The quenching of Na(3 2P) by H2: Interactions and dynamics

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

Nonadiabatic Coupling in Trajectory Surface Hopping: Accurate Time Derivative Couplings by the Curvature-Driven Approximation

Trajectory surface hopping (TSH) is a widely used mixed quantum-classical dynamics method that is used to simulate molecular dynamics with multiple electronic states. In TSH, time-derivative coupling is employed to propagate the electronic coefficients and in that way to determine when the electronic state on which the nuclear trajectory is propagated switches. In this work, we discuss nonadiabatic TSH dynamics algorithms employing the curvature-driven approximation and overlap-based time derivative couplings, and we report test calculations on six photochemical reactions where we compare the results to one another and to calculations employing analytic nonadiabatic coupling vectors. We correct previous published results thanks to a bug found in the software. We also provide additional, more detailed studies of the time-derivative couplings. Our results show good agreement between curvature-driven algorithms and overlap-based algorithms.

Semiclassical Multistate Dynamics for Six Coupled 5A' States of O + O2

Dynamics simulations of high-energy O₂-O collisions play an important role in simulating thermal energy content and heat flux in flows around hypersonic vehicles. To carry out such dynamics simulations efficiently requires accurate global potential energy surfaces and (in most algorithms) state couplings for many energetically accessible electronic states. The ability to treat collisions involving many coupled electronic states has been a challenge for decades. Very recently, a new diabatization method, the parametrically managed diabatization by deep neural network (PM-DDNN), has been developed. The PM-DDNN method uses a deep neural network architecture with an activation function parametrically dependent on input data to discover and fit the diabatic potential energy matrix (DPEM) as a function of geometry, and the adiabatic potential energy surfaces are obtained by diagonalization of a small matrix with analytic matrix elements. Here, we applied the PM-DDNN method to the six lowest-energy potential energy surfaces in the ⁵A' manifold of O₃ to perform simultaneous diabatization and fitting; the data are obtained by extended multistate complete-active-space second-order perturbation theory. We then used the adiabatic surfaces for dynamics calculations with three methods: coherent switching with decay of mixing (CSDM), curvature-driven CSDM (κCSDM), and electronically curvature-driven CSDM (eκCSDM). The κCSDM calculations require only adiabatic potential energies and gradients. The three dynamical methods are in good agreement. We then calculated electronically nonadiabatic, electronically inelastic, and dissociative cross sections for seven initial collision energies, five initial vibrational levels, and four initial rotational levels. Trends in the electronically inelastic cross sections as functions of the initial collision energy and vibrational level were rationalized in terms of the coordinate ranges where the gaps between the second and third potential energy surfaces are small.

Constructing Diabatic Potential Energy Matrices with Neural Networks Based on Adiabatic Energies and Physical Considerations: Toward Quantum Dynamic Accuracy

A permutation invariant polynomial-neural network (PIP-NN) approach for constructing the global diabatic potential energy matrices (PEMs) of the coupled states of molecules is proposed. Specifically, the diabatization scheme is based merely on the adiabatic energy data of the system, which is ideally a most convenient way due to not requiring additional ab initio calculations for the data of the derivative coupling or any other physical properties of the molecule. Considering the permutation and coupling characteristics of the system, particularly in the presence of conical intersections, some vital treatments for the off-diagonal terms in diabatic PEM are essentially needed. Taking the photodissociation of H₂O(X~/B~)/NH₃(X~/A~) and nonadiabatic reaction Na(3p) + H₂ → NaH(Σ⁺) + H for example, this PIP-NN method is shown to build up the global diabatic PEMs effectively and accurately. The root-mean-square errors of the adiabatic potential energies in the fitting for three different systems are all small (<10 meV). Further quantum dynamic calculations show that the absorption spectra and product branching ratios in both H₂O(X~/B~) and NH₃(X~/A~) nonadiabatic photodissociation are well reproduced on the new diabatic PEMs, and the nonadiabatic reaction probability of Na(3p) + H₂ → NaH(Σ⁺) + H obtained on the new diabatic PEMs of the 1²A₁ and 1²B₂ states is in reasonably good agreement with previous theoretical result as well, validating this new PIP-NN method.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Nonadiabatic Dynamics of 1,3-Cyclohexadiene by Curvature-Driven Coherent Switching with Decay of Mixing

The photoinduced ring-opening reaction of 1,3-cyclohexadiene to produce 1,3,5-hexatriene is a classic electrocyclic reaction and is also a prototype for many reactions of biological and synthetic importance. Here, we simulate the ultrafast nonadiabatic dynamics of the reaction in the manifold of the three lowest valence electronic states by using extended multistate complete-active-space second-order perturbation theory (XMS-CASPT2) combined with the curvature-driven coherent switching with decay of mixing (κCSDM) dynamical method. We obtain an excited-state lifetime of 79 fs, and a product quantum yield of 40% from the 500 trajectories initiated in the S₁ excited state. The obtained lifetime and quantum yield values are very close to previously reported experimental and computed values, showing the capability of performing a reasonable nonadiabatic ring-opening dynamics with the κCSDM method that does not require nonadiabatic coupling vectors, time derivatives, or diabatization. In addition, we study the ring-opening reaction by initiating the trajectories in the dark state S₂. We also optimize the S₀/S₁ and S₁/S₂ minimum-energy conical intersections (MECIs) by XMS-CASPT2; for S₁/S₂, we optimized both an inner and an outer local-minimum-energy conical intersections (LMECIs). We provide the potential energy profile along the ring-opening coordinate by joining selected critical points via linear synchronous transit paths. We find the inner S₁/S₂ LMECI to be more crucial than the outer one.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping

Direct dynamics by mixed quantum-classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive time steps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature-driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computation time and accuracy as compared to previous mixed quantum-classical nonadiabatic dynamics algorithms. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

Nonadiabatic Molecular Dynamics by Multiconfiguration Pair-Density Functional Theory

We present the first implementation of multiconfiguration pair-density functional theory (MC-PDFT) ab initio molecular dynamics. MC-PDFT is a multireference electronic structure method that in many cases has a similar accuracy (or even better accuracy) the complete active space second-order perturbation theory (CASPT2) at a significantly lower computational cost. In this study, we introduced MC-PDFT analytical gradients into the SHARC molecular dynamics program for ab initio, nonadiabatic molecular dynamics simulations. We verify our implementation by examining the intersystem crossing dynamics of thioformaldehyde, and we observe excellent agreement with recent CASPT2 and experimental findings. Moreover, with MC-PDFT, we could perform dynamics simulations with the 12 electron in 10 orbitals active space that was computationally too expensive for direct dynamics with CASPT2.

Direct coherent switching with decay of mixing for intersystem crossing dynamics of thioformaldehyde: The effect of decoherence

We evaluate the effect of electronic decoherence on intersystem crossing in the photodynamics of thioformaldehyde. First, we show that the state-averaged complete-active-space self-consistent field electronic structure calculations with a properly chosen active space of 12 active electrons in 10 active orbitals can predict the potential energy surfaces and the singlet-triplet spin-orbit couplings quite well for CH₂S, and we use this method for direct dynamics by coherent switching with decay of mixing (CSDM). We obtain similar dynamical results with CSDM or by adding energy-based decoherence to trajectory surface hopping, with the population of triplet states tending to a small steady-state value over 500 fs. Without decoherence, the state populations calculated by the conventional trajectory surface hopping method or the semiclassical Ehrenfest method gradually increase. This difference shows that decoherence changes the nature of the results not just quantitatively but qualitatively.

Diabatization by Machine Intelligence

Understanding nonadiabatic dynamics is important for chemical and physical processes involving multiple electronic states. Direct nonadiabatic dynamics simulations are often employed to observe such processes on a femtosecond time scale. One often needs to do the simulation on a longer time scale, but direct simulation based on electronic structure calculations of the surfaces and couplings is expensive due to the large number of electronic structure calculations needed for ensemble averaging or simulation of longer-time processes. An alternative approach is to construct an analytical representation of potential energy surfaces (PESs) and couplings, which allows for faster dynamics calculations. Diabatic representations are preferred for such purposes because of the smoothness of the surfaces and couplings and the scalar nature of the couplings. However, many diabatization procedures are complicated by the need to consider orbitals or vector coupling elements, and these can make the process very labor-intensive. To circumvent these difficulties, we here propose diabatization by a deep neural network (DDNN) based on a new architecture for a deep neural network that requires neither orbital input nor vector input. The DDNN method allows convenient and semiautomatic diabatization, and it is demonstrated here for a model problem and for producing diabatic potential energy matrices for thiophenol.

Time-Derivative Couplings for Self-Consistent Electronically Nonadiabatic Dynamics

Electronically nonadiabatic dynamics methods based on a self-consistent potential, such as semiclassical Ehrenfest and coherent switching with decay of mixing, have a number of advantages but are computationally slower than approximations based on an unaveraged potential because they require evaluation of all components of the nonadiabatic coupling vector. Here we introduce a new approximation to the self-consistent potential that does not have this computational drawback. The new approximation uses time-derivative couplings evaluated by overlap integrals of electronic wave functions to approximate the nonadiabatic coupling terms in the equations of motion. We present a numerical test of the method for ethylene that shows there is little loss of accuracy in the ensemble-averaged results. This new approximation to the self-consistent potential makes direct dynamics calculations with self-consistent potentials more efficient for complex systems and makes them practically affordable for some cases where the cost was previously too high.

Conservation of Angular Momentum in Direct Nonadiabatic Dynamics

Direct nonadiabatic dynamics is used to study processes involving multiple electronic states from small molecules to materials. Compared with dynamics with fitted analytical potential energy surfaces, direct dynamics is more user-friendly in that it obtains all needed energies, gradients, and nonadiabatic couplings (NACs) by electronic structure calculations. However, the NAC that is usually used does not conserve angular momentum or the center of mass in widely used mixed quantum-classical nonadiabatic dynamics algorithms, in particular, trajectory surface hopping, semiclassical Ehrenfest, and coherent switching with decay of mixing. We show that by using a projection operator to remove the translational and rotational components of the originally computed NAC, one can restore the conservation.

New diabatic potential energy surfaces of the NaH2 system and dynamics studies for the Na(3p) + H2 → NaH + H reaction

The Na(3p) + H2(X1Σg+) → NaH(X1Σ+) + H(2S) reaction plays an important role in the field of diabatic reaction dynamics. A set of new diabatic potential energy surfaces (PESs) of the NaH2 system are structured, which include the diabatic coupling between the lowest two adiabatic states. The electronic structure calculations are performed on the multi-reference configuration interaction level with the cc-pwCVQZ and aug-cc-PVQZ basis sets for Na and H atoms. 32402 geometries are chosen to construct the diabatic data by a unitary transformation based on the molecular property method. The diabatic matrix elements of [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) are fitted by the artificial neural network model. The spectroscopic constants of diatoms obtained from the present PESs are consistent with the experimental data. The topographical and intersection characteristics of the [Formula: see text] and [Formula: see text] surfaces are discussed. Based on the new PESs, the time-dependent quantum wave packet calculations are carried out to study the reaction mechanism of the title reaction in detail.

A neural network potential energy surface for the NaH2 system and dynamics studies on the H(2S) + NaH(X1Σ+) → Na(2S) + H2(X1Σg+) reaction

In order to study the dynamics of the reaction H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺), a new potential energy surface (PES) for the ground state of the NaH₂ system is constructed based on 35 730 ab initio energy points. Using basis sets of quadruple zeta quality, multireference configuration interaction calculations with Davidson correction were carried out to obtain the ab initio energy points. The neural network method is used to fit the PES, and the root mean square error is very small (0.00639 eV). The bond lengths, dissociation energies, zero-point energies and spectroscopic constants of H₂(X¹Σ_g⁺) and NaH(X¹Σ⁺) obtained on the new NaH₂ PES are in good agreement with the experiment data. On the new PES, the reactant coordinate-based time-dependent wave packet method is applied to study the reaction dynamics of H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺), and the reaction probabilities, integral cross-sections (ICSs) and differential cross-sections (DCSs) are obtained. There is no threshold in the reaction due to the absence of an energy barrier on the minimum energy path. When the collision energy increases, the ICSs decrease from a high value at low collision energy. The DCS results show that the angular distribution of the product molecules tends to the forward direction. Compared with the LiH₂ system, the NaH₂ system has a larger mass and the PES has a larger well at the H-NaH configuration, which leads to a higher ICS value in the H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺) reaction. Because the H(²S) + NaH(X¹Σ⁺) → Na(²S) + H₂(X¹Σ_g⁺) reaction releases more energy, the product molecules can be excited to a higher vibrational state.

A New Algorithm for Efficient Direct Dynamics Calculations of Large-Curvature Tunneling and Its Application to Radical Reactions with 9-15 Atoms

We present a new algorithm for carrying out large-curvature tunneling calculations that account for extreme corner-cutting tunneling in hydrogen atom, proton, and hydride transfer reactions. The algorithm is based on two-dimensional interpolation in a physically motived set of variables that span the space of tunneling paths and tunneling energies. With this new algorithm, we are able to carry out density functional theory direct dynamics calculations of the rate constants, including multidimensional tunneling, for a set of hydrogen atom transfer reactions involving 9-15 atoms and up to 7 nonhydrogenic atoms. The reactions considered involve the abstraction of a hydrogen atom from hydrocarbons by a trifluoromethyl radical, and in particular, we consider the reactions of CF3 with CH4, C2H6, and C3H8. We also calculate several kinetic isotope effects. The electronic structure is treated by the MPWB1K/6-31+G(d,p) method, which is validated by comparison to experimental results and to CBS-Q, MCG3, and G3SX(MP3) calculations for CF3 + CH4. Harmonic vibrational frequencies along the reaction path are calculated in curvilinear coordinates with scaled frequencies, and anharmonicity is included in the lowest-frequency torsion.

Nonintuitive Diabatic Potential Energy Surfaces for Thioanisole

Diabatization of potential energy surfaces is a technique that enables convenient molecular dynamics simulations of electronically nonadiabatic processes, but diabatization itself is nonunique and can be inconvenient; the best methods to achieve diabatization are still under study. Here, we present the diabatization of two electronic states of thioanisole in the S-CH3 bond stretching and C-C-S-C torsion two-dimensional nuclear coordinate space containing a conical intersection. We use two systematic methods: the (orbital-dependent) 4-fold way and the (orbital-free) Boys localization diabatization method. These very different methods yield strikingly similar diabatic potential energy surfaces that cross at geometries where the adiabatic surfaces are well separated and do not exhibit avoided crossings, and the contours of the diabatic gap and diabatic coupling are similar for the two methods. The validity of the diabatization is supported by comparing the nonadiabatic couplings calculated from the diabatic matrix elements to those calculated by direct differentiation of the adiabatic states.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.

Atom-Cage Charge Transfer in Endohedral Metallofullerenes: Trapping Atoms Within a Sphere-Like Ridge of Avoided Crossings

Endohedral fullerences have great potential for a variety of techological applications. Here we consider B@C60 and show that the amount of charge transfer from the semimetal boron atom to the cage is a strong function of the radial distance of the atom from the center of the fullerene, and it is controlled by multistate conical intersections whose associated ridge of avoided crossings has the topology of a Euclidean sphere. The potential energy surfaces of B@C60 are characterized by two kinds of local minima: those with a boron atom located in the geometric center of the fullerene, and those with a boron atom bound to the fullerene inner wall. At the lowest-energy minimum, at the center, the boron atom is neutral, whereas the transition to the wall is accompanied by an electron transfer from boron to the fullerene cage. The two kinds of minima are separated by a ridge of avoided crossings that forms a surface with a nearly spherical shape. The properties of such systems may be altered by controlling the populations of the two kinds of minima, for example, by application of an external field. Such switchable atom-cage charge transfer may find applications in novel molecular devices.

Metal-organic charge transfer can produce biradical states and is mediated by conical intersections

The present paper illustrates key features of charge transfer between calcium atoms and prototype conjugated hydrocarbons (ethylene, benzene, and coronene) as elucidated by electronic structure calculations. One- and two-electron charge transfer is controlled by two sequential conical intersections. The two lowest electronic states that undergo a conical intersection have closed-shell and open-shell dominant configurations correlating with the 4s(2) and 4s(1)3d(1) states of Ca, respectively. Unlike the neutral-ionic state crossing in, for example, hydrogen halides or alkali halides, the path from separated reactants to the conical intersection region is uphill and the charge-transferred state is a biradical. The lowest-energy adiabatic singlet state shows at least two minima along a single approach path of Ca to the π system: (i) a van der Waals complex with a doubly occupied highest molecular orbital, denoted Φ(2)(1), and a small negative charge on Ca and (ii) an open-shell singlet (biradical) at intermediate approach (Ca...C ≈2.5-2.7 Å) with molecular orbital structure (1)(2), where (2) is an orbital showing significant charge transfer form Ca to the π-system, leading to a one-electron multicentered bond. A third minimum (iii) at shorter distances along the same path corresponding to a closed-shell state with molecular orbital structure has also been found; however, it does not necessarily represent the ground state at a given CaC distance in all three systems. The topography of the lowest adiabatic singlet potential energy surface is due to the one- and two-electron bonding patterns in Ca-π complexes.

Valence bond theory for chemical dynamics

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.

Conical intersections and semiclassical trajectories: Comparison to accurate quantum dynamics and analyses of the trajectories

Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic de-excitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%-60%. The semiclassical Ehrenfest method has an overall error of 66%, and the self-consistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of approximately 32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed.