Rapid Route-Finding for Bifurcating Organic Reactions

Bispericyclic Ambimodal Dimerization of Pentafulvene: The Origin of Asynchronicity and Kinetic Selectivity of the Endo Transition State

The propensity of fulvenes to undergo dimerization has long been known, although the in-depth mechanism and electronic behavior during dimerization are still elusive. Herein, we made an attempt to gain insights into the reactivity of pentafulvene for Diels-Alder (DA) and [6 + 4]-cycloadditions via conventional and ambimodal routes. The result emphasizes that pentafulvene dimerization preferentially proceeds through a unique bifurcation mechanism where two DA pathways merge together to produce two degenerate [4 + 2]-cycloadducts from a single TS. Despite the [6 + 4]-cycloadduct being thermodynamically preferred, [4 + 2]-cycloaddition reactions are kinetically driven. Singlet biradicaloid is involved in through-space 6e- delocalization as a secondary orbital interaction that originates asynchronicity and stabilizes the bispericyclic transition state (TS). The transformation of various actively participating intrinsic bonding orbitals (IBOs) unambiguously forecasts the formation of multiple products from a single TS and rationalizes the mechanism of ambimodal reactions that are rather difficult to probe with other analyses. The changes in active IBOs clearly distinguish the conventional reactions from bifurcation reactions and can be employed to characterize and confirm the ambimodal mechanism. This report gains a crucial theoretical insight into the mechanism of bifurcation, the origin of asynchronicity, and electronic behavior in ambimodal TS, which will certainly be of enormous value for future studies.

Vibrational synchronization and its reaction pathway influence from an entropic intermediate in a dirhodium catalyzed allylic C-H activation/Cope rearrangement reaction

In reactions with consecutive transition states without an intermediate, and an energy surface bifurcation, atomic motion generally determines product selectivity. Understanding this dynamic-based selectivity can be straightforward if there is extremely fast descent from the first transition state to a product. However, in cases where a nonstatistical roaming/entropic intermediate occurs prior to product formation the motion that influences selectivity can be difficult to identify. Here we report quasiclassical direct dynamics trajectories for the dirhodium catalyzed reaction between styryldiazoacetate and 1,4-cyclohexadiene and prior experiments by Davies showed competitive allylic C-H insertion and Cope products. Trajectories confirmed the proposed energy surface bifurcation and revealed that dirhodium vinylcarbenoid when reacting with 1,4-cyclohexadiene can induce either a dynamically concerted pathway or a dynamically stepwise pathway with a nonstatistical entropic tight ion-pair intermediate. In the dynamically stepwise reaction pathway C-H insertion versus Cope selectivity is highly influenced by whether or not vibrational synchronization occurs in the nonstatistical entropic intermediate. This vibrational synchronization highlights the possible need for an entropic intermediate to have organized transition state-like motion to proceed to a product.

Dynamically or Kinetically Controlled? Computational Study of the Mechanisms of Electrophilic Aminoalkenylation of Heteroaromatics with Keteniminium Ions

Quantum chemical calculations and molecular dynamics simulations were applied to study the electrophilic aminoalkenylation of heteroaromatics with keniminium ions. Post-transition state bifurcation (PTSB) was found in the electrophilic addition step for the aminoalkenylation of pyrroles and indoles, and the selectivity for these reactions was dynamically controlled. However, the aminoalkenylation of furan was kinetically controlled because no apparent PTSB was found in the electrophilic addition step. The substituents on the keteniminium ions can also affect the dynamic results for the aminoalkenylations to pyrroles: the C2-aminoalkenylated product is much more favored over the C3-aminoalkenylated product for keteniminium ions with electron-donating substituents, while the product ratio (C2 product/C3 product) decreased when stronger electron-withdrawing substituents were applied.

Modeling Multi-Step Organic Reactions: Can Density Functional Theory Deliver Misleading Chemistry?

Many organic reactions are characterized by a complex mechanism with a variety of transition states and intermediates of different chemical natures. Their correct and accurate theoretical characterization critically depends on the accuracy of the computational method used. In this work, we study a complex ambimodal cycloaddition with five transition states, two intermediates, and three products, and we ask whether density functional theory (DFT) can provide a correct description of this type of complex and multifaceted reaction. Our work fills a gap in that most systematic benchmarks of DFT for chemical reactions have considered much simpler reactions. Our results show that many density functionals not only lead to seriously large errors but also differ from one another in predicting whether the reaction is ambimodal. Only a few of the available functionals provide a balanced description of the complex and multifaceted reactions. The parameters varied in the tested functionals are the ingredients, the treatment of medium-range and nonlocal correlation energy, and the inclusion of Hartree-Fock exchange. These results show a clear need for more benchmarks on the mechanisms of large molecules in complex reactions.

Reaction dynamics as the missing puzzle piece: the origin of selectivity in oxazaborolidinium ion-catalysed reactions

The selectivity in a group of oxazaborolidinium ion-catalysed reactions between aldehyde and diazo compounds cannot be explained using transition state theory. VRAI-selectivity, developed to predict the outcome of dynamically controlled reactions, can account for both the chemo- and the stereo-selectivity in these reactions, which are controlled by reaction dynamics. Subtle modifications to the substrate or catalyst substituents alter the potential energy surface, leading to changes in predominant reaction pathways and altering the barriers to the major product when reaction dynamics are considered. In addition, this study suggests an explanation for the mysterious inversion of enantioselectivity resulting from the inclusion of an orthoiPrO group in the catalyst.

Origins of Periselectivity and Regioselectivity in Ambimodal Tripericyclic [8+6]/[6+4]/[4+2] Intramolecular Cycloadditions of a Heptafulvenyl-Fulvene

Quantum mechanical calculations and molecular dynamics simulations have elucidated the reaction mechanism for intramolecular cycloadditions of a heptafulvenyl-fulvene tethered by a trimethylene chain. Prior experiments by Liu and Houk reported the formation of only an endo-[8+6] cycloadduct at 185 °C. Liu et al. later reported an exo-[4+2] Diels-Alder cycloadduct as the major product at 140 °C (Tetrahedron, 1999, 55, 9171). Cycloadditions involve Diels-Alder and an ambimodal intramolecular tripericyclic [8+6]/[6+4]/[4+2] cycloaddition. The mechanistic details explain the experimental reports of temperature dependence on the periselectivity of intramolecular cycloadditions. Additional calculations with multireference-based methods CASSCF and NEVPT2 highlight the artifacts of DFT methods and single-reference wavefunction-based CCSD(T) in the description of complete potential energy surface involving various cycloadditions of the heptafulvenyl-fulvene.

Dynamics study of the post-transition-state-bifurcation process of the (HCOOH)H+ → CO + H3O+/HCO+ + H2O dissociation: application of machine-learning techniques

The process of protonated formic acid dissociating from the transition state was studied using ring-polymer molecular dynamics (RPMD), classical MD, and quasi-classical trajectory (QCT) simulations. Temperature had a strong influence on the branching fractions for the HCO⁺ + H₂O and CO + H₃O⁺ dissociation channels. The RPMD and classical MD simulations showed similar behavior, but the QCT dynamics were significantly different owing to the excess energies in the quasi-classical trajectories. Machine-learning analysis identified several key features in the phase information of the vibrational motions at the transition state. We found that the initial configuration and momentum of a hydrogen atom connected to a carbon atom and the shrinking coordinate of the CO bond at the transition state play a role in the dynamics of HCO⁺ + H₂O production.

Kinetic, Thermodynamic, and Dynamic Control in Normal vs. Cross [2 + 2] Cycloadditions of Ene-Keteniminium Ions: Computational Understanding, Prediction, and Experimental Verification

Almost all reported intramolecular [2 + 2] reactions of ene-keteniminium ions gave normal [2 + 2] products with a fused bicycle framework, but not cross [2 + 2] products with a bicyclo[3.1.1]heptane skeleton, a highly pursued bioisostere in pharmaceutical chemistry. How to rationalize this and design new cross [2 + 2] reactions? Theoretical studies using density functional theory, high-level ab initio single-point energy calculations, and molecular dynamics showed that this [2 + 2] reaction has all three patterns of regiochemical control: the reaction is controlled either kinetically, thermodynamically, or dynamically. A carbocation model of forming endo and exo carbocations has been proposed to rationalize the reaction outcomes, revealing that the tethers (between alkenes and keteniminium ions), substituents (on the alkenes), and alkene configurations in ene-keteniminium ions play critical roles. These understandings were further used to predict that introducing a substituent in the terminal position of alkene with a trans configuration in ene-keteniminium ions can realize the cross [2 + 2] reaction, which is dynamically controlled for alkyl substituents or kinetically controlled for aryl substituents. These and more other predictions were realized experimentally, and many cross [2 + 2] products with a bicyclo[3.1.1]heptane skeleton can be achieved. Both molecular dynamics and new experiments have also been applied to correct a key but misassigned [2 + 2] product reported in the literature, further supporting the insightful mechanisms reported here.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Computational Design of a Tetrapericyclic Cycloaddition and the Nature of Potential Energy Surfaces with Multiple Bifurcations

An ambimodal transition state (TS) that leads to formation of four different pericyclic reaction products ([4 + 6]-, [2 + 8]-, [8 + 2]-, and [6 + 4]-cycloadducts) without any intervening minima has been designed and explored with DFT computations and quasiclassical molecular dynamics. Direct dynamics simulations propagated from the ambimodal TS show the evolution of trajectories to give the four cycloadducts. The topography of the PES is a key factor in product selectivity. A good correlation is observed between geometrical resemblance of the products to the ambimodal TS (measured by the RMSD) and the ratio of products formed in the dynamics simulations.

Symmetric Post-Transition State Bifurcation Reactions with Berry Pseudomagnetic Fields

We investigate how the Berry force (i.e., the pseudomagnetic force operating on nuclei as induced by electronic degeneracy and spin-orbit coupling (SOC)) might modify a post-transition state bifurcation (PTSB) reaction path and affect product selectivity for situations when multiple products share the same transition state. To estimate the magnitude of this effect, Langevin dynamics are performed on a model system with a valley-ridge inflection (VRI) point in the presence of a magnetic field (that mimics the Berry curvature). We also develop an analytic model for such selectivity that depends on key parameters such as the surface topology, the magnitude of the Berry force, and the nuclear friction. Within this dynamical model, static electronic structure calculations (at the level of generalized Hartree-Fock with spin-orbit coupling (GHF+SOC) theory) suggest that electronic spin induced Berry force effects may indeed lead to noticeable changes in methoxy radical isomerization.

C-H Insertion in Dirhodium Tetracarboxylate-Catalyzed Reactions despite Dynamical Tendencies toward Fragmentation: Implications for Reaction Efficiency and Catalyst Design

Rh-catalyzed C-H insertion reactions to form β-lactones suffer from post-transition state bifurcations, with the same transition states leading to ketones and ketenes via fragmentation in addition to β-lactones. In such a circumstance, traditional transition state theory cannot predict product selectivity, so we employed ab initio molecular dynamics simulations to do so and provide a framework for rationalizing the origins of said selectivity. Weak interactions between the catalyst and substrate were studied using energy decomposition and noncovalent interaction analyses, which unmasked an important role of the 2-bromophenyl substituent that has been used in multiple β-lactone-forming C-H insertion reactions. Small and large catalysts were shown to behave differently, with the latter providing a means of overcoming dynamically preferred fragmentation by lowering the barrier for the recombination of the product fragments in the grip of the large catalyst active site cavity.

Total Synthesis and Prediction of Ulodione Natural Products Guided by DFT Calculations**

A biomimetic synthetic strategy has resulted in a two‐step total synthesis of (±)‐ulodione A and the prediction of two potential natural products, (±)‐ulodiones C and D. This work was guided by computational investigations into the selectivity of a proposed biosynthetic Diels–Alder dimerization, which was then utilized in the chemical synthesis. This work highlights how biosynthetic considerations can both guide the design of efficient synthetic strategies and lead to the anticipation of new natural products.

Chemoton 2.0: Autonomous Exploration of Chemical Reaction Networks

Fueled by advances in hardware and algorithm design, large-scale automated explorations of chemical reaction space have become possible. Here, we present our approach to an open-source, extensible framework for explorations of chemical reaction mechanisms based on the first-principles of quantum mechanics. It is intended to facilitate reaction network explorations for diverse chemical problems with a wide range of goals such as mechanism elucidation, reaction path optimization, retrosynthetic path validation, reagent design, and microkinetic modeling. The stringent first-principles basis of all algorithms in our framework is key for the general applicability that avoids any restrictions to specific chemical systems. Such an agile framework requires multiple specialized software components of which we present three modules in this work. The key module, Chemoton, drives the exploration of reaction networks. For the exploration itself, we introduce two new algorithms for elementary-step searches that are based on Newton trajectories. The performance of these algorithms is assessed for a variety of reactions characterized by a broad chemical diversity in terms of bonding patterns and chemical elements. Chemoton successfully recovers the vast majority of these. We provide the resulting data, including large numbers of reactions that were not included in our reference set, to be used as a starting point for further explorations and for future reference.

Collective Synthesis of Illudalane Sesquiterpenes via Cascade Inverse Electron Demand (4 + 2) Cycloadditions of Thiophene S,S-Dioxides

Thiophene S,S-dioxides are underutilized tools for the de novo construction of benzene rings in organic synthesis. We report a collective synthesis of nine illudalane sesquiterpenes using bicyclic thiophene S,S-dioxides as generalized precursors to the indane core of the natural products. Exploiting furans as unusual dienophiles in this inverse electron demand Diels-Alder cascade, this concise and convergent approach enables the synthesis of these targets in as little as five steps. Theoretical studies rationalize the reactivity of thiophene S,S-dioxides with both electron-poor and electron-rich dienophiles and reveal reaction pathways involving either nonpolar pericyclic or bifurcating ambimodal cycloadditions. Overall, this work demonstrates the wider potential of thiophene S,S-dioxides as convenient and flexible precursors to polysubstituted arenes.

Analysing a billion reactions with the RInChI

The RInChI is a canonical identifier for reactions which is widely used in reaction databases. It can be used to handle large collections of reactions and to link information from diverse data sources. How much information can it handle? Studies of the SAVI database, which contains more than a billion reactions, demonstrate that the RInChI is useful in analysing such a large collection of molecular data, and the reduced form of the Web-RInChIKey contains enough information to be an effective differentiator of reactions. Issues of NH tautomerism and stereochemistry are handled effectively. The RInChI illustrates that some of the properties of the algorithmically-generated SAVI database differ from SPRESI, which is a collection of experimental data. The RInChI has different properties to Reaction SMILES and both approaches provide useful and distinct information. We recommend that the RInChI be included in data models for reactions.

Reaction Space Projector (ReSPer) for Visualizing Dynamic Reaction Routes Based on Reduced-Dimension Space

To analyze chemical reaction dynamics based on a reaction path network, we have developed the "Reaction Space Projector" (ReSPer) method with the aid of the dimensionality reduction method. This program has two functions: the construction of a reduced-dimensionality reaction space from a molecular structure dataset, and the projection of dynamic trajectories into the low-dimensional reaction space. In this paper, we apply ReSPer to isomerization and bifurcation reactions of the Au₅ cluster and succeed in analyzing dynamic reaction routes involved in multiple elementary reaction processes, constructing complicated networks (called "closed islands") of nuclear permutation-inversion (NPI) isomerization reactions, and elucidating dynamic behaviors in bifurcation reactions with reference to bundles of trajectories. Interestingly, in the second application, we find a correspondence between the contribution ratios in the ability to visualize and the symmetry of the morphology of closed islands. In addition, the third application suggests the existence of boundaries that determine the selectivity in bifurcation reactions, which was discussed in the phase space. The ReSPer program is a versatile and robust tool to clarify dynamic reaction mechanisms based on the reduced-dimensionality reaction space without prior knowledge of target reactions.

Stereoelectronic and dynamical effects dictate nitrogen inversion during valence isomerism in benzene imine

Non-classical processes such as heavy-atom tunneling and post transition-state dynamics govern stereoselectivity for benzene imine ⇌ 1H-azepine.

Influence of Water and Enzyme on the Post-Transition State Bifurcation of NgnD-Catalyzed Ambimodal [6+4]/[4+2] Cycloaddition

The enzyme NgnD catalyzes an ambimodal cycloaddition that bifurcates to [6+4]- and [4+2]-adducts. Both products have been isolated in experiments, but it remains unknown how enzyme and water influence the bifurcation selectivity at the femtosecond time scale. Here, we study the impact of water and enzyme on the post-transition state bifurcation of NgnD-catalyzed [6+4]/[4+2] cycloaddition by integrating quantum mechanics/molecular mechanics quasiclassical dynamics simulations and biochemical assays. The ratio of [6+4]/[4+2] products significantly differs in the gas phase, water, and enzyme. Biochemical assays were employed to validate computational predictions. The study informs how water and enzyme affect the bifurcation selectivity through perturbation of the reaction dynamics in the femtosecond time scale, revealing the fundamental roles of condensed media in dynamically controlling the chemical selectivity for biosynthetic reactions.

Bifurcating reactions: distribution of products from energy distribution in a shared reactive mode

Bifurcating reactions yield two different products emerging from one single transition state and are therefore archetypal examples of reactions that cannot be described within the framework of the traditional Eyring's transition state theory (TST). With the growing number and importance of these reactions in organic and biosynthetic chemistry, there is also an increasing demand for a theoretical tool that would allow for the accurate quantification of reaction outcome at low cost. Here, we introduce such an approach that fulfils these criteria, by evaluating bifurcation selectivity through the energy distribution within the reactive mode of the key transition state. The presented method yields an excellent agreement with experimentally reported product ratios and predicts the correct selectivity for 89% of nearly 50 various cases, covering pericyclic reactions, rearrangements, fragmentations and metal-catalyzed processes as well as a series of trifurcating reactions. With 71% of product ratios determined within the error of less than 20%, we also found that the methodology outperforms three other tested protocols introduced recently in the literature. Given its predictive power, the procedure makes reaction design feasible even in the presence of complex non-TST chemical steps.

Reactive Mode Composition Factor (RMCF) analysis is a powerful tool to forecast the product distribution of bifurcating reactions through analysis of the kinetic energy distribution within the first transition state traversed by the reacting system.

Melding of Experiment and Theory Illuminates Mechanisms of Metal-Catalyzed Rearrangements: Computational Approaches and Caveats

This review summarizes approaches and caveats in computational modeling of transition-metal-catalyzed sigmatropic rearrangements involving carbene transfer. We highlight contemporary examples of combined synthetic and theoretical investigations that showcase the synergy achievable by integrating experiment and theory.

1 Introduction

2 Mechanistic Models

3 Theoretical Approaches and Caveats

3.1 Recommended Computational Tools

3.2 Choice of Functional and Basis Set

3.3 Conformations and Ligand-Binding Modes

3.4 Solvation

4 Synergy of Experiment and Theory – Case Studies

4.1 Metal-Bound or Free Ylides?

4.2 Conformations and Ligand-Binding Modes of Paddlewheel Complexes

4.3 No Metal, Just Light

4.4 How To ‘Cope’ with Nonstatistical Dynamic Effects

5 Outlook

A transferable active-learning strategy for reactive molecular force fields

Predictive molecular simulations require fast, accurate and reactive interatomic potentials. Machine learning offers a promising approach to construct such potentials by fitting energies and forces to high-level quantum-mechanical data, but doing so typically requires considerable human intervention and data volume. Here we show that, by leveraging hierarchical and active learning, accurate Gaussian Approximation Potential (GAP) models can be developed for diverse chemical systems in an autonomous manner, requiring only hundreds to a few thousand energy and gradient evaluations on a reference potential-energy surface. The approach uses separate intra- and inter-molecular fits and employs a prospective error metric to assess the accuracy of the potentials. We demonstrate applications to a range of molecular systems with relevance to computational organic chemistry: ranging from bulk solvents, a solvated metal ion and a metallocage onwards to chemical reactivity, including a bifurcating Diels-Alder reaction in the gas phase and non-equilibrium dynamics (a model SN2 reaction) in explicit solvent. The method provides a route to routinely generating machine-learned force fields for reactive molecular systems.

Pathway Bifurcations in the Activation of Allylic Halides by Palladium and Their Influence on the Dynamics of η1 and η3 Allyl Intermediates

Transition-metal-catalyzed allylic substitution often exhibits complex product selectivity patterns, which have been primarily attributed to π ↔ σ ↔ π isomerization of the η¹ and η³ allyl intermediates. Product selectivity may be even further complicated if η¹- and η³-allyls share a single transition state (TS), leading to their formation resulting in a post-transition-state bifurcation (PTSB). In this work, density functional theory calculations using ab initio molecular dynamics (AIMD) have been carried out that support the presence of a PTSB in Pd-catalyzed allylic halide activation directly influencing product selectivity. The AIMD results initiated from the TS predict the η¹-allyl to be favored in the gas phase and a low dielectric (ε < 2.5) for trialkylphosphines, while the selectivity shifts toward the η³-allyl in higher dielectrics. The minimum energy path is also predicted to shift in product preference, consistent with the dynamics predictions. The bifurcation in allylic chloride activation is predicted to largely favor the η³-allyl at any solvent polarity. A PTSB was also discovered to be present in Ni and Pt allylic activation but with less bifurcation. These results offer a unique view into the mechanism of metal-catalyzed allylic substitution.

Machine learning classification of disrotatory IRC and conrotatory non-IRC trajectory motion for cyclopropyl radical ring opening

Quasiclassical trajectory analysis is now a standard tool to analyze non-minimum energy pathway motion of organic reactions. However, due to the large amount of information associated with trajectories, quantitative analysis of the dynamic origin of reaction selectivity is complex. For the electrocyclic ring opening of cyclopropyl radical, more than 4000 trajectories were run showing that allyl radicals are formed through a mixture of disrotatory intrinsic reaction coordinate (IRC) motion as well as conrotatory non-IRC motion. Geometric, vibrational mode, and atomic velocity transition-state features from these trajectories were used for supervised machine learning analysis with classification algorithms. Accuracy >80% with a random forest model enabled quantitative and qualitative assessment of transition-state trajectory features controlling disrotatory IRC versus conrotatory non-IRC motion. This analysis revealed that there are two key vibrational modes where their directional combination provides prediction of IRC versus non-IRC motion.

VRAI-selectivity: calculation of selectivity beyond transition state theory

In recent years, a growing number of organic reactions in the literature have shown selectivity controlled by reaction dynamics rather than by transition state theory. Such reactions are difficult to analyse because the transition state theory approach often does not capture the subtlety of the energy landscapes the compounds traverse and, therefore, cannot accurately predict the selectivity. We present an algorithm that can predict the major product and selectivity for a wide range of potential energy surfaces where the product distribution is influenced by reaction dynamics. The method requires as input calculation of the transition states, the intermediate (if present) and the product geometries. The algorithm is quick and simple to run and, except for two reactions with long alkyl chains, calculates selectivity more accurately than transition state theory alone.

Cycloadditions of Cyclopentadiene and Cycloheptatriene with Tropones: All Endo-[6+4] Cycloadditions Are Ambimodal

The cycloadditions of cyclopentadiene and cycloheptatriene with tropone are some of the earliest published examples of [6+4] cycloaddition reactions. We report quantum mechanical studies (ωB97X-D and DLPNO-CCSD(T)) of transition structures and products of these reactions, as well as quasi-classical molecular dynamics simulations of reaction trajectories. The study reveals that these cycloadditions involve ambimodal transition states resulting in a web of products by pericyclic interconversion pathways. Combined with these studies, calculations of simple parent systems and a thorough meta-analysis of literature examples reveal the general concept that all endo-[6+4] cycloadditions are ambimodal.

Using experimental and computational approaches to probe an unusual carbon-carbon bond cleavage observed in the synthesis of benzimidazole N-oxides

Experimental and computational studies have been performed in order to investigate an unusual carbon-carbon bond cleavage that occurs in the preparation of certain benzimidazole N-oxides from anilines. The key factor determining the outcome of the reaction was found to be the substituents on the amine functionality of the aniline.

Construction of Two-Dimensional Potential Energy Surfaces of Reactions with Post-Transition-State Bifurcations

Reactions with post-transition-state bifurcations (PTSBs) involve initial ambimodal transition-state structures followed by an unstable region leading to two possible products. PTSBs are seen in many organic, organometallic, and biosynthetic reactions, but analyzing the origins of selectivity for these reactions is challenging, in large part due to the complex nature of the potential energy surfaces involved, which precludes analyses based on single intrinsic reaction coordinate (IRC; steepest-descent path in mass-weighted coordinate). While selectivity can be predicted using molecular dynamics simulation, connecting results from such calculations to the topography of potential energy surfaces is difficult. In the present work, a method for generating two-dimensional potential energy surfaces for PTSBs is described. The first dimension starts with the IRC for the first transition-state structure, followed by a modified reaction coordinate that reaches the second transition-state structure, which interconverts the two products of a bifurcating reaction path. The IRC for the second transition-state structure constitutes the second dimension. In addition, a method for mapping trajectories from Born-Oppenheimer molecular dynamics simulations onto these surfaces is described. Both approaches are illustrated with representative examples from the field of organic chemistry. The 2D-PESs for five asymmetric cases tested have clear tilted topography after the first transition-state structure, and the tilted direction correlates well with the selectivity observed from previous dynamic simulation. Instead of selecting reaction coordinates by chemical intuition, our method provides a general means to construct two-dimensional potential energy surfaces for reactions with post-transition-state bifurcations.