The unimolecular dissociation of H2CO on the lowest triplet potential-energy surface

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Enabling a Unified Description of Both Internal Conversion and Intersystem Crossing in Formaldehyde: A Global Coupled Quasi-Diabatic Hamiltonian for Its S0, S1, and T1 States

In our recent work, a diabatic Hamiltonian that couples the S₀ and S₁ states of formaldehyde was constructed using a robust fitting-and-diabatizing procedure with artificial neural networks, which is capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, based on the diabatization of S₀ and S₁, the spin-orbit couplings between singlet states (S₀, S₁) and triplet state T₁ are also determined in the same diabatic representation. The diabatized spin-orbit couplings are then fit with a symmetrized neural-network functional form. The ab initio spin-orbit couplings are well reproduced in large configuration space. Together with the neural-network-based potential energy surface for T₁, the full quasi-diabatic Hamiltonian for the S₀, S₁, and T₁ states is completed, enabling a unified description of both internal conversion and intersystem crossing in formaldehyde. The vibrational levels on the three adiabatic states are found to be in good agreement with known experimental band origins.

A new (multi-reference configuration interaction) potential energy surface for H2CO and preliminary studies of roaming

We report a new global potential energy surface (PES) for H2CO, based on precise fitting of roughly 67 000 MRCI/cc-pVTZ energies. This PES describes the global minimum, the cis- and trans-HCOH isomers, and barriers relevant to isomerization, formation of the molecular (H2+CO) and radical (H+HCO) products, and the loose so-called roaming transition-state saddle point. The key features of the PES are reviewed and compared with a previous PES, denoted by PES04, based on five local fits that are 'stitched' together by switching functions (Zhang et al. 2004 J. Phys. Chem. A108, 8980-8986 (doi:10.1021/jp048339l)). Preliminary quasi-classical trajectory calculations are performed at the total energy of 36 233 cm-1 (103 kcal mol-1), relative to the H2CO global minimum, using the new PES, with a particular focus on roaming dynamics. When compared with the results from PES04, the new PES findings show similar rotational distributions, somewhat more roaming and substantially higher H2 vibrational excitation.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Kinetics and dynamics of the C(3P) + H2O reaction on a full-dimensional accurate triplet state potential energy surface

A full-dimensional accurate PES for the C(³P) + H₂O reaction is developed using the PIP-NN method.

Exploring Multiple Potential Energy Surfaces: Photochemistry of Small Carbonyl Compounds

In theoretical studies of chemical reactions involving multiple potential energy surfaces (PESs) such as photochemical reactions, seams of intersection among the PESs often complicate the analysis. In this paper, we review our recipe for exploring multiple PESs by using an automated reaction path search method which has previously been applied to single PESs. Although any such methods for single PESs can be employed in the recipe, the global reaction route mapping (GRRM) method was employed in this study. By combining GRRM with the proposed recipe, all critical regions, that is, transition states, conical intersections, intersection seams, and local minima, associated with multiple PESs, can be explored automatically. As illustrative examples, applications to photochemistry of formaldehyde and acetone are described. In these examples as well as in recent applications to other systems, the present approach led to discovery of many unexpected nonadiabatic pathways, by which some complicated experimental data have been explained very clearly.

Different equation-of-motion coupled cluster methods with different reference functions: the formyl radical

The doublet and quartet excited states of the formyl radical have been studied by the equation-of-motion (EOM) coupled cluster (CC) method. The S(z) spin-conserving singles and doubles (EOM-EE-CCSD) and singles, doubles, and triples (EOM-EE-CCSDT) approaches, as well as the spin-flipped singles and doubles (EOM-SF-CCSD) method have been applied, subject to unrestricted Hartree-Fock (HF), restricted open-shell HF, and quasirestricted HF references. The structural parameters, vertical and adiabatic excitation energies, and harmonic vibrational frequencies have been calculated. The issue of the reference function choice for the spin-flipped (SF) method and its impact on the results has been discussed using the experimental data and theoretical results available. The results show that if the appropriate reference function is chosen so that target states differ from the reference by only single excitations, then EOM-EE-CCSD and EOM-SF-CCSD methods give a very good description of the excited states. For the states that have a non-negligible contribution of the doubly excited configurations one is able to use the SF method with such a reference function, that in most cases the performance of the EOM-SF-CCSD method is better than that of the EOM-EE-CCSD approach.

QUILD: QUantum-regions interconnected by local descriptions

A new program for multilevel (QM/QM and/or QM/MM) approaches is presented that is able to combine different computational descriptions for different regions in a transparent and flexible manner. This program, designated QUILD (for QUantum-regions Interconnected by Local Descriptions), uses adapted delocalized coordinates (Int J Quantum Chem 2006, 106, 2536) for efficient geometry optimizations of equilibrium and transition-state structures, where both weak and strong coordinates may be present. The Amsterdam Density Functional (ADF) program is used for providing density functional theory and MM energies and gradients, while an interface to the ORCA program is available for including RHF, MP2, or semiempirical descriptions. The QUILD optimization setup reduces the number of geometry steps needed for the Baker test-set of 30 organic molecules by approximately 30% and for a weakly-bound test-set of 18 molecules by approximately 75% compared with the old-style optimizer in ADF, i.e., a speedup of roughly a factor four. We report two examples of using geometry optimizations with numerical gradients, for spin-orbit relativistic ZORA and for excited-state geometries. Finally, we show examples of its multilevel capabilities for a number of systems, including the multilevel boundary region of amino acid residues, an S(N)2 reaction in the gas-phase and in solvent, and a DNA duplex.

Photodissociation dynamics of the reaction H2CO-->H+HCO via the singlet (S0) and triplet (T1) surfaces

We have explored the photodissociation dynamics of the reaction H(2)CO+hnu-->H+HCO in the range of 810-2600 cm(-1) above the reaction threshold. Supersonically cooled formaldehyde was excited into selected J(Ka,Kc) rotational states of six vibrational levels (1(1)4(1), 5(1), 2(2)6(1), 2(2)4(3), 2(3)4(1), and 2(4)4(1)) in the A((1)A2) state. The laser induced fluorescence spectra of the nascent HCO fragment provided detailed product state distributions. When formaldehyde was excited into the low-lying levels 1(1)4(1), 5(1), and 2(2)6(1), at E(avail)<1120 cm(-1), the product state distribution can be modeled qualitatively by phase space theory. These dynamics are interpreted as arising from a reaction path on the barrierless S0 surface. When the initial states 2(2)4(3) and 2(3)4(1) were excited (E(avail)=1120-1500 cm(-1)), a second type of product state distribution appeared. This second distribution peaked sharply at low N, Ka and was severely truncated in comparison with those obtained from the lower lying states. At the even higher energy of 2(4)4(1) (E(avail) approximately 2600 cm(-1)) the sharply peaked distribution appears to be dominant. We attribute this change in dynamics to the opening up of the triplet channel to produce HCO. The theoretical height of the barrier on the T1 surface lies between 1700 and 2100 cm(-1) and so we consider the triplet reaction to proceed via tunneling at the intermediate energies and proceed over the barrier at the higher energies. Considerable population was observed in the excited (0,0,1) state for all initial H(2)CO states that lie above the appearance energy. Rotational populations in the (0,0,1) state dropped more rapidly with (N,Ka) than did the equivalent populations in (0,0,0). This indicates that, although individual rotational states are highly populated in (0,0,1), the total v3=1 population might not be so large. Specific population was also measured in the almost isoenergetic Kc and J states. No consistent population preference was found for either asymmetry or spin-rotation component.

State-selective photodissociation dynamics of formaldehyde: Near threshold studies of the H+HCO product channel

The laser-induced photodissociation of formaldehyde in the wavelength range 309<lambda<330 nm has been investigated using H (Rydberg) atom photofragment translational spectroscopy. Photolysis wavelengths corresponding to specific rovibronic transitions in the A (1)A2<--X (1)A1 2(0)(1)4(0)(3), 2(0)(2)4(0)(1), 2(0)(2)4(0)(3), 2(0)(3)4(0)(1), and 2(0)(1)5(0)(1) bands of H(2)CO were studied. The total kinetic energy release spectra so derived can be used to determine partial rotational state population distributions of the HCO cofragment. HCO product state distributions have been derived following the population of various different N(Ka) levels in the A (1)A2 2(2)4(3) and 2(3)4(1) states. Two distinct spectral signatures are identified, suggesting competition between dissociation pathways involving the X (1)A1 and the a (3)A2 potential energy surfaces. Most rovibrational states of H(2)CO(A 1A(2)) investigated in this work produceH+HCO(X (2)A') photofragments with a broad kinetic energy distribution and significant population in high energy rotational states of HCO. Photodissociation via the A (1)A2 2(2)4(3) 1(1,1) (and 1(1,0)) rovibronic states yields predominantly HCO fragments with low internal energy, a signature that these rovibronic levels are perturbed by the a (3)A2 state. The results also suggest the need for further careful measurements of the H+HCO quantum yield from H(2)CO photolysis at energies approaching, and above, the barrier to C-H bond fission on the a (3)A2 potential energy surface.

Analysis of Quantum Yields for the Photolysis of Formaldehyde at λ > 310 nm

Experimental quantum yields of the photolysis of formaldehyde at lambda > 310 nm are combined with absolute and relative rate calculations for the molecular elimination H2CO --> H2 + CO (1), the bond fission H2CO --> H + HCO (2), and the intramolecular hydrogen abstraction H2CO --> H ... HCO --> H2 + CO (3) taking place in the electronic ground state. Temperature and pressure dependencies of the quantum yields are analyzed with the goal to achieve consistency between experiment and modeling. Two wavelength ranges with considerably different properties are considered: 340-360 nm, where channel 1 competes with collisional deactivation of excited molecules, and 310-340 nm, which is dominated by the competition between the formation of radical and molecular products. The close relation between photolysis and pyrolysis of formaldehyde, such as analyzed for the pyrolysis in the companion paper, is documented and an internally consistent treatment of the two reaction systems is provided. The quantum yields are modeled and represented in analytical form such that values outside the available experimental range can be predicted to some extent.

Refined Analysis of the Thermal Dissociation of Formaldehyde

New experimental results for the thermal dissociation of formaldehyde to radical and molecular products (Proc. Combust. Inst. 2007, 31, in press) form the basis of the present analysis of the respective low-pressure rate coefficients k(Rad,0) and k(Mol,0) of the reaction. The article supersedes an earlier analysis (J. Phys. Chem. A 2005, 109, 8320) which used less accurate and more preliminary input information. In addition, refined rotational factors F(rot) are determined and specific energy and angular momentum dependent branching ratios from a more detailed analysis of photolysis quantum yields (J. Phys. Chem. A 2007, 111, 3868) are employed as well. It is emphasized again that pyrolysis and photolysis are intimately related and should be analyzed in an internally consistent manner. The combination of the new with earlier experimental results for pyrolysis rates allows one to fit the height of the energy barrier for the molecular elimination channel with improved precision. A value of E0,1 = 81.7(+/-0.5) kcal mol(-1) is obtained. In addition, employing anharmonicity factors F(anh) from the earlier work, a total average energy transferred per collision of -DeltaE/hc = 100(+/-20) cm(-1) is fitted from the experiments in the bath gas Ar. This value is consistent with the value -DeltaE/hc = 80(+/-40) cm(-1) for the bath gas N(2) such as fitted from photolysis quenching experiments (using the same molecular parameters as for the pyrolysis). Rate coefficients for the temperature range 1200-3500 K are represented in the form k(Mol,0)/[Ar] = 7.3 x 10(14) T -6.1 exp(-47300 K/T) cm(3) molecule(-1) s(-1) and k(Rad,0)/[Ar] = 2.1 x 10(12) T -5.5 exp(-47300 K/T) cm(3) molecule(-1) s(-1) (accuracy +/-25%) and recommended for use in combustion chemistry.

Combined CASSCF and MR-CI Study on Photoinduced Dissociation and Isomerization of Acryloyl Chloride

The potential energy surfaces of isomerization and dissociation reactions for CH2CHCOCl in the S0, T1, T2, and S1 states have been mapped with DFT, CASSCF, MP2, and MR-CI calculations. Rate constants for adiabatic and nonadiabatic processes have been calculated with the RRKM rate theory, in conjugation with the vibronic interaction method. Mechanistic photochemistry of CH2CHCOCl at 230-310 nm has been characterized through the computed potential energy surfaces and rate constants. Upon photoexcitation of CH2CHCOCl at 310 nm, the S1-->T1 intersystem crossing is the dominant primary process, which is followed by the 1,3-Cl migration along the T1 pathway. Meanwhile, the S1-->S0 internal conversion occurs with considerable probability and the subsequent trans-cis isomerization proceeds in the ground state. The C-Cl bond cleavage is an exclusive primary channel upon photoexcitation of gaseous CH2CHCOCl at 230 nm. The direct C-Cl bond cleavage is partially blocked by effects of the matrix, and the internal conversion from S1 to S0 becomes an important process for the excited molecule to deactivate in the condensed phase. The present calculations not only provide a reasonable explanation of the experimental findings, but also give new insight into the mechanistic photochemistry of CH2CHCOCl.

Probing mechanistic photochemistry of glyoxal in the gas phase by ab initio calculations of potential-energy surfaces and adiabatic and nonadiabatic rates

In the present work, the wavelength-dependent mechanistic photochemistry of glyoxal in the gas phase has been explored by ab initio calculations of potential-energy surfaces, surface crossing points, and adiabatic and nonadiabatic rates. The CHOCHO molecules in S1 by photoexcitation at 393-440 nm mainly decay to the ground state via internal conversion, which is followed by molecular eliminations to form CO, H2CO,H2, and HCOH. Upon photodissociation of CHOCHO at 350-390 nm, intersystem crossing to T1 followed by the C-C bond cleavage is the dominant process in this wavelength range, which is responsible for the formation of the CHO radicals. The C-C and C-H bond cleavages along the S1 pathway are energetically accessible upon photodissociation of CHOCHO at 290-310 nm, which can compete with the S1-->T1 intersystem crossing process. The present study predicts that the C-H bond cleavage on the S1 surface is probably a new photolysis pathway at high excitation energy, which has not been observed experimentally. In addition, the trans-cis isomerization is predicted to occur more easily in the ground state than in the excited states.

New insights on reaction dynamics from formaldehyde photodissociation

We review the photodissociation dynamics of formaldehyde with an emphasis on recent calculations that make use of a global ab initio-based potential energy surface for the S(0) state. These calculations together with recent experiments reveal striking departures from conventional transition state theory for the formation of the molecular products H(2) + CO. The evidence for this departure is reviewed in detail by examining properties of the new potential surface and results of quasiclassical trajectory dynamics calculations using this surface. We also review very recent work on the dynamics governing the formation of radical products, H + HCO. These products can be formed on the T(1) surface as well as the S(0) one, and we present some results contrasting the dynamics on these two surfaces. This work makes use of a new semi-global ab initio-based T(1) potential energy surface.

Theory of Multichannel Thermal Unimolecular Reactions. 2. Application to the Thermal Dissociation of Formaldehyde

The thermal dissociation of formaldehyde proceeds on three channels, the molecular-elimination channel H2CO --> H2 + CO (1), the radical-forming bond-fission channel H2CO --> H + HCO (2), and the bond-fission-initiated, intramolecular-hydrogen-abstraction channel H2CO --> H...HCO --> H2 + CO (3) which also forms molecular products. The kinetics of this system in the low-pressure range of the unimolecular reaction is shown to be governed by a subtle superposition of collisional channel coupling to be treated by solving a master equation, of rotational channel switching accessible through ab initio calculations of the potential as well as spectroscopic and photophysical determinations of the threshold energies and channel branching above the threshold energy for radical formation which can be characterized through formaldehyde photolysis quantum yields as well as classical trajectory calculations. On the basis of the available information, the rate coefficients for the formation of molecular and radical fragments are analyzed and extrapolated over wide ranges of conditions. The modeled rate coefficients in the low-pressure range of the reaction (neglecting tunneling) over the range 1400-3200 K in the bath-gas Ar in this way are represented by k0,Mol/[Ar] approximately 9.4 x 10(-9) exp(-33,140 K/T) cm3 molecule(-1) s(-1) and k0,Rad/[Ar] approximately 6.2 x 10(-9) exp(-36,980 K/T) cm3 molecule(-1) s(-1). The corresponding values for the bath-gas Kr, on which the analysis relies in particular, are k0,Mol/[Kr] approximately 7.7 x 10(-9) exp(-33,110 K/T) and k0,Rad/[Kr] approximately 4.1 x 10(-9) exp(-36 910 K/T) cm3 molecule(-1) s(-1). While the threshold energy E0,2 for channels 2 and 3 is taken from spectroscopic measurements, the threshold energy E0,1 for channel 1 is fitted on the basis of experimental ratios k0,Rad/k0,Mol in combination with photolysis quantum yields. The derived value of E0,1(1) = 81.2 (+/-0.9) kcal mol(-1) is in good agreement with results from recent ab initio calculations, 81.9 (+/-0.3) kcal mol(-1), but is higher than earlier results derived from photophysical experiments, 79.2 (+/-0.8) kcal mol(-1). Rate coefficients for the high-pressure limit of the reaction are also modeled. The results of the present work markedly depend on the branching ratio between channels 2 and 3. Expressions of this branching ratio from classical trajectory calculations and from photolysis quantum yield measurements were tested. At the same time, a modeling of the photolysis quantum yields was performed. The formaldehyde system so far presents the best characterized multichannel dissociation reaction. It may serve as a prototype for other multichannel dissociation reactions.

Fully state-resolved photodissociation of formaldehyde, H2CO→H+HCO: K conservation and a rigorous test of statistical theories

The photodissociation dynamics of the reaction H2CO+hnu --> H + HCO have been investigated in the range 60-400 cm(-1) above the reaction threshold. Supersonically cooled formaldehyde was excited into 15 specific J, K(a), K, rotational states i n two vibrational lev el s 2(1) 4(1) 6(1) and 2(2) 4(1) in the A(1A2) state. The laser-induced fluorescence spectra of the nascent HCO fragment provided detailed product state distributions (PSDs), resolved by N, K(a), K(c), and J. When just the overall molecular rotation N is considered the PSDs are in remarkable agreement with calculations based on phase space theory (PST). However, when the projection of N onto the molecular frame (K(a),K(c)) is included the distributions show consistent deviations from PST. In particular, there is a tendency to preserve the initial parent rotational motion about the a and b axes. The effect is that states with higher initial K(a) in H2CO produce higher final K(a) in the HCO fragment. There is also a tendency for the upper/lower members of the asymmetry doublets in H2CO to map onto the same upper/lower set of product state asymmetry doublets. Finally, there are oscillations in some of the detailed PSDs that remain unexplained.

Ab initio n-electron valence state perturbation theory study of the adiabatic transitions in carbonyl molecules: Formaldehyde, acetaldehyde, and acetone

The application of the recently developed second-order n-electron valence state perturbation theory (NEVPT2) to small carbonyl molecules (formaldehyde, acetaldehyde, and acetone) is presented. The adiabatic transition energies are computed for the singlet and triplet n-->pi(*), pi-->pi(*), and sigma-->pi(*) states performing a full geometry optimization of the relevant states at the single state CASSCF level and taking into account the zero point energy correction in the harmonic approximation. The agreement with the known experimental values and with previously published high level calculations confirms that NEVPT2 is an efficient tool to be used for the interpretation of molecular electronic spectra. Moreover, different insight into the nature of the excited states has been obtained. Some of the transitions presented here have never been theoretically computed previously [(3)(pi-->pi(*)) and (3)(sigma-->pi(*)) adiabatic transitions in acetaldehyde and acetone] or have been studied only using moderate level (single reference based) ab initio methods (all adiabatic transitions in acetaldehyde). In the present work a consistent disagreement between NEVPT2 and experiment has been found for the (3)(pi-->pi(*)) adiabatic transition in all molecules: this result is attributed to the low intensity of the transition to the first vibrational levels of the excited state. The n-->pi(*) singlet and triplet vertical transition energies are also reported for all the molecules.

Quasiclassical trajectory study of formaldehyde unimolecular dissociation: H2CO→H2+CO, H+HCO

We report quasiclassical trajectory calculations of the dynamics of the two reaction channels of formaldehyde dissociation on a global ab initio potential energy surface: the molecular channel H(2)CO-->H(2) + CO and the radical H(2)CO-->H + HCO. For the molecular channel, it is confirmed that above the threshold of the radical channel a second, intramolecular hydrogen abstraction pathway is opened to produce CO with low rotation and vibrationally hot H(2). The low-j(CO) and high-nu(H(2) ) products from the second pathway increase with the total energy. The competition between the molecular and radical pathways is also studied. It shows that the branching ratio of the molecular products decreases with increasing energy, while the branching ratio of the radical products increases. The results agree well with very recent velocity-map imaging experiments of Suits and co-workers and solves a mystery first posed by Moore and co-workers. For the radical channel, we present the translational energy distributions and HCO rotation distributions at various energies. There is mixed agreement with the experiments of Wittig and co-workers, and this provides an indirect confirmation of their speculation that the triplet surface plays a role in the formation of the radical products.

Photochemistry of formaldehyde under tropospheric conditions

We report new results on the absorption cross sections and photochemical quantum yields for radical (H + HCO) production from formaldehyde in the wavelength interval from 308-320 nm, obtained at resolutions of better than 0.1 nm. The absorption cross sections, measured at resolutions close to the limit for Doppler broadening of HCHO, show rotationally resolved fine structure, with maximum values higher than those obtained in previous, lower resolution, studies. In this wavelength region, absorption cross sections peak at 2.3 x 10(-19) cm2 molecule(-1), but band-integrated values are in excellent accord with previous measurements. HCO absorption coefficients, measured by cavity ring-down spectroscopy following UV photolysis of HCHO at wavelengths across the 2(0)(1)5(0)(1), 2(0)(2)4(0)(3) and 2(0)(3)4(0)(1) bands of the A1A2-X1A1 transition, generally mimic the parent absorption band profiles. Division of these absorption coefficients by the high resolution parent absorption cross sections gives relative quantum yields for the H + HCO radical product channel that can be put on an absolute scale using single-wavelength literature values. These quantum yields are observed to show some variation with parent excitation wavelength (and thus with excited vibronic level). Addition of 200 Torr of N2 increases the HCO quantum yields.

Photodissociation of acetic acid in the gas phase: an ab initio study

Photodissociation of acetic acid in the gas phase was investigated using ab initio molecular orbital methods. The stationary structures on the ground-state potential energy surfaces were mainly optimized at the MP2 level of theory, while those on the excited-state surfaces were determined by complete active space SCF calculations with a correlation-consistent basis set of cc-pVDZ. The reaction pathways leading to different photoproducts are characterized on the basis of the computed potential energy surfaces and surface crossing points. The calculations reproduce the experimental results well and provide additional insight into the mechanism of the ultraviolet photodissociation of acetic acid and related compounds.