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Mean absolute errors of CBS extrapolations and mean absolute basis set errors of the CCSD-F12b correlation energy with Ansatz 3C(FIX) for a set of fourteen systems containing first and second row elements. Basis sets are referred to by their cardinal number, n , and CBS extrapolations by the cardinal number of the largest basis set used in the extrapolation.
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Accurate extrapolation to the complete basis set (CBS) limit of valence correlation energies calculated with explicitly correlated MP2-F12 and CCSD(T)-F12b methods have been investigated using a Schwenke-style approach for molecules containing both first and second row atoms. Extrapolation coefficients that are optimal for molecular systems contain...
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... MAEs in the extrapolated correlation energies and the mean absolute basis set errors for the VnZ-F12 and AVnZ series of basis sets are plotted in Fig. 2 for the CCSD- F12b method with Ansatz 3CFIX. Although the MAE in an extrapolation of the VDZ-F12 and VTZ-F12 basis set ener- gies 0.52 mE h seems relatively high compared to the analogous MP2-F12 extrapolation see Fig. 1, Fig. 2 makes it clear that this is still a considerable improvement over the raw VQZ-F12 or AV5Z CCSD-F12b ...Citations
... Calculations used the frozen core approximation and the diagonal fixed amplitude ansatz 3C(FIX) 25 with a Slater geminal exponent value of β = 1.0 a −1 0 . 24 For the auxiliary basis sets (ABS) required in explicitly correlated calculations, the resolution of the identity OptRI 26 basis, and the cc-pV5Z/JKFIT 27 and aug-cc-pwCV5Z/MP2FIT 28 basis sets for density fitting were employed. The quantum chemistry package MOLPRO2015 29,30 was used for calculations unless stated otherwise. ...
\textit{Ab initio} quantum chemical methods can produce accurate molecular potential energy surfaces (PESs) capable of predicting the fundamental vibrational wavenumbers to within 1~cm$^{-1}$. However, for high-resolution applications this is simply...
... For verification purposes, MP2 Hessians in the same basis set were also calculated analytically [83] using Gaussian 16; [84] we found harmonic frequencies from the analytical and semi-numerical Hessians to differ by only on the order of 0.03 cm −1 , which is negligible in the context of this work. The explicitly correlated density-fitted DF-MP2-F12 method [85] was employed with analytic gradients [86,87] and the 3 * C(FIX, HY1) Ansatz, in which the extended Brillouin condition is assumed and the "HY1" hybrid approximation is used for matrix elements [88] over the F12 geminal [89], together with fixed geminal amplitudes [89,90]. The CCSD(T)(F12 * ) [91] geometry optimizations and frequency calculations were carried out fully numerically for want of an analytical gradient. ...
... For CABS, we used Yousaf and Peterson's cc-pVnZ-F12/OptRI [106]. Slater-type geminal terms of the F12 form [1-exp (γ )]/γ were used with a β geminal exponent of 1.0 for both triple-and quadruple-ζ OBS, as recommended in Table V of Ref. [90]. In the text below, 'VnZ-F12' signifies the cc-pVnZ-F12 basis sets. ...
... Statistics without them are RMSD = 1.9 for VTZ-F12 and 0.9 cm −1 for VQZ-F12, which is more in line with HFREQ2014. A T,Q extrapolation (with an exponent of 4.5960, Table X in Hill et al. [90]) yields RMSD = 1.0 cm −1 including all modes, and 0.8 cm −1 excluding ω 4 and ω 5 . ...
... The explicitly correlated density-fitted DF-MP2-F12 method [85] was employed with analytic gradients [86,87] and the 3*C(FIX, HY1) Ansatz, in which the extended Brillouin condition is assumed and the "HY1" hybrid approximation is used for matrix elements [88] over the F12 geminal, [89] together with fixed geminal amplitudes. [89,90] The CCSD(T)(F12*) [91] geometry optimizations and frequency calculations were carried out fully numerically for want of an analytical gradient. ...
... [102] The shorthand haVnZ+d refers in this paper to the combination of cc-pVnZ on hydrogen with aug-cc-pVnZ on first-row atoms and aug-cc-pV(n+d)Z on second-row atoms. Table V of Ref. [90] In the text below, "VnZ-F12" signifies the cc-pVnZ-F12 basis sets. ...
Minimally empirical G4-like composite wavefunction theories [E. Semidalas and J. M. L. Martin, \textit{J. Chem. Theory Comput.} {\bf 16}, 4238-4255 and 7507-7524 (2020)] trained against the large and chemically diverse GMTKN55 benchmark suite have demonstrated both accuracy and cost-effectiveness in predicting thermochemistry, barrier heights, and noncovalent interaction energies. Here, we assess the spectroscopic accuracy of top-performing methods: G4-\textit{n}, cc-G4-\textit{n}, and G4-\textit{n}-F12, and validate them against explicitly correlated coupled cluster CCSD(T*)(F12*) harmonic vibrational frequencies and experimental data from the HFREQ2014 dataset, of small first- and second-row polyatomics. G4-T is three times more accurate than plain CCSD(T)/def2-TZVP, while G4-T$_{\rm ano}$ is two times superior to CCSD(T)/ano-pVTZ. Combining CCSD(T)/ano-pVTZ with MP2-F12 in a parameter-free composite scheme results to a root-mean-square deviation of ~5 cm$^{-1}$ relative to experiment, comparable to CCSD(T) at the complete basis set limit. Application to the harmonic frequencies of benzene reveals a significant advantage of composites with ANO basis sets -- MP2/ano-pV\textit{m}Z and [CCSD(T)-MP2]/ano-pVTZ (\textit{m} = Q or 5) -- over similar protocols based on CCSD(T)/def2-TZVP. Overall, G4-type composite energy schemes, particularly when combined with ANO basis sets in CCSD(T), are accurate and comparatively inexpensive tools for computational vibrational spectroscopy.
... 16,17 For instance, the MP2 total atomization energies of acetylene, ethylene, and ethane, extrapolated from augmented spdfgh and spdfghi basis sets are within ~0.1 kcal/mol from results 18 obtained using explicitly correlated MP2-F12 with a truncated spdf basis set. 19 For the specific geminal form, Ten-no's F12 geminals 3,5 of the form F(r12) = (1exp(γr12))/γ have become the de facto standard: for reasons of computational convenience, inspired by the pioneering work of Persson and Taylor, 20 the Slater function is approximated as a linear combination of (usually six) Gaussians. ...
We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12 (n=D,T), for the d-block elements. The cc-pVDZ-F12 basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12 are [9s8p6d3f2g] for 3d-block elements and [7s7p6d3f2g] for 4d and 5d-block elements. Our VnZ(-PP)-F12 basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). This latter combination is hence a viable alternative if user-defined basis sets cannot be specified for some technical reason. While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters. 2
... The activation energies (E a ) were calculated at the MP2/6-311++G(2d,p) and CCSD(T)/6-311++G(2d,p)//MP2/6-311++G(2d,p) levels, respectively. CCSD(T) is a high-level electron correlation method [77][78][79], within the chemical accuracy of 1.0 kcal/mol in the total energies [80]. It can be thought of as the "gold standard" in computational chemistry for single-reference systems, in particular in kinetics [81]. ...
Controlling the selectivity of a detonation initiation reaction of explosive is essential to reduce sensitivity, and it seems impossible to reduce it by strengthening the external electric field. To verify this, the effects of external electric fields on the initiation reactions in NH2NO2∙∙∙NH3, a model system of the nitroamine explosive with alkaline additive, were investigated at the MP2/6-311++G(2d,p) and CCSD(T)/6-311++G(2d,p) levels. The concerted effect in the intermolecular hydrogen exchange is characterized by an index of the imaginary vibrations. Due to the weakened concerted effects by the electric field along the −x-direction opposite to the “reaction axis”, the dominant reaction changes from the intermolecular hydrogen exchange to 1,3-intramolecular hydrogen transference with the increase in the field strengths. Furthermore, the stronger the field strengths, the higher the barrier heights become, indicating the lower sensitivities. Therefore, by increasing the field strength and adjusting the orientation between the field and “reaction axis”, not only can the reaction selectivity be controlled, but the sensitivity can also be reduced, in particular under a super-strong field. Thus, a traditional concept, in which the explosive is dangerous under the super-strong external electric field, is theoretically broken. Compared to the neutral medium, a low sensitivity of the explosive with alkaline can be achieved under the stronger field. Employing atoms in molecules, reduced density gradient, and surface electrostatic potentials, the origin of the reaction selectivity and sensitivity change is revealed. This work provides a new idea for the technical improvement regarding adding the external electric field into the explosive system.
... 4 Continued progress in hardware technologies, 5 accompanied by the development of more realistic representations of electrostatic interactions, has enabled not only molecular simulations of progressively larger systems but also the use of more rigorous polarizable FFs 6-10 that go beyond the pairwise additive approximation adopted by conventional fixed-charge FFs. [11][12][13][14] At the same time, the development of efficient algorithms for correlated electronic structure methods, such as coupled cluster theory, [15][16][17] has enabled routine calculations of interaction energies for molecular clusters with chemical accuracy. [18][19][20] This has led to the emergence of a new class of analytical potentials that quantitatively reproduce each individual term of the many-body expansion (MBE) of the energy 21 calculated using correlated electronic structure methods. ...
Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. Here, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body inter- actions, which implies that DNN potentials may have limited ability to predict properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.
... 4 Continued progress in hardware technologies, 5 accompanied by the development of more realistic representations of electrostatic interactions, has enabled not only molecular simulations of progressively larger systems but also the use of more rigorous polarizable FFs 6-10 that go beyond the pairwise additive approximation adopted by conventional fixed-charge FFs. [11][12][13][14] At the same time, the development of efficient algorithms for correlated electronic structure methods, such as coupled cluster theory, [15][16][17] has enabled routine calculations of interaction energies for molecular clusters with chemical accuracy. [18][19][20] This has led to the emergence of a new class of analytical potentials that quantitatively reproduce each individual term of the many-body expansion (MBE) of the energy 21 calculated using correlated electronic structure methods. ...
Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.
... For the explicitly correlated calculations, the CCSD and (T) correlation energies were extrapolated separately, as previously recommended, due to their different convergences. 80 are the correlation energies evaluated with those respective basis sets. F is the constant optimized for first and second row p-block element containing molecules by Hill et al. 80 with the CCSD correlation energy F = 1.363388 80 and with the (T) correlation energy F = 1.769474 83 A previous study 27 on the thermochemistry of molecules containing 3d transition metals showed that the specific coefficients are not particularly sensitive to the system, despite being calibrated on systems containing only first and second row p-block elements. ...
... 80 are the correlation energies evaluated with those respective basis sets. F is the constant optimized for first and second row p-block element containing molecules by Hill et al. 80 with the CCSD correlation energy F = 1.363388 80 and with the (T) correlation energy F = 1.769474 83 A previous study 27 on the thermochemistry of molecules containing 3d transition metals showed that the specific coefficients are not particularly sensitive to the system, despite being calibrated on systems containing only first and second row p-block elements. The core valence contribution to the total energy was calculated at the same level of theory as the base calculation in FPD, e.g., either CCSD(T) or CCSD(T)-F12b. ...
... 80 are the correlation energies evaluated with those respective basis sets. F is the constant optimized for first and second row p-block element containing molecules by Hill et al. 80 with the CCSD correlation energy F = 1.363388 80 and with the (T) correlation energy F = 1.769474 83 A previous study 27 on the thermochemistry of molecules containing 3d transition metals showed that the specific coefficients are not particularly sensitive to the system, despite being calibrated on systems containing only first and second row p-block elements. The core valence contribution to the total energy was calculated at the same level of theory as the base calculation in FPD, e.g., either CCSD(T) or CCSD(T)-F12b. ...
The thermochemistry of halocarbon species containing iodine and bromine is examined through an extensive interplay between new Feller-Peterson-Dixon (FPD) style composite methods and a detailed analysis of all available experimental and theoretical determinations using the thermochemical network that underlies the Active Thermochemical Tables (ATcT). From the computational viewpoint, a slower convergence of the components of composite thermochemistry methods is observed relative to species that solely contain first row elements, leading to a higher computational expense for achieving comparable levels of accuracy. Potential systematic sources of computational uncertainty are investigated, and, not surprisingly, spin-orbit coupling is found to be a critical component, particularly for iodine containing molecular species. The ATcT analysis of available experimental and theoretical determinations indicates that prior theoretical determinations have significantly larger uncertainties than originally reported, particularly in cases where molecular spin-orbit effects were ignored. Accurate and reliable heats of formation are reported for 38 halogen containing systems, based on combining the current computations with previous experimental and theoretical work via the ATcT approach.
... where L refers to the basis set cardinal number, and α is the basis set extrapolation exponent. Following Hill et al., 65 we have used α = 4.355 and 2.531 for the RI-MP2-F12/ V{T,Q}Z-F12 and RI-MP2/AV{T,Q}Z energies, respectively. While extrapolating the RI-MP2-F12 energies to the CBS limit, the self-consistent field (SCF) component was taken from the largest basis set calculation with CABS 61 correction, and only MP2-F12 components were extrapolated. ...
We report an update and enhancement of the ACONFL (conformer energies of large alkanes [J. Phys. Chem. A2022,126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical coupled-cluster with singles, doubles, and perturbative triples [i.e., CCSD(T)] reference data obtained from the MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/aug-cc-pV{D,T}Z calculations. Then, we explored the performance of a variety of single and composite localized-orbital CCSD(T) approximations, ultimately finding an affordable localized natural orbital CCSD(T) [LNO-CCSD(T)]-based post-MP2 correction that agrees to 0.006 kcal/mol mean absolute deviation with the revised canonical reference data. In tandem with canonical MP2-F12 complete basis set extrapolation, this was then used to re-evaluate the ACONF16 and ACONF20 subsets for n-hexadecane and n-icosane, respectively. Combining those with the revised canonical reference data for the dodecane conformers (i.e., ACONF12 subset), a revised ACONFL set was obtained. It was then used to assess the performance of different localized-orbital coupled-cluster approaches, such as pair natural orbital localized CCSD(T) [PNO-LCCSD(T)] as implemented in MOLPRO, DLPNO-CCSD(T0) and DLPNO-CCSD(T1) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, at their respective "Normal", "Tight", "vTight", and "vvTight" accuracy settings. For a given accuracy threshold and basis set, DLPNO-CCSD(T1) and DLPNO-CCSD(T0) perform comparably. With "VeryTightPNO" cutoffs, explicitly correlated DLPNO-CCSD(T1)-F12/VDZ-F12 is the best pick among all the DLPNO-based methods tested. To isolate basis set incompleteness from localized-orbital-related truncation errors (domain, LNOs), we have also compared the localized coupled-cluster approaches with canonical DF-CCSD(T)/aug-cc-pVTZ for the ACONF12 set. We found that gradually tightening the cutoffs improves the performance of LNO-CCSD(T), and using a composite scheme such as vTight + 0.50[vTight - Tight] improves things further. For DLPNO-CCSD(T1), "TightPNO" and "VeryTightPNO" offer a statistically similar accuracy, which gets slightly better when TCutPNO is extrapolated to the complete PNO space limit. Similar to Brauer et al.'s [Phys. Chem. Chem. Phys.2016,18 (31), 20905-20925] previous report for the S66x8 noncovalent interactions, the dispersion-corrected direct random phase approximation (dRPA)-based double hybrids perform remarkably well for the ACONFL set. While the revised reference data do not affect any conclusions on the less accurate methods, they may upend orderings for more accurate methods with error statistics on the same order as the difference between reference datasets.
... 4 Continued progress in hardware technologies, 5 accompanied by the development of more realistic representations of electrostatic interactions, has enabled not only simulations of progressively larger systems but also the use of more rigorous polarizable FFs 6-10 that go beyond the pairwise additive approximation adopted by conventional point-charge FFs. [11][12][13][14] At the same time, the development of efficient algorithms for correlated electronic structure methods, such as coupled cluster theory, [15][16][17] has enabled routine, chemically accurate calculations of interaction energies for molecular clusters. [18][19][20] This has led to the emergence of a new class of analytical potentials that quantitatively reproduce each individual term of the many-body expansion (MBE) of the energy 21 calculated using correlated electronic structure methods. ...
Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.
