DFT and ab initio calculations on two reactions between hydrogen atoms and the fire suppressants 2-H heptafluoropropane and CF3Br

Reaction enthalpies and barrier heights of the reactions CF3Br+H-->CF3+HBr {reaction (1)} and CF3CHFCF3+H-->CF3CFCF3+H2 {reaction (2)} have been calculated at the near state-of-the-art ab initio level, and also by employing the B3LYP, BH&HLYP, BB1K, MPW1K, MPWB1K and TPSS1KCIS functionals. In addition, the integrated molecular orbital+molecular orbital (IMOMO) method has been used to study reaction (2). The ab initio benchmark values of the reaction enthalpy (298 K) and barrier height (0 K) of reaction (2) are reported for the first time {-(0.7+/-0.7) and 13.3+/-0.5 kcal/mole respectively}. When density functional theory (DFT) results are compared with ab initio benchmarks for both reactions (1) and (2), the MPWB1K functional is found to have the best performance of the six functionals used. The IMOMO method with the RCCSD/aug-cc-pVTZ and/or RCCSD(T)/aug-cc-pVTZ levels, as the high levels of calculation on the model system, gives reaction enthalpies and barrier heights of reaction (2), which agree with ab initio benchmark values to within 1 kcal/mole. Computed key geometrical parameters and imaginary vibrational frequencies of the transition state structures of reactions (1) and (2) obtained at different levels of calculation are compared. The magnitudes of the computed imaginary vibrational frequencies of the transition states of both reactions considered are found to be very sensitive to the levels of calculation used to obtain them. The heat of formation (298 K) of CF3CFCF3 calculated at the near state-of-the-art level has a value of -(318+/-3) kcal/mole.     

Testing the performance of density functionals for the calculation of energetic properties of complex-forming radical-molecule reactions

The performance of some popular and some more recent density functional methods for the calculation of energies of stationary points on the potential surfaces of radical-molecule reactions was examined. The functionals studied are B3-LYP, BH&H, BH&H-LYP, MPW1K, MPWB1K, TPSS, TPSSh, BB1K, M05 and M05-2X, in conjunction with nine different AO basis sets. The reaction energies, barrier heights and the relative energies of the pre-and post-reaction complexes were compared with those obtained at the CCSD(T)/CBS limit for the reactions of OH radicals with HOOH and CH₃OOH. Very poor barrier heights are provided by the B3-LYP, TPSS and TPSSh functionals. The best overall performance was obtained with the BB1K, MPW1K and MPWB1K functionals. In these reactions all of the studied functionals provide converged results only if they are used with large basis sets like aug-cc-pVTZ and def2-TZVP. The data show that before relying on a functional for a specific reaction, it is desirable to make some test calculations on the performance. The same functional can predict some relative energies very well and some others very poorly even in systems including chemically similar reactants.     

MPW1K Performs Much Better than B3LYP in DFT Calculations on Reactions that Proceed by Proton-Coupled Electron Transfer (PCET)

DFT calculations have been performed with the B3LYP and MPW1K functional on the hydrogen atom abstraction reactions of ethenoxyl with ethenol and of phenoxyl with both phenol and alpha-naphthol. Comparison with the results of G3 calculations shows that B3LYP seriously underestimates the barrier heights for the reaction of ethenoxyl with ethenol by both proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms. The MPW1K functional also underestimates the barrier heights, but by much less than B3LYP. Similarly, comparison with the results of experiments on the reaction of phenoxyl radical with alpha-naphthol indicates that the barrier height for the preferred PCET mechanism is calculated more accurately by MPW1K than by B3LYP. These findings indicate that the MPW1K functional is much better suited than B3LYP for calculations on hydrogen abstraction reactions by both HAT and PCET mechanisms.     

Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions

This paper develops two new hybrid meta exchange-correlation functionals for thermochemistry, thermochemical kinetics, and nonbonded interactions. The new functionals are called PW6B95 (6-parameter functional based on Perdew-Wang-91 exchange and Becke-95 correlation) and PWB6K (6-parameter functional for kinetics based on Perdew-Wang-91 exchange and Becke-95 correlation). The resulting methods were comparatively assessed against the MGAE109/3 main group atomization energy database, against the IP13/3 ionization potential database, against the EA13/3 electron affinity database, against the HTBH38/4 and NHTBH38/04 hydrogen-transfer and non-hydrogen-transfer barrier height databases, against the HB6/04 hydrogen bonding database, against the CT7/04 charge-transfer complex database, against the DI6/04 dipole interaction database, against the WI7/05 weak interaction database, and against the new PPS5/05 pi-pi stacking interaction database. From the assessment and comparison of methods, we draw the following conclusions, based on an analysis of mean unsigned errors: (i) The PW6B95, MPW1B95, B98, B97-1, and TPSS1KCIS methods give the best results for a combination of thermochemistry and nonbonded interactions. (ii) PWB6K, MPWB1K, BB1K, MPW1K, and MPW1B95 give the best results for a combination of thermochemical kinetics and nonbonded interactions. (iii) PWB6K outperforms the MP2 method for nonbonded interactions. (iv) PW6B95 gives errors for main group covalent bond energies that are only 0.41 kcal (as measured by mean unsigned error per bond (MUEPB) for the MGAE109 database), as compared to 0.56 kcal/mol for the second best method and 0.92 kcal/mol for B3LYP.     

An assessment of theoretical procedures for predicting the thermochemistry and kinetics of hydrogen abstraction by methyl radical from benzene

The reaction enthalpy (298 K), barrier (0 K), and activation energy and preexponential factor (600-800 K) have been examined computationally for the abstraction of hydrogen from benzene by the methyl radical, to assess their sensitivity to the applied level of theory. The computational methods considered include high-level composite procedures, including W1, G3-RAD, G3(MP2)-RAD, and CBS-QB3, as well as conventional ab initio and density functional theory (DFT) methods, with the latter two classes employing the 6-31G(d), 6-31+G(d,p) and/or 6-311+G(3df,2p) basis sets, and including ZPVE/thermal corrections obtained from 6-31G(d) or 6-31+G(d,p) calculations. Virtually all the theoretical procedures except UMP2 are found to give geometries that are suitable for subsequent calculation of the reaction enthalpy and barrier. For the reaction enthalpy, W1, G3-RAD, and URCCSD(T) give best agreement with experiment, while the large-basis-set DFT procedures slightly underestimate the endothermicity. The reaction barrier is slightly more sensitive to the choice of basis set and/or correlation level, with URCCSD(T) and the low-cost BMK method providing values in close agreement with the benchmark G3-RAD value. Inspection of the theoretically calculated rate parameters reveals a minor dependence on the level of theory for the preexponential factor. There is more sensitivity for the activation energy, with a reasonable agreement with experiment being obtained for the G3 methods and the hybrid functionals BMK, BB1K, and MPW1K, especially in combination with the 6-311+G(3df,2p) basis set. Overall, the high-level G3-RAD composite procedure, URCCSD(T), and the cost-effective DFT methods BMK, BB1K, and MPW1K give the best results among the methods assessed for calculating the thermochemistry and kinetics of hydrogen abstraction by the methyl radical from benzene.     

Activation energies of pericyclic reactions: performance of DFT, MP2, and CBS-QB3 methods for the prediction of activation barriers and reaction energetics of 1,3-dipolar cycloadditions, and revised activation enthalpies for a standard set of hydrocarbon pericyclic reactions

Activation barriers and reaction energetics for the three main classes of 1,3-dipolar cycloadditions, including nine different reactions, were evaluated with the MPW1K and B3LYP density functional methods, MP2, and the multicomponent CBS-QB3 method. The CBS-QB3 values were used as standards for 1,3-dipolar cycloaddition activation barriers and reaction energetics, and the density functional theory (DFT) and MP2 methods were benchmarked against these values. The MPW1K/6-31G* method and basis set performs best for activation barriers, with a mean absolute deviation (MAD) value of 1.1 kcal/mol. The B3LYP/6-31G* method and basis set performs best for reaction enthalpies, with a MAD value of 2.4 kcal/mol, while the MPW1K method shows large errors for reaction energetics. The MP2 method gives the expected systematic underestimation of barriers. Concerted and nearly synchronous transition structures are predicted by all DFT and MP2 methods. Also reported are revised estimated 0 K experimental activation enthalpies for a standard set of hydrocarbon pericyclic reactions and updated comparisons to experiment for DFT, ab initio, and multicomponent methods. B3LYP and MPW1K methods with MAD values of 1.5 and 2.1 kcal/mol, respectively, fortuitously outperform the multicomponent CBS-QB3 method, which has a MAD value of 2.3. The MAD value of the O3LYP functional improves to 2.4 kcal/mol from the previously reported 3.0 kcal/mol.     

Trends in R-X bond dissociation energies (R = Me, Et, i-Pr, t-Bu; X = H, CH3, OCH3, OH, F): a surprising shortcoming of density functional theory

The performance of a variety of high-level composite procedures, as well as lower-cost density functional theory (DFT)- and second-order perturbation theory (MP2)-based methods, for the prediction of absolute and relative R-X bond dissociation energies (BDEs) was examined for R = Me, Et, i-Pr and t-Bu, and X = H, CH(3), OCH(3), OH and F. The methods considered include the high-level G3(MP2)-RAD and G3-RAD procedures, a variety of pure and hybrid DFT methods (B-LYP, B3-LYP, B3-P86, KMLYP, B1B95, MPW1PW91, MPW1B95, BB1K, MPW1K, MPWB1K and BMK), standard restricted (open-shell) MP2 (RMP2), and two recently introduced variants of MP2, namely spin-component-scaled MP2 (SCS-MP2) and scaled-opposite-spin MP2 (SOS-MP2). The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the lower-level DFT- and MP2-based procedures. The best DFT methods (KMLYP and particularly BMK) provide very reasonable predictions for the absolute heats of formation and R-X BDEs for the systems studied. However, all of the DFT methods overestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu, leading in some cases to incorrect qualitative behavior. In contrast, the MP2-based methods generally show larger errors (than the best DFT methods) in the absolute heats of formation and BDEs, but better behavior for the relative BDEs, although they do tend to underestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu. The potentially less computationally expensive SOS-MP2 method offers particular promise as a reliable method that might be applicable to larger systems.     

Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics

We present a number of near-exact, nonrelativistic, Born-Oppenheimer reference data sets for the parametrization of more approximate methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochemistry protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small molecules that cover varying degrees of nondynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calculated DFT values with experimental atomization energies is hampered by comparatively large experimental uncertainties in many experimental values and compounds errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. We find that the optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimolecular and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x, y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochemistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochemistry and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochemistry, B2GP-PLYP appears to be the more robust toward nondynamical correlation and strongly polar character. We additionally find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.     

Theoretical investigation of the hydrogen abstraction reaction of the OH radical with CH3CHF2 (HFC152-a): a dual level direct density functional theory dynamics study

The hydrogen abstraction reaction of the OH radical with CH(3)CHF(2) (HFC152-a) has been studied theoretically over a wide temperature range, 200-3000 K. Two different reactive sites of the molecule, CH(3) and CHF(2) groups have been investigated precisely, and results confirm that CHF(2) position of the molecule is a highly reactive site. In this study, three recently developed hybrid density functional theories, namely, MPWB1K, MPW1B95, and MPW1K, are used. The MPWB1K/6-31+G(d,p) method gives the best result for kinetic calculations, including barrier heights, reaction path information and geometry of transition state structures and other stationary points. To refine the barrier height of each channel, a single point energy calculation was performed in MPWB1K/MG3S method. The obtained rate constants by dual level direct dynamics with the interpolated single point energy method (VTST-ISPE) using DFT quantum computational methods, are consistent with available experimental data. The canonical variational transition state theory (CVT) with the zero-curvature and also the small-curvature tunneling correction methods is used to calculate the rate constants. Over the temperature range 200-3000 K, the variation effect, tunneling contribution, branching ratio of each channel are calculated. The rate constants and their temperature dependency in the form of a fitted three-parameter Arrhenius expression are k(1)(T) = 2.00 x 10(-19)(T)(2.24) exp(-1273/T), k(2)(T) = 1.95 x 10(-19)(T)(2.46) exp(-2374/T), and k(T) = 3.13 x 10(-19)(T)(2.47) exp(- 1694/T) cm(3) molecule(-1) s(-1). For the H abstraction from the CHF(2) group, a nonclassical reflection effect is detected as a dominant quantum effect.     

Kinetics and Thermodynamics of Reactions Involving Criegee Intermediates: An Assessment of Density Functional Theory and Ab Initio Methods Through Comparison with CCSDT(Q)/CBS Data

Reactions involving Criegee intermediates (CIs, R₁R₂COO) are important in atmospheric ozonolysis models. In recent years, density functional theory (DFT) and CCSD(T)-based ab initio methods are increasingly being used for modeling reaction profiles involving CIs. We obtain highly accurate CCSDT(Q)/CBS reaction energies and barrier heights for ring-closing reactions involving atmospherically important CIs (R₁/R₂ = H, Me, OH, OMe, F, CN, cyclopropene, ethylene, acetaldehyde, and acrolein). We use this benchmark data to evaluate the performance of DFT, double-hybrid DFT (DHDFT), and ab initio methods for the kinetics and thermodynamics of these reactions. We find that reaction energies are more challenging for approximate theoretical procedures than barrier heights. Overall, taking both reaction energies and barrier heights into account, only one of the 58 considered DFT methods (the meta-GGA MN12-L) attains near chemical accuracy, with root-mean-square deviations (RMSDs) of 3.5 (barrier heights) and 4.7 (reaction energies) kJ mol⁻¹. Therefore, MN12-L is recommended for investigations where CCSD(T)-based methods are not computationally feasible. For reaction barrier heights performance does not strictly follow Jacob's Ladder, for example, DHDFT methods do not perform better than conventional DFT methods. Of the ab initio methods, the cost-effective CCSD(T)/CBS(MP2) approach gives the best performance for both reaction energies and barrier heights, with RMSDs of 1.7 and 1.4 kJ mol⁻¹, respectively. All the considered Gaussian-n methods show good performance with RMSDs below the threshold of chemical accuracy for both reaction energies and barrier heights, where G4(MP2) shows the best overall performance with RMSDs of 2.9 and 1.5 kJ mol⁻¹, respectively. © 2019 Wiley Periodicals, Inc.     

Ab initio calculation of torsion and inversion barriers of the amino group in aminopyrimidines

Calculations of the barriers to internal rotation and inversion of the amino group in substituted pyrimidines have been performed. Torsion and inversion barriers were determined by several ab initio methods: HF, HF/MP2, MP4, CISD, QCISD, QCISD(T), CCSD, and CCSD(T). DFT method also employed. Dependencies of the calculated barrier heights on the basis set and the electron correlation level and on the substitution position of the nitrogen atom in the ring were studied. We have determined that for certain molecules relatively low level calculations may eventually provide adequate results, but in general, higher level calculations are necessary.     

密度泛函法计算C1-C14正构烃生成焓及C-C键裂解能

采用密度泛函理论(DFT)方法研究了费托石脑油裂解反应中涉及到C₁-C₁₄正构烃和自由基中间体的生成焓及其C-C键解离能(BDE)。 结果表明,在所有评价的密度泛函理论方法（B97-1、BB1K、B1B95、MPWB1K和MPW1B95）中,MPW1B95/6-311G(d,p)方法计算最精确。 以此方法为基准,进一步对高碳烃及其裂解产物的标准生成焓和C-C键解离能进行了预测。 与可得到的实验数据相比,MPW1B95/6-311G(d,p)方法预测的烃和自由基的平均生成焓分别为0.8和2.7 kJ/mol,C-C键解离能的平均绝对误差只有3.1 kJ/mol,表明此方法不仅可准确计算正构烃标准生成焓和C-C键解离能,而且还能正确预测C-C键解离能变化趋势。     

A direct ab initio dynamics study of the water-assisted tautomerization of formamide

Direct ab initio dynamics calculations based on a canonical variational transition-state theory with several multidimensional semiclassical tunneling approximations were carried out to obtain rate constants for the water-assisted tautomerization of formamide. The accuracy of the density functionals, namely, B-LYP, B3-LYP, and BH&H-LYP, were examined. We found that the BH&H-LYP method yields the most accurate transition-state properties when comparing it to ab initio MP2 and QCISD results, whereas B-LYP and B3-LYP methods predict barrier heights too low. Reaction path information was calculated at both the MP2 and nonlocal hybrid BH&H-LYP levels using the 6–31G(d,p) basis set. At the BH&H-LYP level, we found that the zero-point energy motion lowers the barrier to tautomerization in the formamide-water complex by 3.6 kcal/mol. When tunneling is considered, the activation energy at the BH&H-LYP level at 300 K is 17.1 kcal/mol. This is 3.4 kcal/mol below the zero-point-corrected barrier and 7.0 kcal/mol below the classical barrier. Excellent agreement between BH&H-LYP and MP2 rate constants further supports the use of BH&H-LYP for rate calculations of large systems. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 861–874, 1997     

Benchmark study of DFT functionals for late-transition-metal reactions

The performance of a wide variety of DFT exchange-correlation functionals for a number of late-transition-metal reaction profiles has been considered. Benchmark ab-initio reference data for the prototype reactions Pd + H2, Pd + CH4, Pd + C2H6 (both C-C and C-H activation), and Pd + CH3Cl are presented, while ab-initio data of lesser quality were obtained for the catalytic hydrogenation of acetone and for the low-oxidation-state and high-oxidation-state mechanisms of the Heck reaction. "Kinetics" functionals such as mPW1K, PWB6K, BB1K, and BMK clearly perform more poorly for late-transition-metal reactions than for main-group reactions, as well as compared to general-purpose functionals. There is no single "best functional" for late-transition-metal reactions, but rather a cluster of several functionals (PBE0, B1B95, PW6B95, and TPSS25B95) that perform about equally well; if main-group thermochemical performance is additionally considered, then B1B95 and PW6B95 emerge as the best performers. TPSS25B95 and TPSS33B95 offer attractive performance compromises if weak interactions and main-group barrier heights, respectively, are also important. In the ab-initio calculations, basis set superposition errors (BSSE) can be greatly reduced by ensuring that the metal spd shell has sufficient radial flexibility in the high-exponent range. Optimal HF percentages in hybrid functionals depend on the class of systems considered, increasing from anions to neutrals to cations to main-group barrier heights; transition-metal barrier heights represent an intermediate situation. The use of meta-GGA correlation functionals appears to be quite beneficial.     

How well can density functional methods describe hydrogen bonds to pi acceptors?

We employed four newly developed density functional theory (DFT) methods for the calculation of five pi hydrogen bonding systems, namely, H2O-C6H6, NH3-C6H6, HCl-C6H6, H2O-indole, and H2O-methylindole. We report new coupled cluster calculations for HCl-C6H6 that support the experimental results of Gotch and Zwier. Using the best available theoretical and experimental results for all five systems, our calculations show that the recently proposed MPW1B95, MPWB1K, PW6B95, and PWB6K methods give accurate energetic and geometrical predictions for pi hydrogen bonding interactions, for which B3LYP fails and PW91 is less accurate. We recommend the most recent DFT method, PWB6K, for investigating larger pi hydrogen bonded systems, such as those that occur in molecular recognition, protein folding, and crystal packing.     

Comparison of some representative density functional theory and wave function theory methods for the studies of amino acids

Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-311++G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-311++G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-311++G(d,p), aug-cc-pVDZ, 6-311++G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-311++G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.     

Generalized hybrid-orbital method for combining density functional theory with molecular mechanicals.

The generalized hybrid orbital (GHO) method has previously been formulated for combining molecular mechanics with various levels of quantum mechanics, in particular semiempirical neglect of diatomic differential overlap theory, ab initio Hartree-Fock theory, and self-consistent charge density functional tight-binding theory. To include electron-correlation effects accurately and efficiently in GHO calculations, we extend the GHO method to density functional theory in the generalized-gradient approximation and hybrid density functional theory (denoted by GHO-DFT and GHO-HDFT, respectively) using Gaussian-type orbitals as basis functions. In the proposed GHO-(H)DFT formalism, charge densities in auxiliary hybrid orbitals are included to calculate the total electron density. The orthonormality constraints involving the auxiliary Kohn-Sham orbitals are satisfied by carrying out the hybridization in terms of a set of L?wdin symmetrically orthogonalized atomic basis functions. Analytical gradients are formulated for GHO-(H)DFT by incorporating additional forces associated with GHO basis transformations. Scaling parameters are introduced for some of the one-electron integrals and are optimized to obtain the correct charges and geometry near the QM/MM boundary region. The GHO-(H)DFT method based on the generalized gradient approach (GGA) (BLYP and mPWPW91) and HDFT methods (B3 LYP, mPW1PW91, and MPW1 K) is tested-for geometries and atomic charges-against a set of small molecules. The following quantities are tested: 1) the C--C stretch potential in ethane, 2) the torsional barrier for internal rotation around the central C--C bond in n-butane, 3) proton affinities for a set of alcohols, amines, thiols, and acids, 4) the conformational energies of alanine dipeptide, and 5) the barrier height of the hydrogen-atom transfer between n-C4H10 and n-C4H9, where the reaction center is described at the MPW1 K/6-31G(d) level of theory.     

DFT studies of the phosphinidene derivative HPNaF and its insertion reaction with R–H(R=F,OH, NH<Subscript>2</Subscript>, CH<Subscript>3</Subscript>)

The formations of the phosphinidene derivative HPNaF and its insertion reactions with R–H (R=F, OH, NH₂, CH₃) have been systematically investigated employing the density functional theory (DFT), such as the B3LYP and MPW1PW91 methods. A comparison with the results of MP2 calculations shows that MPW1PW91 underestimates the barrier heights for the four reactions considered. Similarly, the same is also true for the B3LYP method depending on the selected reactions, but by much less than MPW1PW91, where the barrier heights of the four reactions are 25.2, 85.7, 119.0, and 142.4 kJ/mol at the B3LYP/6-311+G* level of theory, respectively. All the mechanisms of the four reactions are identical to each other, i.e., an intermediate has been located during the insertion reaction. Then, the intermediate could dissociate to substituted phosphinidane(H₂RP) and NaF with a barrier corresponding to their respective dissociation energies. Correspondingly, the reaction energies for the four reactions are −92.2, −68.1, −57.2, and −44.3 kJ/mol at the B3LYP/6-311+G* level of theory, respectively, where both the B3LYP and MPW1PW91 methods underestimate the reaction energies compared with the MP2 results. The linear correlations between the calculated barrier heights and the reaction energies have also been observed. As a result, the relative reactivity among the four insertion reactions should be as follows: H–F > H–OH > H–NH₂ > H–CH₃.