Time-dependent quantum wave-packet description of H and D atom tunneling in N–H and N–D photodissociation of methylamine and methylamine-d[sub 2]

Hybrid Density Functional Valence Bond Method with Multistate Treatment

Recently, a hybrid density functional valence bond (VB) method, λ-DFVB(U), has been proposed and shown to give accuracy that is comparable to that of CASPT2 in calculations of atomization energies, atomic excitation energies, and reaction barriers, while its computational cost is approximately the same as the valence bond self-consistent-field (VBSCF) method. However, the interaction between electronic states is not included in λ-DFVB(U) since the last step of λ-DFVB(U) is not a diagonalization of the Hamiltonian matrix on the electronic state basis. Therefore, λ-DFVB(U) gives the wrong topology of the potential energy surfaces (PESs) near the conical intersection region. In the present paper, we propose a novel hybrid density functional VB method with multistate treatment, named λ-DFVB(MS), in which an effective Hamiltonian matrix is constructed on the basis of the diabatic states obtained by the valence-bond-based compression approach for the diabatization scheme, and the interaction between electronic states can be included through the diagonalization of the effective Hamiltonian matrix. Test calculations show that λ-DFVB(MS) gives the correct topology of the PESs near the conical intersection region. We also show that the VBSCF wave function with selected VB structures can be applied as a reference in λ-DFVB(MS).

Photodissociation dynamics of methylamine in the blue edge of the A-band. II. The NH2 + CH3 channel

The photodissociation dynamics leading to the C-N bond cleavage in methylamine (CH3NH2) are investigated upon photoexcitation in the blue edge of the first absorption A-band, in the 198-204 nm range. Velocity map images of the generated methyl (CH3) fragment detected in specific vibrational modes, i.e., ν = 0, ν1 = 1, and ν2 = 1, through resonance enhanced multiphoton ionization, are presented along with the corresponding translational energy distributions and the angular analysis. The experimental results are complemented by high-level ab initio calculations of potential energy curves as a function of the C-N bond distance. While a similar single Boltzmann-type contribution is observed in all the translational energy distributions measured, the speed-dependent anisotropy parameter obtained through the angular analysis reveals the presence of two different mechanisms. Prompt dissociation through the conical intersection between the Ã1A' first excited state and the ground state located in the exit channel is, indeed, revealed as a minor channel. In contrast, slow dissociation on the ground state, presumably from frustrated N-H bond cleavage trajectories, constitutes the major reaction pathway leading to the methyl formation.

Photodissociation dynamics of methylamine in the blue edge of the A-band. I. The H-atom elimination channel

The photodissociation dynamics of methylamine (CH3NH2) upon excitation in the blue edge of the first absorption A-band, in the 198-203 nm range, are investigated by means of nanosecond pump-probe laser pulses and velocity map imaging combined with H(2S)-atom detection through resonance enhanced multiphoton ionization. The images and corresponding translational energy distributions for the H-atoms produced show three different contributions associated with three reaction pathways. The experimental results are complemented by high-level ab initio calculations. The potential energy curves computed as a function of the N-H and C-H bond distances allow us to draw a picture of the different mechanisms. Major dissociation occurs through N-H bond cleavage and it is triggered by an initial geometrical change, i.e., from a pyramidal configuration of the C-NH2 with respect to the N atom to a planar geometry. The molecule is then driven into a conical intersection (CI) seam where three outcomes can take place: first, threshold dissociation into the second dissociation limit, associated with the formation of CH3NH(Ã), is observed; second, direct dissociation after passage through the CI leading to the formation of ground state products; and third, internal conversion into the ground state well in advance to dissociation. While the two last pathways were previously reported at a variety of wavelengths in the 203-240 nm range, the former had not been observed before to the best of our knowledge. The role of the CI and the presence of an exit barrier in the excited state, which modify the dynamics leading the two last mechanisms, are discussed considering the different excitation energies used.

Linearized Pair-Density Functional Theory

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-SCF multireference method that has been successful at computing ground- and excited-state energies. However, MC-PDFT is a single-state method in which the final MC-PDFT energies do not come from diagonalization of a model-space Hamiltonian matrix, and this can lead to inaccurate topologies of potential energy surfaces near locally avoided crossings and conical intersections. Therefore, in order to perform physically correct ab initio molecular dynamics with electronically excited states or to treat Jahn-Teller instabilities, it is necessary to develop a PDFT method that recovers the correct topology throughout the entire nuclear configuration space. Here we construct an effective Hamiltonian operator, called the linearized PDFT (L-PDFT) Hamiltonian, by expanding the MC-PDFT energy expression to first order in a Taylor series of the wave function density. Diagonalization of the L-PDFT Hamiltonian gives the correct potential energy surface topology near conical intersections and locally avoided crossings for a variety of challenging cases including phenol, methylamine, and the spiro cation. Furthermore, L-PDFT outperforms MC-PDFT and previous multistate PDFT methods for predicting vertical excitations from a variety of representative organic chromophores.

Compressed-State Multistate Pair-Density Functional Theory

Multiconfiguration pair-density functional theory (MC-PDFT) is a multireference method that can be used to calculate excited states. However, MC-PDFT potential energy surfaces have the wrong topology at conical intersections because the last step of MC-PDFT is not a diagonalization of a model-space Hamiltonian matrix, as done in, for example, multistate second-order perturbation theory (MS-CASPT2). We have previously proposed methods that solve this problem by diagonalizing a model-space effective Hamiltonian matrix, where the diagonal elements are MC-PDFT energies for intermediate states, and the off-diagonal elements are evaluated by wave function theory. One previous method is called variational multistate PDFT (VMS-PDFT), whose intermediate states maximize the trace of the effective Hamiltonian, namely, the sum of the MC-PDFT energies of the model-space states; the VMS-PDFT is very robust but is more computationally expensive than another method, extended multistate PDFT (XMS-PDFT), in which the transformation to intermediate states is accomplished without needing any density functional evaluations. However, although VMS-PDFT was accurate in all cases tested, XMS-PDFT was accurate in only some of them. In the present paper, we propose a new method, called compressed-state multistate PDFT (CMS-PDFT), that is as efficient as XMS-PDFT and as accurate as VMS-PDFT. The new method maximizes the trace of the classical Coulomb energy of the intermediate states such that the electron densities of the intermediate states are compressed. We show that CMS-PDFT performs robustly even where XMS-PDFT fails.

Multi-state pair-density functional theory

Multi-configuration pair-density functional theory (MC-PDFT) has previously been applied successfully to carry out ground-state and excited-state calculations. However, because they include no interaction between electronic states, MC-PDFT calculations in which each state's PDFT energy is calculated separately can give an unphysical double crossing of potential energy surfaces (PESs) in a region near a conical intersection. We have recently proposed state-interaction pair-density functional theory (SI-PDFT) to treat nearly degenerate states by creating a set of intermediate states with state interaction; although this method is successful, it is inconvenient because two SCF calculations and two sets of orbitals are required and because it puts the ground state on an unequal footing with the excited states. Here we propose two new methods, called extended-multi-state-PDFT (XMS-PDFT) and variational-multi-state-PDFT (VMS-PDFT), that generate the intermediate states in a balanced way with a single set of orbitals. The former uses the intermediate states proposed by Granovsky for extended multi-configuration quasi-degenerate perturbation theory (XMC-QDPT); the latter obtains the intermediate states by maximizing the sum of the MC-PDFT energies for the intermediate states. We also propose a Fourier series expansion to make the variational optimizations of the VMS-PDFT method convenient, and we implement this method (FMS-PDFT) both for conventional configuration-interaction solvers and for density-matrix-renormalization-group solvers. The new methods are tested for eight systems, exhibiting avoided crossings among two to six states. The FMS-PDFT method is successful for all cases for which it has been tested (all cases in this paper except O3 for which it was not tested), and XMS-PDFT is successful for all eight cases except the mixed-valence case. Since both XMS-PDFT and VMS-PDFT are less expensive than XMS-CASPT2, they will allow well-correlated calculations on much larger systems for which perturbation theory is unaffordable.

State-interaction pair density functional theory for locally avoided crossings of potential energy surfaces in methylamine

State-interaction pair-density functional theory agrees well with extended MS-CASPT2 in regions of strong state coupling near conical intersections.

Control of Nonadiabatic Passage through a Conical Intersection by a Dynamic Resonance

Nonadiabatic processes, dominated by dynamic passage of reactive fluxes through conical intersections (CIs), are considered to be appealing means for manipulating reaction paths, particularly via initial vibrational preparation. Nevertheless, obtaining direct experimental evidence of whether specific-mode excitation affects the passage at the CI is challenging, requiring well-resolved time- or frequency-domain experiments. Here promotion of methylamine-d2 (CH3ND2) molecules to spectral-resolved rovibronic states on the excited S1 potential energy surface, coupled to sensitive D photofragment probing, allowed us to follow the N-D bond fission dynamics. The branching ratios between slow and fast D photofragments and the internal energies of the CH3ND(X̃) photofragments confirm correlated anomalies for predissociation initiated from specific rovibronic states. These anomalies reflect the existence of a dynamic resonance that strongly depends on the energy of the initially excited rovibronic states, the evolving vibrational mode on the repulsive S1 part during N-D bond elongation, and the manipulated passage through the CI that leads to CH3ND radicals excited with C-N-D bending. This resonance plays an important role in the bifurcation dynamics at the CI and can be foreseen to exist in other photoinitiated processes and to control their outcome.

Evidence for quantum effects in the predissociation of methylamine isotopologues

The H product distributions obtained from the predissociation of methylamine isotopologues are extremely sensitive to the energy difference between the initially prepared vibrational states and the conical intersections and not only to the nature of the pre-excited nuclear motions.