An efficient and near linear scaling pair natural orbital based local coupled cluster method

Molecular energies from an incremental fragmentation method

The systematic molecular fragmentation method by Collins and Deev [J. Chem. Phys. 125, 104104 (2006)] has been used to calculate total energies and relative conformational energies for a number of small and extended molecular systems. In contrast to the original approach by Collins, we have tested the accuracy of the fragmentation method by utilising an incremental scheme in which the energies at the lowest level of the fragmentation are calculated on an accurate quantum chemistry level while lower-cost methods are used to correct the low-level energies through a high-level fragmentation. In this work, the fragment energies at the lowest level of fragmentation were calculated using the random-phase approximation (RPA) and two recently developed extensions to the RPA while the incremental corrections at higher levels of the fragmentation were calculated using standard density functional theory (DFT) methods. The complete incremental fragmentation method has been shown to reproduce the supermolecule results with a very good accuracy, almost independent on the molecular type, size, or type of decomposition. The fragmentation method has also been used in conjunction with the DFT-SAPT (symmetry-adapted perturbation theory) method which enables a breakdown of the total nonbonding energy contributions into individual interaction energy terms. Finally, the potential problems of the method connected with the use of capping hydrogen atoms are analysed and two possible solutions are supplied.

The multilevel CC3 coupled cluster model

We present an efficient implementation of the closed shell multilevel coupled cluster method where coupled cluster singles and doubles (CCSD) is used for the inactive orbital space and CCSD with perturbative triples (CC3) is employed for the smaller active orbital space. Using Cholesky orbitals, the active space can be spatially localized and the computational cost is greatly reduced compared to full CC3 while retaining the accuracy of CC3 excitation energies. For the small organic molecules considered we achieve up to two orders of magnitude reduction in the computational requirements.

Molecular Dipole Moments within the Incremental Scheme Using the Domain-Specific Basis-Set Approach

We present the first implementation of the fully automated incremental scheme for CCSD unrelaxed dipole moments using the domain-specific basis-set approach. Truncation parameters are varied, and the accuracy of the method is statistically analyzed for a test set of 20 molecules. The local approximations introduce small errors at second order and negligible ones at third order. For a third-order incremental CCSD expansion with a CC2 error correction, a cc-pVDZ/SV domain-specific basis set (tmain = 3.5 Bohr), and the truncation parameter f = 30 Bohr, we obtain a mean error of 0.00 mau (-0.20 mau) and a standard deviation of 1.95 mau (2.17 mau) for the total dipole moments (Cartesian components of the dipole vectors). By analyzing incremental CCSD energies, we demonstrate that the MP2 and CC2 error correction schemes are an exclusive correction for the domain-specific basis-set error. Our implementation of the incremental scheme provides fully automated computations of highly accurate dipole moments at reduced computational cost and is fully parallelized in terms of the calculation of the increments. Therefore, one can utilize the incremental scheme, on the same hardware, to extend the basis set in comparison to standard CCSD and thus obtain a better total accuracy.

Sparse maps--A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Third-Order Incremental Dual-Basis Set Zero-Buffer Approach for Large High-Spin Open-Shell Systems

The third-order incremental dual-basis set zero-buffer approach (inc3-db-B0) is an efficient, accurate, and black-box quantum chemical method for obtaining correlation energies of large systems, and it has been successfully applied to many real chemical problems. In this work, we extend this approach to high-spin open-shell systems. In the open-shell approach, we will first decompose the occupied orbitals of a system into several domains by a K-means clustering algorithm. The essential part is that we preserve the active (singly occupied) orbitals in all the calculations of the domain correlation energies. The duplicated contributions of the active orbitals to the correlation energy are subtracted from the incremental expansion. All techniques of truncating the virtual space such as the B0 approximation can be applied. This open-shell inc3-db-B0 approach is combined with the CCSD and CCSD(T) methods and applied to the computations of a singlet-triplet gap and an electron detachment process. Our approach exhibits an accuracy better than 0.6 kcal/mol or 0.3 eV compared with the standard implementation, while it saves a large amount of the computational time and can be efficiently parallelized.

Systematic Error Estimation for Chemical Reaction Energies

For a theoretical understanding of the reactivity of complex chemical systems, accurate relative energies between intermediates and transition states are required. Despite its popularity, density functional theory (DFT) often fails to provide sufficiently accurate data, especially for molecules containing transition metals. Due to the huge number of intermediates that need to be studied for all but the simplest chemical processes, DFT is, to date, the only method that is computationally feasible. Here, we present a Bayesian framework for DFT that allows for error estimation of calculated properties. Since the optimal choice of parameters in present-day density functionals is strongly system dependent, we advocate for a system-focused reparameterization. While, at first sight, this approach conflicts with the first-principles character of DFT that should make it, in principle, system independent, we deliberately introduce system dependence to be able to assign a stochastically meaningful error to the system-dependent parametrization, which makes it nonarbitrary. By reparameterizing a functional that was derived on a sound physical basis to a chemical system of interest, we obtain a functional that yields reliable confidence intervals for reaction energies. We demonstrate our approach on the example of catalytic nitrogen fixation.

Toward Rational Design of 3d Transition Metal Catalysts for CO2 Hydrogenation Based on Insights into Hydricity-Controlled Rate-Determining Steps

Carbon dioxide functionalization attracts much interest due to the current environmental and energy challenges. Our earlier work (Mondal, B.; Neese, F.; Ye, S. Inorg. Chem. 2015, 54, 7192-7198) demonstrated that CO2 hydrogenation mediated by base metal catalysts [M(H)(η(2)-H2)(PP3(Ph))](n+) (M = Co(III) and Fe(II), n = 1, 2; PP3(Ph) = tris(2-(diphenylphosphino)phenyl)phosphine) features discrete rate-determining steps (RDSs). Specifically, the reaction with [Co(III)(H)(η(2)-H2)(PP3(Ph))](2+) passes through a hydride-transfer RDS, whereas the conversion with [Fe(II)(H)(η(2)-H2)(PP3(Ph))](+) traverses a H2-splitting RDS. More importantly, we found that the nature and barrier of the RDS likely correlate with the hydride affinity or hydricity of the dihydride intermediate [M(H)2(PP3(Ph))]((n-1)+) generated by H2-splitting. In the present contribution, following this notion we design a series of potential Fe(II) and Co(III) catalysts, for which the respective dihydride species possess differential hydricities, and computationally investigated their reactivity toward CO2 hydrogenation. Our results reveal that lowering the hydrictiy of [Co(III)(H)2(PP3(Ph))](+) by introducing anionic anchors in PP3(Ph) dramatically decreases the hydride-transfer RDS barrier, as shown for the enhanced reactivity of [Co(H)(η(2)-H2)(CP3(Ph))](+) and [Co(H)(η(2)-H2)(SiP3(Ph))](+) (CP3(Ph) = tris(2-(diphenylphosphino)phenyl)methyl, SiP3(Ph) = tris(2-(diphenylphosphino)phenyl)silyl), while the same ligand modification increases the H2-splitting RDS barriers for [Fe(H)(η(2)-H2)(CP3(Ph))] and [Fe(H)(η(2)-H2)(SiP3(Ph))] relative to that for [Fe(H)(η(2)-H2)(PP3(Ph))](+). Conversely, upon increasing the hydricity of [Fe(II)(H)2(PP3(Ph))] by adding an electron-withdrawing group to PP3(Ph), the transformation with [Fe(H)(η(2)-H2)(PP3(PhNO2))](+) (PP3(PhNO2) = tris(2-(diphenylphosphino)-4-nitrophenyl)phosphine) is predicted to encounter a lower barrier for H2-splitting and a higher barrier for hydride transfer than those for [Fe(H)(η(2)-H2)(PP3(Ph))](+). Thus, we have shown that hydricity can be used as a guide to direct the rational design and development of more efficient catalysts.

Ionization Energies and Aqueous Redox Potentials of Organic Molecules: Comparison of DFT, Correlated ab Initio Theory and Pair Natural Orbital Approaches

The calculation of redox potentials involves large energetic terms arising from gas phase ionization energies, thermodynamic contributions, and solvation energies of the reduced and oxidized species. In this work we study the performance of a wide range of wave function and density functional theory methods for the prediction of ionization energies and aqueous one-electron oxidation potentials of a set of 19 organic molecules. Emphasis is placed on evaluating methods that employ the computationally efficient local pair natural orbital (LPNO) approach, as well as several implementations of coupled cluster theory and explicitly correlated F12 methods. The electronic energies are combined with implicit solvation models for the solvation energies. With the exception of MP2 and its variants, which suffer from enormous errors arising at least partially from the poor Hartree-Fock reference, ionization energies can be systematically predicted with average errors below 0.1 eV for most of the correlated wave function based methods studies here, provided basis set extrapolation is performed. LPNO methods are the most efficient way to achieve this type of accuracy. DFT methods show in general larger errors and suffer from inconsistent behavior. The only exception is the M06-2X functional which is found to be competitive with the best LPNO-based approaches for ionization energies. Importantly, the limiting factor for the calculation of accurate redox potentials is the solvation energy. The errors in the predicted solvation energies by all continuum solvation models tested in this work dominate the final computed reduction potential, resulting in average errors typically in excess of 0.3 V and hence obscuring the gains that arise from choosing a more accurate electronic structure method.

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.

The Effect of Water and Bases on the Clustering of a Cyclohexene Autoxidation Product C6H8O7 with Sulfuric Acid

We investigate the molecular interaction between sulfuric acid and a C6H8O7 ketodiperoxy acid compound (a proxy for highly oxidized products of, e.g., monoterpene autoxidation) in the presence of water, ammonia, or dimethylamine. The molecular geometries are obtained using density functional theory (M06-2X, PW91, and ωB97X-D) with the 6-31++G(d,p) basis set, and the binding energy is corrected utilizing a high-level DLPNO-CCSD(T)/def2-QZVPP calculation. The formation free energies were calculated (ΔG at 298 K and 1 atm), and the stability of the molecular clusters was evaluated. The presence of bases is found to enhance the interaction between ketodiperoxy acid compounds and sulfuric acid. The addition of C6H8O7 compounds to (H2SO4)(NH3) or (H2SO4)((CH3)2NH) clusters is, however, not able to compete with the corresponding uptake of another sulfuric acid molecule, even at a high loading of organic compounds. We furthermore investigate the origin of the weak binding of peroxyacid compounds using atoms in molecules and natural bonding orbital analysis. The weak binding is caused by an internal hydrogen bond and the lack of a strong hydrogen bond acceptor in the peroxyacid group. These findings indicate that autoxidation products containing solely or mainly hydroperoxide and carbonyl functional groups do not participate in the initial step of new particle formation and thereby only contribute to the growth of atmospheric particles.

Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems

A new flavor of the frozen natural orbital complete active space second-order perturbation theory method (FNO-CASPT2, Aquilante et al., J. Chem. Phys. 131, 034113) is proposed herein. In this new implementation, the virtual space in Cholesky decomposition-based CASPT2 computations (CD-CASPT2) is truncated by excluding those orbitals that contribute the least toward preserving a predefined value of the trace of an approximate density matrix, as that represents a measure of the amount of dynamic correlation retained in the model. In this way, the amount of correlation included is practically constant at all nuclear arrangements, thus allowing for the computation of smooth electronic states surfaces and energy gradients-essential requirements for theoretical studies in photochemistry. The method has been benchmarked for a series of relevant biochromophores for which large speed-ups have been recorded while retaining the accuracy achieved in the corresponding CD-CASPT2 calculations. Both vertical excitation energies and gradient calculations have been carried out to establish general guidelines as to how much correlation needs to be retained in the calculation for the results to be consistent with the CD-CASPT2 findings. Our results feature errors within a tenth of an eV for the most difficult cases and have been validated to be used for gradient computations where an up to 3-fold speed-up is observed depending on the size of the system and the basis set employed.

Can density cumulant functional theory describe static correlation effects?

We evaluate the performance of density cumulant functional theory (DCT) for capturing static correlation effects. In particular, we examine systems with significant multideterminant character of the electronic wave function, such as the beryllium dimer, diatomic carbon, m-benzyne, 2,6-pyridyne, twisted ethylene, as well as the barrier for double-bond migration in cyclobutadiene. We compute molecular properties of these systems using the ODC-12 and DC-12 variants of DCT and compare these results to multireference configuration interaction and multireference coupled-cluster theories, as well as single-reference coupled-cluster theory with single, double (CCSD), and perturbative triple excitations [CCSD(T)]. For all systems the DCT methods show intermediate performance between that of CCSD and CCSD(T), with significant improvement over the former method. In particular, for the beryllium dimer, m-benzyne, and 2,6-pyridyne, the ODC-12 method along with CCSD(T) correctly predict the global minimum structures, while CCSD predictions fail qualitatively, underestimating the multireference effects. Our results suggest that the DC-12 and ODC-12 methods are capable of describing emerging static correlation effects but should be used cautiously when highly accurate results are required. Conveniently, the appearance of multireference effects in DCT can be diagnosed by analyzing the DCT natural orbital occupations, which are readily available at the end of the energy computation.

Stabilizing and Modulating Color by Copigmentation: Insights from Theory and Experiment

Natural anthocyanin pigments/dyes and phenolic copigments/co-dyes form noncovalent complexes, which stabilize and modulate (in particular blue, violet, and red) colors in flowers, berries, and food products derived from them (including wines, jams, purees, and syrups). This noncovalent association and their electronic and optical implications constitute the copigmentation phenomenon. Over the past decade, experimental and theoretical studies have enabled a molecular understanding of copigmentation. This review revisits this phenomenon to provide a comprehensive description of the nature of binding (the dispersion and electrostatic components of π-π stacking, the hydrophobic effect, and possible hydrogen-bonding between pigment and copigment) and of spectral modifications occurring in copigmentation complexes, in which charge transfer plays an important role. Particular attention is paid to applications of copigmentation in food chemistry.

Modelling of graphene functionalization

This perspective describes the available theoretical methods and models for simulating graphene functionalization based on quantum and classical mechanics.

Going clean: structure and dynamics of peptides in the gas phase and paths to solvation

The gas phase is an artificial environment for biomolecules that has gained much attention both experimentally and theoretically due to its unique characteristic of providing a clean room environment for the comparison between theory and experiment. In this review we give an overview mainly on first-principles simulations of isolated peptides and the initial steps of their interactions with ions and solvent molecules: a bottom up approach to the complexity of biological environments. We focus on the accuracy of different methods to explore the conformational space, the connections between theory and experiment regarding collision cross section evaluations and (anharmonic) vibrational spectra, and the challenges faced in this field.

First UHF Implementation of the Incremental Scheme for Open-Shell Systems

The incremental scheme makes it possible to compute CCSD(T) correlation energies to high accuracy for large systems. We present the first extension of this fully automated black-box approach to open-shell systems using an Unrestricted Hartree-Fock (UHF) wave function, extending the efficient domain-specific basis set approach to handle open-shell references. We test our approach on a set of organic and metal organic structures and molecular clusters and demonstrate standard deviations from canonical CCSD(T) values of only 1.35 kJ/mol using a triple ζ basis set. We find that the incremental scheme is significantly more cost-effective than the canonical implementation even for relatively small systems and that the ease of parallelization makes it possible to perform high-level calculations on large systems in a few hours on inexpensive computers. We show that the approximations that make our approach widely applicable are significantly smaller than both the basis set incompleteness error and the intrinsic error of the CCSD(T) method, and we further demonstrate that incremental energies can be reliably used in extrapolation schemes to obtain near complete basis set limit CCSD(T) reaction energies for large systems.

Reactivity of Dimeric Tetrazirconium(IV) Wells-Dawson Polyoxometalate toward Dipeptide Hydrolysis Studied by a Combined Experimental and Density Functional Theory Approach

Detailed kinetic studies on the hydrolysis of glycylglycine (Gly-Gly) in the presence of the dimeric tetrazirconium(IV)-substituted Wells-Dawson-type polyoxometalate Na14[Zr4(P2W16O59)2(μ3-O)2(OH)2(H2O)4] · 57H2O (1) were performed by a combination of (1)H, (13)C, and (31)P NMR spectroscopies. The catalyst was shown to be stable under a broad range of reaction conditions. The effect of pD on the hydrolysis of Gly-Gly showed a bell-shaped profile with the fastest hydrolysis observed at pD 7.4. The observed rate constant for the hydrolysis of Gly-Gly at pD 7.4 and 60 °C was 4.67 × 10(-7) s(-1), representing a significant acceleration as compared to the uncatalyzed reaction. (13)C NMR data were indicative for coordination of Gly-Gly to 1 via its amide oxygen and amine nitrogen atoms, resulting in a hydrolytically active complex. Importantly, the effective hydrolysis of a series of Gly-X dipeptides with different X side chain amino acids in the presence of 1 was achieved, and the observed rate constant was shown to be dependent on the volume, chemical nature, and charge of the X amino acid side chain. To give a mechanistic explanation of the observed catalytic hydrolysis of Gly-Gly, a detailed quantum-chemical study was performed. The theoretical results confirmed the nature of the experimentally suggested binding mode in the hydrolytically active complex formed between Gly-Gly and 1. To elucidate the role of 1 in the hydrolytic process, both the uncatalyzed and the polyoxometalate-catalyzed reactions were examined. In the rate-determining step of the uncatalyzed Gly-Gly hydrolysis, a carboxylic oxygen atom abstracts a proton from a solvent water molecule and the nascent OH nucleophile attacks the peptide carbon atom. Analogous general-base activity of the free carboxylic group was found to take place also in the case of polyoxometalate-catalyzed hydrolysis as the main catalytic effect originates from the -C═O···Zr(IV) binding.

Mechanistic Aspects of Aryl-Halide Oxidative Addition, Coordination Chemistry, and Ring-Walking by Palladium

This contribution describes the reactivity of a zero-valent palladium phosphine complex with substrates that contain both an aryl halide moiety and an unsaturated carbon-carbon bond. Although η(2) -coordination of the metal center to a C=C or C≡C unit is kinetically favored, aryl halide bond activation is favored thermodynamically. These quantitative transformations proceed under mild reaction conditions in solution or in the solid state. Kinetic measurements indicate that formation of η(2) -coordination complexes are not nonproductive side-equilibria, but observable (and in several cases even isolated) intermediates en route to aryl halide bond cleavage. At the same time, DFT calculations show that the reaction with palladium may proceed through a dissociation-oxidative addition mechanism rather than through a haptotropic intramolecular process (i.e., ring walking). Furthermore, the transition state involves coordination of a third phosphine to the palladium center, which is lost during the oxidative addition as the C-halide bond is being broken. Interestingly, selective activation of aryl halides has been demonstrated by adding reactive aryl halides to the η(2) -coordination complexes. The product distribution can be controlled by the concentration of the reactants and/or the presence of excess phosphine.

Enhancing NMR Prediction for Organic Compounds Using Molecular Dynamics

NMR spectroscopy is a crucial tool in organic chemistry for the routine characterization of small molecules, structural elucidation of natural products, and study of reaction mechanisms. Although there is evidence that thermal motions strongly affect observed resonances, conventional predictions are performed only on stationary structures. Here we show that quasiclassical molecular dynamics provides a highly accurate and broadly applicable method for improving shielding predictions. Gas-phase values of the absolute shieldings of protons and carbons are predicted to nearly within experimental uncertainty, while the chemical shifts of large systems such as natural products are closely reproduced. Importantly, these results are obtained without the use of any empirical corrections. Our analysis suggests that the linear scaling factors currently employed are primarily a correction for vibrational effects. As a result, our method extends the reach of prediction methods to the study of molecules with unusual dynamics such as the iconic and controversial [18]annulene. Our predictions agree closely with experiment at both low and high temperatures and provide strong evidence that the equilibrium structure of [18]annulene is planar and aromatic.

Quantum chemical benchmark study on 46 RNA backbone families using a dinucleotide unit

We have created a benchmark set of quantum chemical structure-energy data denoted as UpU46, which consists of 46 uracil dinucleotides (UpU), representing all known 46 RNA backbone conformational families. Penalty-function-based restrained optimizations with COSMO TPSS-D3/def2-TZVP ensure a balance between keeping the target conformation and geometry relaxation. The backbone geometries are close to the clustering-means of their respective RNA bioinformatics family classification. High-level wave function methods (DLPNO-CCSD(T) as reference) and a wide-range of dispersion-corrected or inclusive DFT methods (DFT-D3, VV10, LC-BOP-LRD, M06-2X, M11, and more) are used to evaluate the conformational energies. The results are compared to the Amber RNA bsc0χOL3 force field. Most dispersion-corrected DFT methods surpass the Amber force field significantly in accuracy and yield mean absolute deviations (MADs) for relative conformational energies of ∼0.4-0.6 kcal/mol. Double-hybrid density functionals represent the most accurate class of density functionals. Low-cost quantum chemical methods such as PM6-D3H+, HF-3c, DFTB3-D3, as well as small basis set calculations corrected for basis set superposition errors (BSSEs) by the gCP procedure are also tested. Unfortunately, the presently available low-cost methods are struggling to describe the UpU conformational energies with satisfactory accuracy. The UpU46 benchmark is an ideal test for benchmarking and development of fast methods to describe nucleic acids, including force fields.

Control in the Rate-Determining Step Provides a Promising Strategy To Develop New Catalysts for CO2 Hydrogenation: A Local Pair Natural Orbital Coupled Cluster Theory Study

The development of efficient catalysts with base metals for CO2 hydrogenation has always been a major thrust of interest. A series of experimental and theoretical work has revealed that the catalytic cycle typically involves two key steps, namely, base-promoted heterolytic H2 splitting and hydride transfer to CO2, either of which can be the rate-determining step (RDS) of the entire reaction. To explore the determining factor for the nature of RDS, we present herein a comparative mechanistic investigation on CO2 hydrogenation mediated by [M(H)(η(2)-H2)(PP3(Ph))](n+) (M = Fe(II), Ru(II), and Co(III); PP3(Ph) = tris(2-(diphenylphosphino)phenyl)phosphine) type complexes. In order to construct reliable free energy profiles, we used highly correlated wave function based ab initio methods of the coupled cluster type alongside the standard density functional theory. Our calculations demonstrate that the hydricity of the metal-hydride intermediate generated by H2 splitting dictates the nature of the RDS for the Fe(II) and Co(III) systems, while the RDS for the Ru(II) catalyst appears to be ambiguous. CO2 hydrogenation catalyzed by the Fe(II) complex that possesses moderate hydricity traverses an H2-splitting RDS, whereas the RDS for the high-hydricity Co(III) species is found to be the hydride transfer. Thus, our findings suggest that hydricity can be used as a practical guide in future catalyst design. Enhancing the electron-accepting ability of low-hydricity catalysts is likely to improve their catalytic performance, while increasing the electron-donating ability of high-hydricity complexes may speed up CO2 conversion. Moreover, we also established the active roles of base NEt3 in directing the heterolytic H2 splitting and assisting product release through the formation of an acid-base complex.