Influence of the Density Functional and Basis Set on the Relative Stabilities of Oxygenated Isomers of Diiron Models for the Active Site of [FeFe]-Hydrogenase

A series of different density functional theory (DFT) methodologies (24 functionals) in conjunction with a variety of six different basis sets (BSs) was employed to investigate the relative stabilities in the oxygenated isomers of diiron complexes that mimic the active site of [FeFe]-hydrogenase: (μ-pdt)­[Fe­(CO)₂L]­[Fe­(CO)₂L′] (pdt = propane-1,3-dithiolate; L = L′ = CO (<b>1</b>); L = PPh₃, L′ = CO (<b>2</b>); L = PMe₃, L′ = CO (<b>3</b>); L = L′ = PMe₃ (<b>4</b>). Although the enzyme may have a variety of possible sites for oxygenation, the model complexes would necessarily be oxygenated at either the diiron bridging site (<i><b>μ</b></i>-<b>O</b>) or at a sulfur (<b>SO</b>). Previous DFT studies with both B3LYP and TPSS functionals predicted a more stable <i><b>μ</b></i>-<b>O</b> isomer, whereas only the <b>SO</b> isomer was observed experimentally (<i>J. Am. Chem. Soc</i>. <b>2009</b>, 131, 8296–8307). Here, further calculations reveal that the relative stabilities of the <b>SO</b> and <i><b>μ</b></i>-<b>O</b> isomers are extremely sensitive to the choice of the functional, moderately sensitive to the S basis set, but not to the Fe basis set. The relative free energies [<i>G</i>_solv(<i><b>μ</b></i>-<b>O</b>) – <i>G</i>_solv(<b>SO</b>)] range from +10 to −60 kcal/mol, a range much larger than what would have been expected on the basis of the previous DFT results. Benchmarking of these results against coupled cluster with single and double excitation calculations, which predict that the <b>SO</b> isomer is favored, shows that the best performing functionals are BP86 and PBE0, while B97-D, M05, and SVWN overestimate and B2PLYP, BH&HLYP, BMK, M06-HF, and M06-2X underestimate the energy differences. Most of the variation occurs with the <i><b>μ</b></i>-<b>O</b> isomer and appears to be associated with a functional’s ability to predict the strength of the Fe–Fe bond in the reactant. With respect to the S basis set, it appears that the SO bond is sensitive to the nature of the d polarization functions available on the S atom. The S seems to need a d function more diffuse than the d orbital optimized to provide polarization for the S atom alone; that is, S seems to need a d orbital that has strong overlap with the O atom’s valence 2p. Other basis functions and the relative position of the PR₃ (R = Ph and Me) substituent groups have smaller influences on the free energy differences

configuration S2 explain case.

The severe global warming issue currently threatens humans’ existence and development. Countries and international organizations have effectively implemented policies to reduce carbon emissions and investigate low-carbon growth strategies. Reducing carbon emissions is a hot topic that academics and government policy-making departments are concerned about.Through necessary condition analysis (NCA) and fuzzy set qualitative comparative analysis(fsQCA), this paper investigates local governments’ configuration linkage effect and path choice to improve carbon emission performance from six dimensions: energy consumption, industrial structure, technological innovation, government support, economic development, and demographic factors. The research findings include the following: (1) Individual condition does not represent necessary conditions for the government’s carbon performance. Among the two sets of second-order equivalence configurations(S and Q) (five high-level carbon performance configurations), those dominated by economic development or low energy consumption can produce high-level carbon performance. Therefore, the six antecedent conditions dimensions work together to explain how the government can create high levels of carbon performance. (2)According to the regional comparison, China’s eastern, central, and western regions exhibit similarities and differences in the driving forces behind high carbon emission performance. All three regions can demonstrate carbon emission performance when all the factors are combined. However, when constrained by the conditions of each region’s resource endowment, the eastern region emphasizes the advantage of economic and technological innovation, the central region favors government support and demographic factors, and the western region prefers upgrading industrial structure based on a specific level of economic development.</div

configuration S3 explain case.

The severe global warming issue currently threatens humans’ existence and development. Countries and international organizations have effectively implemented policies to reduce carbon emissions and investigate low-carbon growth strategies. Reducing carbon emissions is a hot topic that academics and government policy-making departments are concerned about.Through necessary condition analysis (NCA) and fuzzy set qualitative comparative analysis(fsQCA), this paper investigates local governments’ configuration linkage effect and path choice to improve carbon emission performance from six dimensions: energy consumption, industrial structure, technological innovation, government support, economic development, and demographic factors. The research findings include the following: (1) Individual condition does not represent necessary conditions for the government’s carbon performance. Among the two sets of second-order equivalence configurations(S and Q) (five high-level carbon performance configurations), those dominated by economic development or low energy consumption can produce high-level carbon performance. Therefore, the six antecedent conditions dimensions work together to explain how the government can create high levels of carbon performance. (2)According to the regional comparison, China’s eastern, central, and western regions exhibit similarities and differences in the driving forces behind high carbon emission performance. All three regions can demonstrate carbon emission performance when all the factors are combined. However, when constrained by the conditions of each region’s resource endowment, the eastern region emphasizes the advantage of economic and technological innovation, the central region favors government support and demographic factors, and the western region prefers upgrading industrial structure based on a specific level of economic development.</div

Calibration of variables.

The severe global warming issue currently threatens humans’ existence and development. Countries and international organizations have effectively implemented policies to reduce carbon emissions and investigate low-carbon growth strategies. Reducing carbon emissions is a hot topic that academics and government policy-making departments are concerned about.Through necessary condition analysis (NCA) and fuzzy set qualitative comparative analysis(fsQCA), this paper investigates local governments’ configuration linkage effect and path choice to improve carbon emission performance from six dimensions: energy consumption, industrial structure, technological innovation, government support, economic development, and demographic factors. The research findings include the following: (1) Individual condition does not represent necessary conditions for the government’s carbon performance. Among the two sets of second-order equivalence configurations(S and Q) (five high-level carbon performance configurations), those dominated by economic development or low energy consumption can produce high-level carbon performance. Therefore, the six antecedent conditions dimensions work together to explain how the government can create high levels of carbon performance. (2)According to the regional comparison, China’s eastern, central, and western regions exhibit similarities and differences in the driving forces behind high carbon emission performance. All three regions can demonstrate carbon emission performance when all the factors are combined. However, when constrained by the conditions of each region’s resource endowment, the eastern region emphasizes the advantage of economic and technological innovation, the central region favors government support and demographic factors, and the western region prefers upgrading industrial structure based on a specific level of economic development.</div

Configurations for achieving high/non-high carbon performance.

Note: ● = core condition exists; ⓧ = missing core condition; ● = marginal condition exists; ⓧ = missing marginal condition.</p

Necessity tests for individual conditions of the QCA method.

Necessity tests for individual conditions of the QCA method.</p

configuration Q1 explain case.

The severe global warming issue currently threatens humans’ existence and development. Countries and international organizations have effectively implemented policies to reduce carbon emissions and investigate low-carbon growth strategies. Reducing carbon emissions is a hot topic that academics and government policy-making departments are concerned about.Through necessary condition analysis (NCA) and fuzzy set qualitative comparative analysis(fsQCA), this paper investigates local governments’ configuration linkage effect and path choice to improve carbon emission performance from six dimensions: energy consumption, industrial structure, technological innovation, government support, economic development, and demographic factors. The research findings include the following: (1) Individual condition does not represent necessary conditions for the government’s carbon performance. Among the two sets of second-order equivalence configurations(S and Q) (five high-level carbon performance configurations), those dominated by economic development or low energy consumption can produce high-level carbon performance. Therefore, the six antecedent conditions dimensions work together to explain how the government can create high levels of carbon performance. (2)According to the regional comparison, China’s eastern, central, and western regions exhibit similarities and differences in the driving forces behind high carbon emission performance. All three regions can demonstrate carbon emission performance when all the factors are combined. However, when constrained by the conditions of each region’s resource endowment, the eastern region emphasizes the advantage of economic and technological innovation, the central region favors government support and demographic factors, and the western region prefers upgrading industrial structure based on a specific level of economic development.</div

Carbon emission performance mechanism.

The severe global warming issue currently threatens humans’ existence and development. Countries and international organizations have effectively implemented policies to reduce carbon emissions and investigate low-carbon growth strategies. Reducing carbon emissions is a hot topic that academics and government policy-making departments are concerned about.Through necessary condition analysis (NCA) and fuzzy set qualitative comparative analysis(fsQCA), this paper investigates local governments’ configuration linkage effect and path choice to improve carbon emission performance from six dimensions: energy consumption, industrial structure, technological innovation, government support, economic development, and demographic factors. The research findings include the following: (1) Individual condition does not represent necessary conditions for the government’s carbon performance. Among the two sets of second-order equivalence configurations(S and Q) (five high-level carbon performance configurations), those dominated by economic development or low energy consumption can produce high-level carbon performance. Therefore, the six antecedent conditions dimensions work together to explain how the government can create high levels of carbon performance. (2)According to the regional comparison, China’s eastern, central, and western regions exhibit similarities and differences in the driving forces behind high carbon emission performance. All three regions can demonstrate carbon emission performance when all the factors are combined. However, when constrained by the conditions of each region’s resource endowment, the eastern region emphasizes the advantage of economic and technological innovation, the central region favors government support and demographic factors, and the western region prefers upgrading industrial structure based on a specific level of economic development.</div

Structural diagram of this article.

The severe global warming issue currently threatens humans’ existence and development. Countries and international organizations have effectively implemented policies to reduce carbon emissions and investigate low-carbon growth strategies. Reducing carbon emissions is a hot topic that academics and government policy-making departments are concerned about.Through necessary condition analysis (NCA) and fuzzy set qualitative comparative analysis(fsQCA), this paper investigates local governments’ configuration linkage effect and path choice to improve carbon emission performance from six dimensions: energy consumption, industrial structure, technological innovation, government support, economic development, and demographic factors. The research findings include the following: (1) Individual condition does not represent necessary conditions for the government’s carbon performance. Among the two sets of second-order equivalence configurations(S and Q) (five high-level carbon performance configurations), those dominated by economic development or low energy consumption can produce high-level carbon performance. Therefore, the six antecedent conditions dimensions work together to explain how the government can create high levels of carbon performance. (2)According to the regional comparison, China’s eastern, central, and western regions exhibit similarities and differences in the driving forces behind high carbon emission performance. All three regions can demonstrate carbon emission performance when all the factors are combined. However, when constrained by the conditions of each region’s resource endowment, the eastern region emphasizes the advantage of economic and technological innovation, the central region favors government support and demographic factors, and the western region prefers upgrading industrial structure based on a specific level of economic development.</div

configuration Q2 explain case.

The severe global warming issue currently threatens humans’ existence and development. Countries and international organizations have effectively implemented policies to reduce carbon emissions and investigate low-carbon growth strategies. Reducing carbon emissions is a hot topic that academics and government policy-making departments are concerned about.Through necessary condition analysis (NCA) and fuzzy set qualitative comparative analysis(fsQCA), this paper investigates local governments’ configuration linkage effect and path choice to improve carbon emission performance from six dimensions: energy consumption, industrial structure, technological innovation, government support, economic development, and demographic factors. The research findings include the following: (1) Individual condition does not represent necessary conditions for the government’s carbon performance. Among the two sets of second-order equivalence configurations(S and Q) (five high-level carbon performance configurations), those dominated by economic development or low energy consumption can produce high-level carbon performance. Therefore, the six antecedent conditions dimensions work together to explain how the government can create high levels of carbon performance. (2)According to the regional comparison, China’s eastern, central, and western regions exhibit similarities and differences in the driving forces behind high carbon emission performance. All three regions can demonstrate carbon emission performance when all the factors are combined. However, when constrained by the conditions of each region’s resource endowment, the eastern region emphasizes the advantage of economic and technological innovation, the central region favors government support and demographic factors, and the western region prefers upgrading industrial structure based on a specific level of economic development.</div