation methods is presented. An algorithm is introduced to construct excitation-specific local domains, which include all important molecular orbitals for the excitation as well as for electron correlation. The orbital space dimensions of the resulting compact domains are further decreased utilizing our reduced-cost techniques developed previously [J. Chem. Phys. 148, 094111 (2018)] based on the natural auxiliary function and local natural orbital approaches. Additional methodological improvements for the evaluation of density matrices are also discussed. Benchmark calculations are presented at the second-order algebraic-diagrammatic construction level. Compared to our reduced-cost algorithm significant, up to 3-9-fold speedups are achieved even for systems of smaller than 100 atoms. At the same time, additional errors introduced by domain approximations are highly acceptable, being about 2-4 meV on the average. The presented reduced-scaling algorithm allows us to carry out correlated excited-state calculations using triple-ζ basis sets with diffuse functions for systems of up to 400 atoms or 13 000 atomic orbitals in a matter of days using an 8-core processor.

Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments.

A composite of time-dependent density functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calculation of spectral properties of molecules. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approximation for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-reduction approach is also presented, which further speeds up the calculations. Our benchmark calculations show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.

In-Vitro Pulsatile Flow Testing of Prosthetic Heart Valves: A Round-Robin Study by the ISO Cardiac Valves Working Group.

PURPOSE: Hydrodynamic performance testing is one of the core in vitro assessments required by the ISO 5840 series of standards for all prosthetic heart valves. A round-robin study carried out in 2005 in accordance with ISO 5840:2005 revealed significant variabilities in prosthetic heart valve hydrodynamic performance measurements among the participating laboratories. In order to re-examine the inter-laboratory variability based on the "state-of-the-art" under ISO 5840-1 and 5840-2:2015, the ISO Cardiac Valve Working Groups decided in 2016 to repeat the round-robin study. METHODS: A total of 13 international laboratories participated in the study. The test valves were chosen to be the St. Jude Medical Masters Series mechanical valves (19 mm aortic, 25 mm aortic, 25 mm mitral, and 31 mm mitral), which were circulated among the laboratories. The testing was conducted according to a common test run sequence, with prespecified flow conditions. RESULTS: The study revealed improved, yet still significant variability among different laboratories as compared to the 2005 study. The coefficient of variation ranged from 7.7 to 21.6% for the effective orifice area, from 10.1 to 32.8% for the total regurgitant fraction, and from 14.7 to 45.5% for the mean transvalvular pressure gradient. CONCLUSIONS: The study revealed the ambiguities in the current versions of the ISO 5840 series of standards and the shortcomings of some participating laboratories. This information has allowed the ISO Working Group to incorporate additional clarifying language into the ISO 5840-1, -2, and -3 standards that are currently under revision to improve in vitro assessments. The results presented here can also be used by the testing laboratories to benchmark pulse duplicator systems and to train and certify testing personnel.

Reduced-Scaling Approach for Configuration Interaction Singles and Time-Dependent Density Functional Theory Calculations Using Hybrid Functionals.

An approximation is presented which can efficiently decrease the computational expenses of configuration interaction singles (CIS) and time-dependent density functional theory (TDDFT) methods employing hybrid functionals. The approach is the adaptation of the local density fitting scheme developed for Hartree-Fock (HF) calculations for excited states and reduces the quartic scaling of the methods to cubic. It can also be applied to related methods, such as the time-dependent HF and Tamm-Dancoff approximation TDDFT approaches. Our benchmark calculations show that, for molecules of 50-100 atoms, average speedups of 2-4 can be achieved for CIS and TDDFT calculations at the expense of negligible errors in the calculated excitation energies and oscillator strengths, but for bigger systems or molecules of localized electronic structure significantly larger speedups can be gained. We also demonstrate that the approximation enables excited-state calculations on a single processor even for molecules of 1000 atoms using basis sets augmented with diffuse functions including more than 17 000 atomic orbitals.

Hydrogen bonding effects on the fluorescence properties of 4'-diethylamino-3-hydroxyflavone in water and water-acetone mixtures.

The fluorescence properties of 4'-diethylamino-3-hydroxyflavone (FET), a dye probe sensitive to the polarity as well as the hydrogen bonding ability of its environment, have been studied in acetone-water mixtures by measuring spectra and decay curves over the whole composition range and analyzing the results on the basis of theoretical calculations. In acetone, like in most of organic solvents, the dye showed dual fluorescence, due to an excited state intramolecular proton transfer (ESIPT), in which a quasi-equilibrium between the two excited species, N* and T*, was reached. In acetone-water mixtures with lower molar fractions of water, where the water molecules are largely dispersed, only one type of hydrate could be detected, a complex with 1:1 composition, showing only N* emission, but with a high (0.45) fluorescence quantum yield. At higher water concentrations, the interaction of FET with the hydrogen-bonded water clusters resulted in fluorescence quenching. In neat water the fluorescence quantum yield fell to ~0.001. Theoretical calculations on a FET-acetone complex, a FET-water complex and a FET-water-acetone triple complex (the latter as model for the samples with low water concentrations) concluded that ESIPT was energetically favored in all the models, but the E(N*)-E(T*) energy difference for the water complexes was much lower. The kinetic barrier of ESIPT was found greatly higher in the FET-water complex than in the isolated solute. The intermolecular hydrogen bonds in the water complexes became significantly stronger following the excitation, stabilizing the N* form of the hydrated dye.

An uracil-linked hydroxyflavone probe for the recognition of ATP.

Background: Nucleotides are essential molecules in living systems due to their paramount importance in various physiological processes. In the past years, numerous attempts were made to selectively recognize and detect these analytes, especially ATP using small-molecule fluorescent chemosensors. Despite the various solutions, the selective detection of ATP is still challenging due to the structural similarity of various nucleotides. In this paper, we report the conjugation of a uracil nucleobase to the known 4'-dimethylamino-hydroxyflavone fluorophore. Results: The complexation of this scaffold with ATP is already known. The complex is held together by stacking and electrostatic interactions. To achieve multi-point recognition, we designed the uracil-appended version of this probe to include complementary base-pairing interactions. The theoretical calculations revealed the availability of multiple complex structures. The synthesis was performed using click chemistry and the nucleotide recognition properties of the probe were evaluated using fluorescence spectroscopy. Conclusions: The first, uracil-containing fluorescent ATP probe based on a hydroxyflavone fluorophore was synthesized and evaluated. A selective complexation with ATP was observed and a ratiometric response in the excitation spectrum.

Building Ultra-High-Density Linkage Maps Based on Efficient Filtering of Trustable Markers.

The study is focused on addressing the problem of building genetic maps in the presence of ∼103-104 of markers per chromosome. We consider a spectrum of situations with intrachromosomal heterogeneity of recombination rate, different level of genotyping errors, and missing data. In the ideal scenario of the absence of errors and missing data, the majority of markers should appear as groups of cosegregating markers ("twins") representing no challenge for map construction. The central aspect of the proposed approach is to take into account the structure of the marker space, where each twin group (TG) and singleton markers are represented as points of this space. The confounding effect of genotyping errors and missing data leads to reduction of TG size, but upon a low level of these effects surviving TGs can still be used as a source of reliable skeletal markers. Increase in the level of confounding effects results in a considerable decrease in the number or even disappearance of usable TGs and, correspondingly, of skeletal markers. Here, we show that the paucity of informative markers can be compensated by detecting kernels of markers in the marker space using a clustering procedure, and demonstrate the utility of this approach for high-density genetic map construction on simulated and experimentally obtained genotyping datasets.

Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions.

A reduced-cost density fitting (DF) linear-response second-order coupled-cluster (CC2) method has been developed for the evaluation of excitation energies. The method is based on the simultaneous truncation of the molecular orbital (MO) basis and the auxiliary basis set used for the DF approximation. For the reduction of the size of the MO basis, state-specific natural orbitals (NOs) are constructed for each excited state using the average of the second-order Møller-Plesset (MP2) and the corresponding configuration interaction singles with perturbative doubles [CIS(D)] density matrices. After removing the NOs of low occupation number, natural auxiliary functions (NAFs) are constructed [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], and the NAF basis is also truncated. Our results show that, for a triple-zeta basis set, about 60% of the virtual MOs can be dropped, while the size of the fitting basis can be reduced by a factor of five. This results in a dramatic reduction of the computational costs of the solution of the CC2 equations, which are in our approach about as expensive as the evaluation of the MP2 and CIS(D) density matrices. All in all, an average speedup of more than an order of magnitude can be achieved at the expense of a mean absolute error of 0.02 eV in the calculated excitation energies compared to the canonical CC2 results. Our benchmark calculations demonstrate that the new approach enables the efficient computation of CC2 excitation energies for excited states of all types of medium-sized molecules composed of up to 100 atoms with triple-zeta quality basis sets.

Fast and accurate construction of ultra-dense consensus genetic maps using evolution strategy optimization.

Our aim was to develop a fast and accurate algorithm for constructing consensus genetic maps for chip-based SNP genotyping data with a high proportion of shared markers between mapping populations. Chip-based genotyping of SNP markers allows producing high-density genetic maps with a relatively standardized set of marker loci for different mapping populations. The availability of a standard high-throughput mapping platform simplifies consensus analysis by ignoring unique markers at the stage of consensus mapping thereby reducing mathematical complicity of the problem and in turn analyzing bigger size mapping data using global optimization criteria instead of local ones. Our three-phase analytical scheme includes automatic selection of ~100-300 of the most informative (resolvable by recombination) markers per linkage group, building a stable skeletal marker order for each data set and its verification using jackknife re-sampling, and consensus mapping analysis based on global optimization criterion. A novel Evolution Strategy optimization algorithm with a global optimization criterion presented in this paper is able to generate high quality, ultra-dense consensus maps, with many thousands of markers per genome. This algorithm utilizes "potentially good orders" in the initial solution and in the new mutation procedures that generate trial solutions, enabling to obtain a consensus order in reasonable time. The developed algorithm, tested on a wide range of simulated data and real world data (Arabidopsis), outperformed two tested state-of-the-art algorithms by mapping accuracy and computation time.

Ex vivo hemodynamic assessment of mechanical aortic valve gradients using a high-fidelity pressure wire.

OBJECTIVES: Accurate assessment of prosthetic mechanical valve malfunction is challenging for non-invasive and invasive techniques. We evaluated a 0.014-inch pressure-sensing coronary guidewire to assess mechanical valve dysfunction. BACKGROUND: Several case reports have shown that transaortic pressure gradients can be recorded using a 0.014-inch guidewire during cardiac catheterization. METHODS: We performed an ex vivo study measuring the effects of sequentially crossing the center of each valve with a 6 French coronary angiographic catheter, a 0.035-inch guidewire, and a 0.014-inch pressure-sensing guidewire on valve dysfunction using the following 23 mm bileaflet and tilting-disc aortic valves: St. Jude Regent™, CarboMedics, Medtronic Hall™, and Björk-Shiley Monostut. A left heart model pulse duplicator recorded 10 consecutive cycles. RESULTS: For all valves, the greatest increase in valve regurgitation occurred with the 6 French catheter, causing a reduction in aortic valve back pressure and cardiac output, with an increase in leakage rate, regurgitant fraction, and energy loss. In comparison to the 0.035-inch guidewire, the 0.014-inch guidewire had greater regurgitation for St. Jude, lower for Medtronic Hall, and equivalent for CarboMedics and Björk-Shiley valves. For the CarboMedics valve, the 0.035-inch guidewire caused a significant increase in regurgitant fraction and energy loss, while the pressure wire had no change compared to baseline. CONCLUSIONS: The degree of regurgitation caused by the 0.014-inch guidewire varies with the type of mechanical aortic valve. While prior case reports have shown that valve hemodynamics may be measured using a pressure-sensing guidewire, valve regurgitation occurs when crossing a St. Jude, Medtronic Hall, or Björk-Shiley aortic valve.