Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory

The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD­(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD­(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2–3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2–4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD­(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD­(T) is cheaper or at least not much more expensive than the preceding Hartree–Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree–Fock theory (at least if Hartree–Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF’s) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD­(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD­(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD­(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD­(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD­(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost

Domain Based Pair Natural Orbital Coupled Cluster Studies on Linear and Folded Alkane Chains

In this study the question of what is the last unbranched alkane that prefers a linear conformation over a folded one is revisited from a theoretical point of view. Geometries have been optimized carefully using the most accurate theoretical approach available to date for such systems, namely, doubly hybrid density functional theory in conjunction with larger quadruple-ζ quality basis sets. The resulting geometries deviate significantly from previously reported ones and have a significant impact on the predicted energetics. Electronic energies were calculated using the efficient and accurate domain local pair natural orbital coupled cluster method with single-, double-, and triple substitutions (DLPNO-CCSD­(T)) electronic structure method. Owing to the method’s efficiency, we were able to employ up to quadruple-ζ quality basis sets for all hydrocarbons up to C₁₉H₄₀. In conjunction with carefully designed basis set extrapolation techniques, it is estimated that the electronic energies reported in this study deviate less than 1 kJ/mol from the canonical CCSD­(T) basis set limit. Thermodynamic corrections were calculated with the PW6B95-D3 functional and the def2-QZVP basis set. Our prediction is that the last linear conformer is either C₁₆H₃₄ or C₁₇H₃₆ with the latter being more probable. C₁₈H₃₈ can be safely ruled out as the most stable isomer at 100 K. These findings are in agreement with the elegant experimental studies of Suhm and co-workers. Deviations between the current and previous theoretical results are analyzed in detail

Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory

The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD­(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD­(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2–3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2–4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD­(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD­(T) is cheaper or at least not much more expensive than the preceding Hartree–Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree–Fock theory (at least if Hartree–Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF’s) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD­(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD­(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD­(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD­(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD­(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost

Improved Correlation Energy Extrapolation Schemes Based on Local Pair Natural Orbital Methods

It is well-known that the basis set limit is difficult to reach in correlated post Hartree–Fock ab initio calculations. One possible route forward is to employ basis set extrapolation schemes. In order to avoid prohibitively expensive calculations, the highest level calculation (typically based on the “gold standard” coupled cluster theory with single, double, and perturbative triple excitations, CCSD­(T)) is only performed with the smallest basis set, and the remaining basis set incompleteness is estimated at a lower level of theory, typically second-order Möller-Plesset perturbation theory (MP2). In this work, we provide a comprehensive investigation of alternative schemes where the MP2 extrapolation is replaced by the coupled-electron pair approximation, version 1 (CEPA/1) or the local pair natural orbital version of this method (LPNO-CEPA/1). It is shown that the MP2 method achieves apparent accuracy only due to error cancellation. Systematically more accurate results at small additional computational cost are obtained if the MP2 step is replaced by LPNO-CEPA/1. The errors of LPNO-CEPA/1 relative to canonical CEPA/1 are negligible. Owing to the highly systematic nature of the deviations between canonical and LPNO methods, basis set extrapolation reduces the LPNO errors in the total energies by 1 order of magnitude (∼0.2 kcal/mol) and errors in energy differences to essentially zero. Using the CCSD­(T)/LPNO-CEPA/1-based extrapolation scheme, new reference values are proposed for the recently published S66 set of interaction energies. The deviations between the new values and the original interactions energies are mostly very small but reach values up to 0.3 kcal/mol

Sobre el mecanismo de reacción de la transferencia intermolecular completa de o2 entre los complejos de níquel mononuclear y manganeso con ligandos macrocíclicos

The recently described intermolecular O2 transfer between the side-on Ni-O2 complex [(12-TMC)Ni-O2]+ and the manganese complex [(14-TMC)Mn]2+, where 12-TMC and 14-TMC are 12- and 14-membered macrocyclic ligands, 12-TMC=1,4,7,10-tetramethyl-1,4,7,10-tetraazacyclododecane and 14-TMC=1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane, is studied by means of DFT methods. B3LYP calculations including long-range corrections and solvent effects are performed to elucidate the mechanism. The potential energy surfaces (PESs) compatible with different electronic states of the reactants have been analyzed. The calculations confirm a two-step reaction, with a first rate-determining bimolecular step and predict the exothermic character of the global process. The relative stability of the products and the reverse barrier are in line with the fact that no reverse reaction is experimentally observed. An intermediate with a μ-η1:η1-O2 coordination and two transition states are identified on the triplet PES, slightly below the corresponding stationary points of the quintet PES, suggesting an intersystem crossing before the first transition state. The calculated activation parameters and the relative energies of the two transition sates and the products are in very good agreement with the experimental data. The calculations suggest that a superoxide anion is transferred during the reaction.La transferencia de O2 intermolecular recientemente descrita entre el complejo Ni-O2 lateral [(12-TMC) Ni-O2] + y el complejo de manganeso [(14-TMC) Mn] 2+, donde 12-TMC y 14-TMC son Ligandos macrocíclicos de 12 y 14 miembros, 12-TMC = 1,4,7,10-tetrametil-1,4,7,10-tetraazaciclododecano y 14-TMC = 1,4,8,11-tetrametil-1,4 , 8,11-tetraazaciclotetradecano, se estudia mediante métodos DFT. Los cálculos de B3LYP que incluyen correcciones de largo alcance y efectos de solventes se realizan para dilucidar el mecanismo. Se han analizado las superficies de energía potencial (PES) compatibles con diferentes estados electrónicos de los reactivos. Los cálculos confirman una reacción de dos pasos, con un primer paso bimolecular que determina la velocidad y predicen el carácter exotérmico del proceso global. La estabilidad relativa de los productos y la barrera inversa están en línea con el hecho de que no se observa experimentalmente una reacción inversa. Se identifica un intermedio con una coordinación μ-η1: η1-O2 y dos estados de transición en el triplete PES, ligeramente por debajo de los puntos estacionarios correspondientes del quinteto PES, lo que sugiere un cruce entre sistemas antes del primer estado de transición. Los parámetros de activación calculados y las energías relativas de los dos estados de transición y los productos están muy de acuerdo con los datos experimentales. Los cálculos sugieren que un anión superóxido se transfiere durante la reacción

Theoretical Elucidation of a Classic Reaction: Protonation of the Quadruple Bond of the Octachlorodimolybdate(II,II) [Mo₂Cl₈]^4– Anion

The protonation reaction of the unbridged quadruple metal–metal bond of [Mo₂Cl₈]^4– anion producing the triply bonded hydride [Mo₂(μ-H)­(μ-Cl)₂Cl₆]^3– is studied by accurate Density Functional Theory computations. The reactant, product, stable intermediates, and transition states are located on the potential energy surface. The water solvent is explicitly included in the calculations. Full reaction profiles are calculated and compared to experimental data. The mechanism of the reaction is fully elucidated. This involves two steps. The first is a proton transfer from an oxonium ion to the quadruple bond, being rate determining. The second, involves the internal rearrangement of chlorine atoms and is much faster. Activation energies with a mean value of 19 kcal/mol are calculated, in excellent agreement with experimental values

Exploring the Accuracy Limits of Local Pair Natural Orbital Coupled-Cluster Theory

The domain based local pair natural orbital coupled cluster method with single-, double-, and perturbative triple excitations (DLPNO–CCSD­(T)) is an efficient quantum chemical method that allows for coupled cluster calculations on molecules with hundreds of atoms. Because coupled-cluster theory is the method of choice if high-accuracy is needed, DLPNO–CCSD­(T) is very promising for large-scale chemical application. However, the various approximations that have to be introduced in order to reach near linear scaling also introduce limited deviations from the canonical results. In the present work, we investigate how far the accuracy of the DLPNO–CCSD­(T) method can be pushed for chemical applications. We also address the question at which additional computational cost improvements, relative to the previously established default scheme, come. To answer these questions, a series of benchmark sets covering a broad range of quantum chemical applications including reaction energies, hydrogen bonds, and other noncovalent interactions, conformer energies, and a prototype organometallic problem were selected. An accuracy of 1 kcal/mol or better can readily be obtained for all data sets using the default truncation scheme, which corresponds to the stated goal of the original implementation. Tightening of the three thresholds that control DLPNO leads to mean absolute errors and standard deviations from the canonical results of less than 0.25 kcal/mol (<1 kJ/mol). The price one has then to pay is an increased computational time by a factor close to 3. The applicability of the method is shown to be independent of the nature of the reaction. On the basis of the careful analysis of the results, three different sets of truncation thresholds (termed “LoosePNO”, “NormalPNO”, and “TightPNO”) have been chosen for “black box” use of DLPNO–CCSD­(T). This will allow users of the method to optimally balance performance and accuracy

Electrocardiographic criteria for detecting coronary artery disease in hypertensive patients with ST-segment changes during exercise testing

Purpose: It is well known that patients with arterial hypertension frequently present with ischemic electrocardiographic changes during exercise testing without actually having coronary artery disease (CAD). The purpose of this study was to establish additional electrocardiographic criteria during exercise testing for detecting CAD in hypertensive patients with ischemic ST-segment response. Methods: Three hundred eighty-two consecutive hypertensive patients (224 males, 58 8 years) who presented with ischemic electrocardiographic changes during exercise testing and agreed to undergo coronary arteriography were included in the study. Results: From 382 hypertensive patients undergoing coronary angiography, only 76 (20%) had significant coronary stenosis, whereas 306 (80%) had normal coronary arteries. From 382 patients, 287 (75%) (group A) presented with ST-segment depression during exercise in leads II-III-aVF-V-6, 271 (94%) of which had normal arteries at the angiography. The remaining 95 patients (25%) (group 13) of the studied patients presented with ST-segment depression in II-III-aVF and/or V-4 through V-6, 60 (63%) of which had CAD. Furthermore, 251 patients of group A presented with ST-segment depression during the fourth to sixth minute of the recovery period in V-4 through V-6, 247 (98%) of which had normal arteries. Another 28 patients from group B presented with ST-segment depression during the fourth to eighth minute of the recovery period in V-4 through V-6, 22 (79%) of which had significant coronary artery stenosis. Conclusions: Hypertensive patients who present with ST-segment depression during exercise in leads II-III-aVF and/or V-4 through V-6 and with a prolonged duration of this depression at the recovery phase (fourth to eighth minute) are more likely to have CAD. Absence of ST-segment depression in V-4 and V-5 at the end of exercise or during the seventh and eighth minute of recovery favors a false-positive result. (C) 2009 Elsevier Inc. All rights reserved