Advances in Physical ChemistryVolume 2012 (2012), Article ID 720197, 17 pagesdoi:10.1155/2012/720197

Review Article

Potential Energy Surfaces for Reactions of X Metal Atoms (X = Cu, Zn, Cd, Ga, Al, Au, or Hg) with YH₄ Molecules (Y = C, Si, or Ge) and Transition Probabilities at Avoided Crossings in Some Cases

Octavio Novaro,¹ María del Alba Pacheco-Blas,¹ and Juan Horacio Pacheco-Sánchez²

¹Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364, 01000 Ciudad de México, DF, Mexico²División de Estudios de Posgrado e Investigación, Instituto Tecnológico de Toluca, A.P. 890, 52140 Metepec Edo. Mex, Mexico

Received 14 July 2011; Revised 4 October 2011; Accepted 22 November 2011

Academic Editor: Laimutis Bytautas

Copyright © 2012 Octavio Novaro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

We review ab initio studies based on quantum mechanics on the most important mechanisms of reaction leading to the C–H, Si–H, and Ge–H bond breaking of methane, silane, and germane, respectively, by a metal atom in the lowest states in symmetry: X(2nd excited state, 1st excited state and ground state) + YH₄ H₃XYH H + XYH₃ and XH + YH₃. with X = Au, Zn, Cd, Hg, Al, and G, and Y = C, Si, and Ge. Important issues considered here are (a) the role that the occupation of the d-, s-, or p-shells of the metal atom plays in the interactions with a methane or silane or germane molecule, (b) the role of either singlet or doublet excited states of metals on the reaction barriers, and (c) the role of transition probabilities for different families of reacting metals with these gases, using the H–X–Y angle as a reaction coordinate. The breaking of the Y–H bond of YH₄ is useful in the production of amorphous hydrogenated films, necessary in several fields of industry.

1. Introduction

Here, an overview of potential energy surface (PES) calculations for reactions of a metal atom with a gas molecule has been compiled. Among metal atoms, we consider cadmium, copper, zinc, gallium, aluminum, mercury, and gold, and among gas molecules methane, silane, and germane. The potential energy surfaces of an YH₄ molecule with a metal atom were determined using ab initio Hartree-Fock Self-Consistent Field (HF-SCF) calculations, where the atom core is represented by relativistic effective core potentials (RECPs) [1–5]. These calculations are followed by a Multiconfigurational Self Consistent Field (MC-SCF) study [6]. The correlation energy is accounted for through extensive variational and perturbative second-order multireference Moller-Plesset configuration interaction (MR-CI) analysis of selected perturbations obtained by iterative process calculations using the CIPSI program package [7]. The reference (S) spaces used for the variational CI of the molecular states arising from the three X + CH₄ asymptotes contain between 108 and 428 determinants, which generate between 7 million and 111 million perturbed MP2 determinants near the region of the reactants and the equilibrium geometry of the methyl-metal-hydride intermediate, respectively. This methodology is particularly useful in the study of systems constituted by a few atoms.

Transition probabilities for the interaction of the lowest excited states of the metal X with tetrahedral gas molecules are studied through one-dimensional Landau-Zener theory. The strategy for obtaining the reaction pathways for X + YH₄ interactions has been extensively used in references [8–14] based on the original proposal by Chaquin et al. [15]. The initial approach (starting from 20 a.u.) of the X atom to one Y–H bond was done in a Cs symmetry in a plane containing the X, Y, and two hydrogen atoms. All the angles and distances obtained by a self-consistent field approach to find the molecular geometry of the HXYH₃ intermediate are exhibited in Figure 1. From these parameters, = H–X–Y is the first angle fixed in order to optimize the other angles and distances for each point on a potential energy curve, and taking steps of 10 degrees for the angle. When two energy levels cross each other as a function of time, the semiclassical theory of time-dependent Landau-Zener theory [16, 17] for nonadiabatic transition can be utilized. Zener [17] proposed a transition probability from one potential energy curve to another as a linear velocity function, using the distance as the reaction coordinate. Whereas for an angular velocity using the angle as the reaction coordinate, all developments established by Zener are still valid, given that for determining a time-dependent transition probability, the Schrödinger equation must be used. Thus, the transition probability from one-potential energy curve to another is an angular velocity function, using the angle as the reaction coordinate. Our theoretical results predict the formation of XH + YH₃ or H + XYH₃ products after breaking the intermediate HXYH₃. Some of these products are useful in the industry to get hydrogenated amorphous films (a-Y : H) among the other applications [18–30].

Figure 1: The eight (, , , , ,, and ) geometrical parameters used for the optimal X + YH₄ reaction pathway.

The complexity of the organometallic systems, aggregates, and metallic surfaces makes it difficult to determine the fundamental mechanisms which govern their interactions with hydrocarbons. In this situation, one begins with a study of the interaction of a single metallic atom with a hydrocarbon molecule as a model to understand the conditions that the metallic center in these activations requires. Thus, the study of the interaction of the different metallic atomic states with the methane, silane, or germane molecule is fundamental in elucidating the role of various d-, s-, or p-orbital occupations in a metal atom.

Experimental studies [31–38] carried out on the photolysis induced by the metallic atom excitation in a matrix of methane at low temperatures show that when the C–H bond of methane activates through photoexcited metallic atoms deposited in a matrix at low temperatures, the process only happens with radiation wavelengths previously known to be absorbed in the free atom, allowing it to achieve a transition to an excited state. The very low temperature of the matrix fixes the position and also reduces the internal movements of methane molecules contained in it, allowing the interaction of C–H bonds with deposited metallic atoms.

The photochemical studies on the metal-alkane interaction have attracted the attention of researchers for long time. It is worth mentioning that in 1985 the work entitled “Activation of Methane by Photoexcited Copper Atoms and Photochemistry of Methylcopper Hydride in Solid Methane Matrices,” developed in Lash Miller laboratories of the University of Toronto in Canada by the G.A Ozin group [32] was considered in the publication analysis of Scientific Information Institute (current contents) as the most promising work of that year.

At room temperature and standard pressure, methane (CH₄) is a colorless, odorless, and flammable gas [39], in fact the simplest hydrocarbon. It is the major constituent of natural gas and is released during the decomposition of plants or other organic compounds, as in marshes and coal mines. Methane is the first member of the alkane series. The strength of the carbon hydrogen covalent bond in methane is perhaps the strongest in all hydrocarbons, and, thus, its use as a chemical feedstock is limited. Despite the high activation barrier for breaking the C–H bond, CH₄ is still the main starting material for manufacture of hydrogen in steam reforming. The search for catalysts which can facilitate C–H bond activation in methane (105 kcal mol⁻¹ to break it) and other low alkanes is an area of research with considerable industrial significance [40].

Silane is a chemical compound (SiH₄) analogous to methane, and it is also a gas at room temperature which undergoes spontaneous combustion in air. The name “silane” is also given to a family of compounds that are silicon analogs of alkane hydrocarbons. The radical SiH₃ is termed silyl. The nomenclature parallels that of alkyl radicals. Silane may also carry certain functional group, just as alkanes do. There is (at least in principle) silicon analog for each carbon alkane. Silanes are useful for several industrial and medical applications. For instance, they are used as coupling agents to adhere glass fibers to a polymer matrix, stabilizing the composite material. They can also be used to couple a bioinert layer on a titanium implant. Other applications include water repellents, masonry protection, control of graffiti, applying polycrystalline silicon layers on silicon wafers when manufacturing semiconductors, and sealants. In addition, silane and similar compounds containing Si–H bonds are used as reducing agents in organic and organometallic chemistry [41–47].

Germane is the chemical compound with the formula GeH₄, and an analog of methane. It is the simplest germanium hydride and one of the most useful compounds of germanium. Like the related compounds silane and methane, germane is tetrahedral. It burns in the air to produce GeO₂ and water. Some processes for the industrial manufacture of germane [48], in which our calculations might be useful, are (a) chemical reduction method, (b) an electrochemical reduction method, and (c) a plasma-based method. The gas decomposes near 600 K to germanium and hydrogen. Germane is used in the semiconductor manufacturing for epitaxial growth of germanium [49]. Organogermanium precursors have been examined as less hazardous liquid alternatives to germane for deposition of Ge-containing films [50]. Germane is flammable and toxic.

The quantum chemistry studies presented here provide valuable information about the activation of methane or silane or germane molecules with metal atoms. Products of these reactions are methyl CH₃ or silyl SiH₃ or germyl GeH₃ radicals, which are key in surface growth of amorphous hydrogenated carbon or silicon or germane films (thin films).

Methane CH₄, silane SiH₄, and Germane GeH₄ species turn out to be valuable substances in the industry of the semiconductors since the germane or silane or methane dehydrogenation in gaseous phase is one of the most current methods to obtain semiconductors in the form of amorphous hydrogenated carbon (a-C : H) [51] or silicon (a-Si : H) [52] or germane (a-Ge : H) [53] thin films. The interaction of CH₃, SiH₃, or GeH₃ radicals and atomic hydrogen with the surfaces of carbon, silicon or germane films a-C : H, a-Si : H, or a-Ge : H plays a fundamental role in the understanding of the growth of these plasma films at low temperature. Street [54] says that the dehydrogenated material has a very high defect density which prevents doping, photoconductivity, and the other desirable characteristics of a useful semiconductor. While a real crystal contains defects such as vacancies, interstitial, and dislocations, the elementary defect of an amorphous semiconductor is the coordination defect, when an atom has too many or too few bonds [54]. Defect equilibrium is in general described by a reaction of the type where A–D are different configurations of point defects, dopants, electronic charges, and so forth. The properties of interest are the equilibrium state and the kinetics of the reaction [54]. Calculations as those accomplished by us mentioned previously might help to find these properties. As an example, our calculated energy of the intermediate corresponds to the defect formation energy which determines the equilibrium defect density, as part of the kinetics of reaction.

Methyl radical absorption on carbon or hydrocarbon thin films is key in thin-film growth at low-temperature plasmas (<) using hydrocarbon precursor gases.

The current production procedure of amorphous hydrogenated carbon (a-C : H) or silicon (a-Si : H) films is the deposition by means of the decomposition of methane or silane through glow discharges produced by radio frequency (RF). This method is known as plasma-enhanced chemical vapor deposition (PECVD) [55].

The breaking of the C–H bond of CH₄ is useful for generating amorphous hydrogenated carbon (a-C : H) films, which represent a class of high-technology materials with mechanical, optical, chemical, and electrical properties among polymeric, graphite, and diamondoid films.

The (a-C : H) is of interest to the electronic industry as a viable and cheap semiconductor that can be prepared in an ample rank of layers. The fine layer of a-C : H, also well-known as diamondoid carbon, is used as a revesting material of hard and low friction. The polymeric film a-C : H has a strong photoluminescence and is being developed as an electroluminescent material. It is also used as dielectric in metal-insulator-metal switch in screens of active matrix. The ability of deposition near to room temperatures using cheap methods of chemical vapor deposition (CVD) makes this material useful for the industry. The amorphous nature of these materials and their relative facility of deposition make them ideals for its use in a great amount of applications such as in panels of flat screen and diamondoid technology [56].

The a-C : H films are prepared through a glow discharge of RF in a pure methane atmosphere at different gas pressures in which the methane decomposition generates the methyl CH₃ radical, which plays a preponderant role in the generation of amorphous hydrogenated carbon surfaces [57, 58]. The electronic industry takes profit of the previous proceeding on the formation of diamondoid films.

Dense amorphous hydrocarbons have some of the highest densities among hydrocarbon and fall between crystalline diamonds and adamantanes, according to Angus [59]; this is the property that makes it so attractive to the electronic industry.

In case of diamondoid formation,(1)some excited metallic atoms break the C–H bond of methane with the consequent production of methyl CH₃ radicals [8, 60, 61]. Knowing that a dangling bond is an unsatisfied valence on an immobilized atom, the methyl CH₃ radicals undergo a chemisorption process controlled by the creation of dangling bonds in the a-C : H surface by an atom H. This is a proper process in the formation of diamondoid films in the electronic industry [62],(2)Ramĺrez and Sinclair [63] (and Velasco-Santos et al., [64]) affirm that carbonaceous natural products can have different allotropic forms of the carbon, since the amorphous carbon has graphite transitions at different temperatures when some specific metals are in contact with carbon and act as catalysts,(3)methyl CH₃ radicals can also be generated by photodissociation of aromatic hydrocarbon, consequently amorphous hydrogenated carbon thin films can be produced. Taguchi et al. [65] used two classes of laser (ArF or KrF) and two types of aromatics (benzene C₆H₆ or toluene C₆H₅–CH₃) to generate diamondoid films.

The breaking of Si–H bond of SiH₄ is useful in manufacture of semiconductor films of amorphous hydrogenated silicon (a-Si : H). Before the a-Si : H material has been developed, the research was on amorphous silicon without hydrogen, prepared by sputtering or by thermal evaporation.

There are at least two models for the generation of amorphous hydrogenated silicon (a-Si : H).(i) In the thermodynamic approach [62, 66, 67], the formation of dangling bonds, the principle defect in a-Si:H, is attributed to the breaking of weak Si–Si bonds caused by mobile H that is released from Si–H bonds [68]:(ii) In the Matsuda-Gallagher-Perrin MGP model [66, 67], SiH₃  is assumed to be the only growth precursor. This assumption is based on the (presumed) dominance of this radical in plasmas leading to the device-quality a-Si : H.

The central assumption in the MGP model is that the SiH₃ reaching the a-Si : H can go to a weakly adsorbed (physisorbed) state forming a three-center Si–H–Si bond on a surface Si–H site. The activation of silane molecules has received a lot of attention as much in the experimental aspect [61, 69–72] as in the theoretical [9, 73]. The activation of the Si–H bond is important as much in the processes of polymerization of silane [74, 75], as in organometallic catalytic reactions [76–78].

The growth of amorphous hydrogenated silicon films a-Si : H in silicon substrata through PECVD in silane is widely used in the manufacture of electronic, optoelectronic, and photovoltaic devices. Amorphous semiconductors of thin films are used in an ample variety of applications such as solar cells, TFT, photoreceptors, and apparatus of images [79].

The a-Ge : H films are prepared through a glow discharge of RF in a pure germane atmosphere at different gas pressures in which the germane decomposition generates the germyl GeH₃ radical, which plays a preponderant role in the generation of amorphous hydrogenated germane surfaces [53].

Here we stress some important results at metal-methane, metal-silane, and metal-germane interactions grouped in three different families (coinage metals: Cu and Au. Pseudotransition metals: Zn, Cd, and Hg, and metals: Al and Ga). Castillo et al. [8, 60, 80] carried out calculations of potential energy surfaces of the interactions copper methane and zinc methane with the aim of determining the mechanisms of reaction that involve the three lowest states of the copper atom (²S, ²D, and ²P) as well as to determine the reaction routes that govern the interaction of the three lowest states of the zinc atom (¹S, ³P, and ¹P) in the process of the C–H bond activation of the methane molecule. Luna-García et al. [11, 12, 81] found the interaction potential curves of the mercury-Germane, cadmium-Germane, copper-silane, and copper-germane in the three lowest states of each metal; he improved a computational methodology to get the products of the breaking of the intermediate. Pacheco-Sánchez et al. [13, 14, 40] achieved the calculation of gallium-methane and gallium-silane interactions as much in the ground state as in the two lowest excited states of gallium; he extended Landau-Zener theory [82–85] to use the angle instead of the distance as reaction parameter in transition probability calculations at avoided crossings. Transition probability theory is described here when the reaction parameter is distance or angle. In addition, our group has considered also the following interactions: cadmium methane [86], zinc silane [9], cadmium silane [10], mercury silane [9], gold silane [87], and recently aluminum methane [88].

2. Transition Probability Theory

When two potential energy curves are very near to each other, it seems that they crossover. Actually, in the apparent crossover point, the system is degenerate, since the two different electronic configurations have the same energy [89]. This introduces a resonance energy that separates the surfaces slightly, in such way that they never intersect but only closely approach to each other before repelling. Whereas the wave function of the molecule in a given curve is of one character before the crossing point (CP) and of another character after it, the wave function of the other curve is reversed in turn; an example is given in Figure 2, where we can see that while the wavefunction has 6p¹ character before CP at and 6s¹ character after CP at , the wavefunction has 6s¹ character before CP at and 6p¹ character after CP at . If changes with a finite velocity, the probability that the molecule changes of a wave function to the other when passing through the crossing point is in such way that its electronic state is represented by a linear combination of the type where or according to the reaction coordinate in study. By convenience in the calculation of and , the eigenfunctions and are expressed in terms of two other wave functions and with energies and , respectively, which intersect when they are plotted as functions of the internuclear distance (or angle). Due to the fact that and are not exact eigenfunctions of the whole Hamiltonian at the crossing point, the interaction energy between the two states and have to be included, then and , where is the difference between the exact eigenvalues and and the approximate eigenvalues , : . Normalizing and orthogonalizing all the wavefunctions involved, and following the one-dimensional (distance as reaction coordinate) developments established by Zener [17] for a time-dependent Schrödinger equation, we obtain the transition probability as where The denominator can be expressed as where is the velocity ( or , means linear and means angular velocity) at which the system crosses , and is the difference of the slopes of the two potential surfaces crossing at . Finally, we have for the transition probability of nonadiabatic behavior. The probability for a system remaining in the initial energy surface is then Rosenkewitsch [90] states that Zener [17] has obtained a similar formula to that one obtained by Landau [16] (or (7) above) where is the relative velocity, and and are “forces” acting on the two states. Making the identification which corresponds to the change of pure kinetics energy with time, we can almost have the equation found by Zener ((7) when ), because the exponent of the Landau formula also has a factor of .

Figure 2: Typical graph of transition probabilities. Energy as a function of the insertion angle , where the two solid lines correspond to the avoided crossing at , and the dashed lines to the probable transitions among potential energy surfaces.

Explicit calculations of transition probabilities of nonadiabatic behavior using (7) are straightforward when the reaction coordinate is the distance [91, 92] (in these cases gas is hydrogen and metal is ruthenium [91] and platinum [92]); however, when the latter is the angle, it will be necessary to calculate the angular velocity and the moment of inertia as accomplished in references [40, 82–85, 87, 88] for tetrahedral molecules interacting with metals.

2.1. Interactions of the Cu, Au Coinage Metals with YH₄

Castillo et al. [60] found that copper in its second excited state (²P: 3d¹⁰ 4p¹) breaks the C–H bond of methane, and its avoided crossing with the first excited state allows (²D: 3d⁹ 4s²) to surpass a barrier of 48 kcal mol⁻¹. We have a transition energy of ~83 kcal mol⁻¹ between the states ²P and ²D and transition energy of ~43 kcal mol⁻¹ between the states ²D and ²S (see Table 1 and Figure 3). Transition probability (TP) values at four avoided crossings [82] are obtained when copper is photoexcited to this second excited state Cu (²P: 3d¹⁰ 4p¹), given that this copper atom is inserted in the methane molecule. It is also noteworthy [60] that the ground state is initially repulsive, but due to the avoided crossings, it became attractive after surmounting a rather high barrier. This behavior is initially exhibited at the first minimum (69 kcal mol⁻¹, 26°) of the 5 ²A′ state forming the HCuCH₃ intermediate, which when continuing its path has a probability of crossing towards the 4 ²A′ state with 4p¹ character and a probability of continuing by the same 5 ²A′ state with 4s² character. When following via 4 ²A′ has a probability of crossing towards the 3 ²A′ state with 4p¹ character and a probability of continuing by the same 4 ²A′ state with 4s² character. When continuing via 3 ²A′, a very small potential barrier is surmounted with a probability of crossing towards the 2 ²A′ state with 4p¹ character, and a probability of continuing by the same 3 ²A′ state with 4s² character. When continuing via 2 ²A′, it descends until reaching X ²A′, then it has a probability of crossing towards the X ²A′ state with 4p¹ character and a probability of continuing by the same 2 ²A′ state (see Figure 3) with 4s¹ character. Finally, when continuing via X ²A′ state (with 4p¹ character), while the theoretical energy of the HCuCH₃ intermediate is 14 kcal mol⁻¹, the experimental energy is between 15 and 25 kcal mol⁻¹. From here we can build the corresponding potential energy surfaces leading to the products by calculating the energy against the distance [60]. These products are H + CuCH₃ and HCu + CH₃, with theoretical energies 52 and 41 kcal mol⁻¹, respectively, and experimental energy values 46 and 40 kcal mol⁻¹, respectively, as mentioned in Table 1.

Table 1: Coinage metal family (Cu, Au). Relative energies (kcal mol⁻¹) of the reactants, intermediary HXYH₃ and final products for three states of the metal. X(2nd): metal in second excited state. X(1st): metal in first excited state. X(gs): metal in ground state. : experimentally measured energy. : theoretically calculated energy.

X: Metal
Y: Methane
Y: Silane
Y: Germane

Cua
Aub
Cuc
Cuc

(²S, ²D, ²P)
(²S, ²D, ²P)
(²S, ²D, ²P)
(²S, ²D, ²P)

Expd
Cal.

X(2nd) + YH₄
85
~83
114.3
109.8
87.8
87.7
87.8
87.7

X(1st) + YH₄
34.9
~43
40.23
41.5
34.4
39.0
34.4
39

H + XYH₃
46
52a

30.91

36.0

33.2

HX + YH₃
40
41a
18.25
21.9
27.7
33.2
21.7e
27.1

HXYH₃
15–25
14a

3.34

5.8

1.6

X(gs) + YH₄
0
0
0
0
0
0
0
0

aFrom [80]

bFrom [87]

cFrom [12]

dFrom [93]

eFrom [94].

Figure 3: Insertion mechanism of the three lowest states of the Cu atom (²S, ²P, and ²D) into a C–H bond of methane. ²A′ interaction energy states as a function of the angle theta. The 4p¹ character follows the path from the second excited state to the minimum in the X A′ state, where the final products are formed.

Pacheco-Sánchez et al. [87] have found that Gold in its second excited state (²P: 5d¹⁰ 6p¹), through a series of avoided crossings that diminish the barriers for the ground state and first excited state, breaks the Si–H bond of silane, finally overcoming a barrier of 24.0 kcal mol⁻¹ of the ground state. The experimental transition energy between the excited state (²P: 5d¹⁰ 6p¹) and the ground state (²S: 5d¹⁰ 6s¹) is 114.28 kcal mol⁻¹, which is comparable to the transition energy of 109.8 kcal mol⁻¹ calculated by sPacheco-Sánchez et al. (Table 1). Then, the HAuSiH₃ intermediate encounters four avoided crossings between trajectories C ²A′, B ²A′, A ²A′, and X ²A′ of the energy surfaces. When gold is photoexcited to its second excited state ²P: 5d¹⁰ 6p¹, it initially passes through the avoided crossing around (77 kcal mol⁻¹, 28°) of D ²A′ state, and there are two possibilities of the intermediate formed for following a trajectory. Taking it to pass the avoided crossing, it has a probability [87] for crossing towards C ²A′ maintaining the 6p¹ character, where it finds another avoided crossing, and there is a probability of 0.737 for crossing toward B ²A′ also maintaining the 6p¹ character. Here it finds another avoided crossing, and there is a probability of 0.803 of crossing toward the A ²A′ still maintaining the 6p¹ character (see Figure 4). Henceforth, it finds the last avoided crossing, and there is a probability of 0.541 of crossing to the X ²A′ maintaining the 6p¹ character too, where the products are reached at 120°. Finally, the intermediate with energy 3.34 kcal mol⁻¹ evolves toward the HAu + SiH₃ and AuSiH₃ + H products, whose energies are 21.9 and 30.91 kcal mol⁻¹. These products are of greater energy than the reactants, something typical in an endergonic reaction in which the reaction requires absorption of energy.

Figure 4: Au (²S, ²P, and ²D) with SiH₄ interaction potential energy curves versus the insertion angle towards the HAuSiH₃ intermediate product. The 6p¹ character follows the path from the second excited state to the minimum in the X ²A′ state, where the final products are formed.

Luna-García et al. [12] have found that copper in its second excited state (²P: 3d¹⁰ 4p¹) breaks the Si–H bond of silane, in a manner quite similar to the previous cases surpasses a barrier of 26.0 kcal mol⁻¹ of the ground state. The experimental transition energy between the excited state (²P: 3d¹⁰ 4p¹) and the ground state (²S: 3d¹⁰ 4s¹) is 87.8 kcal mol⁻¹, which agrees with the transition energy of 87.7 kcal mol⁻¹ theoretically calculated (Table 1). The initial formation of the HCuSiH₃ intermediate starts at the minimum (70 kcal mol⁻¹, 20°) with 4p¹ character and encounters four avoided crossings among trajectories 4 ²A′, 3 ²A′, 2 ²A′, and X ²A′ of the energy surfaces (see Figure 5). Finally, due to the endergonic nature of this reaction, the intermediate with energy 5.8 kcal mol⁻¹ (and 4p¹ character) is divided into the HCu + SiH₃ and CuSiH₃ + H products with theoretical energy values of 33.2 and 36.0 kcal mol⁻¹, respectively (see Table 1). In the same Table, we could only report the experimental energy value 27.7 kcal mol⁻¹ of HCu + SiH₃ products.

Figure 5: Potential energy curves of the Cu(²S, ²D, ²P) interaction with SiH₄ as a function of the insertion angle () towards the HCuSiH₃ intermediate product. The 4p¹ character follows the path from the second excited state to the minimum in the X ²A′ state, where the final products take place.

Luna-García et al. [12] have found that again copper in its excited state (²P: 3d¹⁰ 4p¹) breaks a Ge–H bond of germane, overcoming a barrier of 27.0 kcal mol⁻¹ of the ground state. The experimental transition energy between the excited state (²P: 3d¹⁰ 4p¹) and the ground state (²S: 3d¹⁰ 4s¹) is of 87.8 kcal mol⁻¹, which agrees with the transition energy of 87.7 kcal mol⁻¹ theoretically calculated (Table 1). The initial formation of the HCuGeH₃ intermediate starts at the minimum (72 kcal mol⁻¹, 17°) with 4p¹ character and passes through four avoided crossings with the trajectories 4 ²A′, 3 ²A′, 2 ²A′, and X ²A′ of the energy surfaces (see Figure 6). Finally the intermediate with energy 1.6 kcal mol⁻¹ (and 4p¹ character) evolves toward HCu + GeH₃ and CuGeH₃ + H products with 27.1 and 33.2 kcal mol⁻¹, respectively (see Table 1). The latter is due to the endergonic nature of the reaction. In the same table, there is only the experimental energy value 21.7 kcal mol⁻¹ of HCu + GeH₃ products.

Figure 6: Potential energy curves of the Cu(²S, ²D, ²P) interaction with GeH₄ as a function of the insertion angle () towards the HCuGeH₃ intermediate product. The 4p¹ character goes by the path from the second excited state to the minimum in the X ²A′ state, where the final products take place.

2.2. Interactions of the Zn, Cd, and Hg Pseudotransition Metals with YH₄

Castillo et al. [8] found that Zinc in its first excited state (¹P: 3d¹⁰ 4s¹ 4p¹) lying 141 kcal mol⁻¹ high breaks the C–H bond of methane, while the Zn ground state presents a quite high activation barrier of 90.5 kcal mol⁻¹ (see Figure 7, Table 2(a)). The TP of the potential energy surfaces (2 ¹A′ → X ¹A′) is obtained for the reaction: Zn (¹P: 4s¹ 4p¹) + CH₄ → Zn (¹S: 4s²) + CH₄ through one avoided crossing; thenceforth, the products of the reaction Zn + CH₄ are reached. This happens when zinc is photoexcited to the second excited state Zn (¹P: 3d¹⁰ 4s¹ 4p¹), which allows this zinc atom to be inserted in the methane molecule. The latter effect is initially exhibited at the minimum (93 kcal mol⁻¹, 59°) of the 2 ¹A′ state forming the intermediate HZnCH₃, which when continuing its path has a probability [82] of crossing towards the X ¹A′ state and a probability of continuing by the same 2 ¹A′ state. When following via X ¹A′ (see Figure 7), at the minimum of this state, the product formation can be obtained [82]. Finally, acquiring the formation of the HZnCH₃ intermediate with a calculated energy of ~25 kcal mol⁻¹ that passes through the avoided crossing of 2 ¹A′ and X ¹A′ sates, with the subsequent formation of HZn + CH₃ and ZnCH₃ + H final products, with the corresponding energies ~82 and ~93, respectively; as it can be seen in Table 2(a).

Table 2

(a) Pseudotransition metal family (Zn, Cd) interacting with methane. Relative energies (kcal mol⁻¹) of the reactants, intermediate HXCH₃, and final products for three lowest states of the metals.

M: metal
Zna
Cdb

(¹S, ³P, ¹P)
(¹S, ³P, ¹P)

M(2nd) + CH₄
133.7
~141
124.9
125.6

M(1st) + CH₄
93.4
~94
89.3
84.9

H + MCH₃

~93

67.9

HM + CH₃

~82

56.6

HMCH₃

~25

31.9c

M(gs) + CH₄
0
0
0
0

aFrom [80]

bFrom [86]

cFrom [95].

(b) Pseudotransition metal family (Zn, Cd, Hg) interacting with silane. Relative energies (kcal mol⁻¹) of the reactants, the HXSiH₃ intermediary and final products for threelowest states of these metals.

M: metal
Zna
Cdb
Hgb

(¹S, ³P, ¹P)
(¹S, ³P, ¹P)
(¹S, ³P, ¹P)

M(2nd) + SiH₄
133.7
141
124.9
128.5
154.6
157.6

M(1st) + SiH₄
93.4
93.8
89.3
84.4
119.5
114.6

H + MSiH₃

84

89.0

95.4

HM + SiH₃
70.4
74
74
75.5
83.33
87.6

HMSiH₃

11.5

20.7

28.0

M(gs) + SiH₄
0
0
0
0
0
0

aFrom [9]

bFrom [10].

(c) Pseudotransition metal family (Cd, Hg) interacting with germane. Relative energies (kcal mol⁻¹) of the reactants, the HXGeH₃ intermediary, and final products for three lowest states of these metals.

X: metal
Cda
Hga

(¹S, ³P, ¹P)
(¹S, ³P, ¹P)

X(2nd) + GeH₄
124.9
128.5
154.6
157.6

X(1st) + GeH₄
89.3
84.4
119.5
114.6

H + XGeH₃

79.9

87.7

HX + GeH₃
68.9
70.3
75.3
80.0

HXGeH₃

13.6

21.0

X(gs) + GeH₄
0
0
0
0

aFrom [10]

bFrom [93].

Figure 7: Potential energy surfaces of the interaction of both Zn(¹S) + CH₄ and Zn(¹P) + CH₄. The 4p¹ character follows the path from the second excited state to the minimum in the X ¹A′ state, where the final products are formed. In this figure, Zn… Hi means that product H + ZnCH3 arises from sending to infinity the Hi, and Zn… C means that product ZnH + CH3 arises from sending to infinity the HiZn.

Ramírez-Solís and Castillo [86] compared the C3v versus C2v symmetries of Cd (¹S, ³P, ¹P) + CH₄ interactions in the edge on geometry orientation. For C3v symmetry, they calculated two more geometry orientations. Before starting their molecular calculations, they successfully reproduced the lowest states of the atomic spectra of cadmium as mentioned in Table 2(a) which corresponds to 125.6 kcal mol⁻¹ for the second excited state. They did not construct the potential energy surfaces; however, they calculated the breaking of the C–H bond of methane with the consequent formation of an intermediate with energy of 31.9 kcal mol⁻¹ and its decomposition in possible products: HCd + CH₃ and H + CdCH₃ with energy of 56.6 and 67.9 kcal mol⁻¹, respectively (see Table 2(a)).

Luna-García et al. [9] found that Zinc in its singlet second excited state (¹P: 3d¹⁰ 4s¹ 4p¹) breaks the Si–H bond of silane, by reversing the initially repulsive ground state curve, thus, overcoming a barrier of ~80 kcal mol⁻¹ of the latter. The experimental transition energy between the excited state (¹P: 3d¹⁰ 4s¹ 4p¹) and the singlet ground state (¹S: 3d¹⁰ 4s²) is 133.7 kcal mol⁻¹, which is comparable to the calculated transition energy of 141.0 kcal mol⁻¹ of the second excited state of Zinc calculated theoretically (Table 2(b), Figure 8). The formation of the HZnSiH₃ intermediate arising at the minimum (81 kcal mol⁻¹, 60°) comes with 4p¹ character and approaches the avoided crossing between 2 ¹A′ and X ¹A′ states keeping 4p¹ character until the end of the latter state with an energy 11.5 kcal mol⁻¹. Finally, due to the endergonic nature of this reaction, the intermediate leads toward the HZn + SiH₃ and ZnSiH₃ + H products with calculated energies of 74.0 and 84.0 kcal mol⁻¹, respectively (see Table 2(b)). The experimental energy for HZn + SiH₃ products is 70.4 kcal mol⁻¹ in agreement with that calculated theoretically. We have not calculated transition probabilities yet.

Figure 8: Potential energy curves of the Zn(¹S, ¹P) interaction with SiH₄ as a function of the insertion angle () towards the HZnSiH₃ intermediate product. The 4p1 character follows the path from the second excited state to the minimum in the X ¹A′ state, where the final products are formed.

Luna-García et al. [10] found that cadmium in its singlet second excited state (¹P: 4d¹⁰ 5s¹ 5p¹) breaks the Si–H bond of silane, creating a barrier of ~89 kcal mol⁻¹ for the ground state. The experimental transition energy between the excited state (¹P: 4d¹⁰ 5s¹ 5p¹) and the ground state (¹S: 4d¹⁰ 5s²) is 124.9 kcal mol⁻¹, which is comparable to the transition energy of 128.5 kcal mol⁻¹ calculated theoretically (Table 2(b), Figure 9). The formation of the HCdSiH₃ intermediate at the minimum (92 kcal mol⁻¹, 45°) comes with 5p¹ character, passes through the avoided crossing between 2 ¹A′ and X ¹A′ pathways, and keeps 5p¹ character until the minimum (20.7 kcal mol⁻¹, 180°) of the X ¹A′ state is reached (see Figure 9). Finally, the intermediate is broken reaching the HCd + SiH₃ and CdSiH₃ + H products with calculated energies of 75.5 and 89 kcal mol⁻¹, respectively (see Table 2(b)). The experimental energy for HCd + SiH₃ is 74.0 kcal mol⁻¹. We have not calculated transition probabilities yet.

Figure 9: Potential energy curves of the Cd(¹S, ¹P) interaction with SiH₄ as a function of the insertion angle () towards the HCdSiH₃ intermediate product. The 5p¹ character follows the path from the second excited state to the minimum in the X ¹A′ state, where the final products are formed.

Luna-García et al. [9] found that mercury in its singlet second excited state (¹P: 5d¹⁰ 6s¹ 6p¹) breaks the Si–H bond of silane, leading to a ground state barrier of ~102 kcal mol⁻¹. The experimental transition energy between the excited state (¹P: 5d¹⁰ 6s¹ 6p¹) and the singlet ground state (¹S: 5d¹⁰ 6s²) is 154.6 kcal mol⁻¹, which agrees to the transition energy of 157.6 kcal mol⁻¹ theoretically calculated (see Figure 10 and Table 2(b)). The formation of the HHgSiH₃ intermediate arising at the minimum (106 kcal mol⁻¹, 70°) comes with 6p¹ character and passes through an avoided crossing between trajectories 2 ¹A′ and X ¹A′ of the energy surfaces maintaining 6p¹ character. The transition probability [84] at the avoided crossing among the latter states is obtained when mercury is photoexcited to the Hg ¹P: 5d¹⁰ 6s¹ 6p¹ excited state, allowing it to be inserted in silane (SiH₄) molecule. When the reaction pathway passes the crossing point and continues its way has a probability of crossing toward curve X ¹A with 6p¹ character and a probability of of continuing in the same curve 2 ¹A′ (see Figure 10) with 6s² character. When going toward the X ¹A′ state, it allows the formation of a stable intermediate at the minimum (28 kcal mol⁻¹, 180°) of the state. Finally, the latter is broken and reaches either the HHg + SiH₃ or HgSiH₃ + H products with energies 87.6 and 95.4 kcal mol⁻¹, respectively.

Figure 10: Potential energy curves of the Hg(¹S, ¹P) interaction with SiH₄ as a function of the insertion angle () towards the HHgSiH₃ intermediate product. The 6p₁ character follows the path from the second excited state to the minimum in the X ¹A′ state, where the final products are formed.

Luna-García et al. [11] have found that Cadmium in its singlet second excited state (¹P: 4d¹⁰ 5s¹ 5p¹) breaks the Ge–H bond of germane, while producing a ground state barrier of 83.6 kcal mol⁻¹ (see Figure 11). The experimental transition energy between the excited state (¹P: 4d¹⁰ 5s¹ 5p¹) and the ground state (¹S: 4d¹⁰ 5s²) is 124.9 kcal mol⁻¹, which agrees with the transition energy of 128.5 kcal mol⁻¹ calculated theoretically (Table 2(c)). The formation of the HCdGeH₃ intermediate at (89 kcal mol⁻¹, 50°) comes with 5p¹ character and goes by an avoided crossing between the 2 ¹A′ and X ¹A′ states maintaining a 5p¹ character until the next minimum at (13.6 kcal mol⁻¹, 180°) (see Figure 11). Finally the intermediate is broken in the HCd + GeH₃ and CdGeH₃ + H products with calculated energies 70.3 and 79.9 kcal mol⁻¹, respectively. The experimental energy for HCd + GeH₃ is 68.9 kcal mol⁻¹. We have not calculated the transition probabilities yet.

Figure 11: Potential energy curves of the Cd(¹S, ¹P) interaction with GeH₄ as a function of the insertion angle () towards the HCdGeH₃ intermediate product. The 5p¹ character follows the path from the second excited state to the minimum in the X ¹A′ state, where the final products are formed.

Luna-García et al. [11] have found that mercury in its excited state (¹P: 5d¹⁰ 6s¹ 6p¹) breaks the Ge–H bond of germane, while forming a ground state barrier of 86.1 kcal mol⁻¹. The experimental transition energy between the excited state (¹P: 5d¹⁰ 6s¹ 6p¹) and the ground state (¹S: 5d¹⁰ 6s²) amounts to 154.6 kcal mol⁻¹, in good agreement with the transition energy of 157.6 kcal mol⁻¹ theoretically calculated (Table 2(c)). The transition probability [84] between the PES is obtained for the reaction Hg ¹P(5d¹⁰ 6s¹ 6p¹) + GeH₄ → Hg ¹S(5d¹⁰ 6s²) + GeH₄. When mercury is photoexcited to the Hg (¹P:5d¹⁰ 6s¹ 6p¹) second excited state, the mercury atom is inserted in germane (GeH₄) molecule. This effect is observed in the minimum (90 kcal mol⁻¹, 60°) of the 2 ¹A′ state arriving with 6p¹ character, where the HHgGeH₃ intermediate is formed. When this intermediate continues its way, it has a probability of crossing toward X ¹A state with 6p¹ character and a probability of of continuing in the same 2 ¹A′ state (see Figure 12) with 6s² character. When going toward the X ¹A′ state, it leads to the formation of the product at the minimum (21 kcal mol⁻¹, 180°) of the state. Finally, the intermediate evolves towards the HHg + GeH₃ and HgGeH₃ + H products with calculated energies 80 and 87.7 kcal mol⁻¹, respectively, while the experimental energy for HHg + GeH₃ is 75.3 kcal mol⁻¹.

Figure 12: Potential energy curves of the Hg(¹S, ¹P) interaction with GeH₄ as a function of the insertion angle () towards the HHgGeH₃ intermediate product. The6p¹ character followed the path from the second excited state to the minimum in the X ¹A′ state, where the final products are formed.

2.3. Interactions of the Al, Ga Metals with YH₄

Pacheco-Blas et al. [88] found that the aluminum in its doublet second excited state (²D: 3s² 3d¹) breaks the C–H bond of methane, as does the 2 ²A′ state after surpassing an activation barrier of 14.0 kcal mol⁻¹ (see Figure 13). The experimental transition energy between this second excited state (²D: 3s² 3d¹) and the ground state (²P: 3s² 3p¹) is 92.5 kcal mol⁻¹ and agrees with the transition energy of 93.9 kcal mol⁻¹ theoretically calculated (see Table 3(a)). The transition probability [88] among the corresponding PES for the reaction Al ²D(3s² 3d¹) + CH₄ → Al ²P(3s² 3p¹) + CH₄ starts with the formation of the HAlCH₃ intermediate and goes through two avoided crossings with the 3 ²A′, 2 ²A′, and X ²A′ states. When aluminum is photoexcited to its Al ²D: 3s² 3d¹ second excited state, it is inserted into a C–H bond of methane at the minimum (87 kcal mol⁻¹, 20°) in the 3 ²A′ state with 3d¹ character. Under these conditions, the HAlCH₃ intermediate is formed. As the latter continues its path, it has a probability of 0.85 of crossing toward the 2 ²A′ state with 3d¹ character going to the Al ²D: 3s² 4s¹ first state and a probability of 0.15 of continuing in the same 3 ²A′ state with 4s¹ character. When the intermediate continues its pathway, there is a probability of 0.89 for crossing from the 2 ²A′ state to the X ²A′ with 3d¹ character (see Figure 13), where the most stable intermediate is found at = 120° and 6.5 kcal mol⁻¹. When this occurs, the final products are reached from the Al + CH₄ reaction, that is, to say, the intermediate is broken in the HAl + CH₃ and AlCH₃ + H products with calculated energies 42.8 and 48.2 kcal mol⁻¹, respectively. In this case, the corresponding experimental [36] energy is 45.0 kcal mol⁻¹ in both cases.

Table 3

(a) Metal family (Al, Ga) interacting with methane. Relative energies (kcal mol⁻¹) of the reactants, intermediary HXCH₃ and final products for three lowest states of the metal.

X: metal
Ala
Gab

(²P, ²S, ²D)
(²P, ²S, ²P)

X(2nd) + CH₄
92.5
93.9
93.1
93.7

X(1st) + CH₄
72.24
73.4
69.3
72.7

H + XCH₃
45.0
48.2

45.7

HX + CH₃
45.0
42.8
38.9c
40.2

HXCH₃
⋯
6.5
4.9d
6.1

X(gs) + CH₄
0
0
0
0

aFrom [88]

bFrom [14]

cFrom [97]

dFrom [98].

(b) Metal family (Al, Ga) interacting with silane. Relative energies (kcal mol⁻¹) of the reactants, the HXSiH₃ intermediary and final products for three lowest states of the metals.

X: metal
Ala
Gab

(²P, ²S, ²D)
(²P, ²S, ²P)

X(2nd) + SiH₄
92.5

93.1
93.7

X(1st) + SiH₄
72.24

69.3
71.7

H + XSiH₃

45.3

HX + SiH₃

24.5c
26.1

HXSiH₃

6.21d

6.1

X(gs) + SiH₄
0
0
0
0

aFrom [88]

bFrom [13]

cFrom [97]

dFrom [99].

Figure 13: Potential energy curves of the Al (²P, ²S, and ²D) interaction with CH₄ versus insertion angle toward the HAlCH₃ intermediate product. The 3d¹ character follows the path from the second excited state to the minimum in the X ²A′ state, where the final products are formed.

Pacheco-Sánchez et al. [14] have found that gallium in its doublet first excited state (²S: 4s² 5s¹) breaks the C–H bond of methane, producing in the lowest state an activation barrier of 53.7 kcal mol⁻¹. The experimental transition energy among the excited state (²S: 4s² 5s¹) and the ground state (²P: 4s² 4p¹) is 69.3 kcal mol⁻¹, in agreement with the transition energy 72.7 kcal mol⁻¹ theoretically calculated (see Table 3(a)), within the 3 kcal mol⁻¹ of tolerance. The transition probability [14] among the corresponding PES for the reaction Ga ²S(4s² 5s¹) + CH₄ → Ga ²P(4s² 4p¹) + CH₄ starts with the formation of the intermediate HGaCH₃ and passes through two avoided crossings with 3 ²A′, 2 ²A′, and X ²A′ states. When gallium is photoexcited to its Ga ²S: 4s² 5s¹ first excited state, it is inserted into a C–H bond of methane at the minimum (60 kcal mol⁻¹, 25°) in the 3 ²A′ state with 5s¹ character. Under these conditions, the intermediate product HGaCH₃ is formed. As the latter continues its path, it has a probability of 0.715 [83] (the branching fraction is 0.73 [96]) of crossing toward the 2 ²A′ state with 5s¹ character going to the Ga ²P: 4s² 4p¹ ground state and a probability of 0.285 of continuing by the same 3 ²A′ state with 4p¹ character. When the intermediate continues its pathway, there is a probability of 0.46 for crossing from the 2 ²A′ state to X²A′ with 5s¹ character (see Figure 14), where the most stable intermediate is found at and 6.1 kcal mol⁻¹. Finally, this intermediate is broken in the products HGa + CH₃ and GaCH₃ + H with calculated energies 40.2 and 45.7 kcal mol⁻¹, respectively. The corresponding experimental energy is 38.9 kcal mol⁻¹ in HGa + CH₃ case.

Figure 14: Potential energy curves of the interaction of Ga(²P), Ga(²S), and Ga(²P) with CH₄ towards the GaCH₃ intermediate. Energy versus insertion angle (). The 5s¹ character follows the path from the first excited state to the minimum in the X ²A′ state, where the final products emerge.

Pacheco-Sánchez et al. [13] have found that gallium in its doublet first excited state (²S: 4s² 5s¹) breaks the Si–H bond of silane, overcoming a barrier of 51.0 kcal mol⁻¹ of the ground state. The experimental transition energy between the excited state (²S: 4s² 5s¹) and the ground state (²P:4s² 4p¹) is 69.3 kcal mol⁻¹, which agrees to the transition energy of 71.7 kcal mol⁻¹ theoretically calculated (Table 3(b)). The transition probability [13] among the corresponding PES for the reaction Ga ²S(4s² 5s¹) + SiH₄ → Ga ²P(4s² 4p¹) + SiH₄ starts with the formation of the intermediary molecule HGaSiH₃ passing through two avoided crossings among 3 ²A′, 2 ²A′, and X ²A′ states. The probability [85] that it crosses from 3 ²A′ state to 2 ²A′ state is and a probability of continuing along the same 3 ²A′ state. When crossing towards the 2 ²A′ state in its descent, it has a probability of crossing towards the X ²A′ state and a probability of continuing along the same 2 ²A′ state (see Figure 15). Finally at the minimum (6.1 kcal mol⁻¹, 120°) of the X ²A′ state, the intermediate is broken into the HGa + SiH₃ and GaSiH₃ + H products with energies 26.1 and 45.3 kcal mol⁻¹, respectively. The corresponding experimental energy is 24.5 kcal mol⁻¹ in HGa + SiH₃ case.

Figure 15: Potential energy curves of the interaction of Ga(²P), Ga(²S), and Ga(²P) with SiH₄ towards the GaSiH₃ intermediate. Energy versus insertion angle (). The 5s¹ character followed the path from the first excited state to the minimum in the X ²A′ state, where the final products are formed.

Lefcourt and Ozin [100] optimized geometry of Al–SiH₄ interaction for ²A₁ state in C2v symmetry with the single point SCF energy and calculated that the geometry-optimized structure does not differ very much at all from the initial geometry, a situation that is reflected in the converged energy which is only approximately 1/100 of a hartree lower (~6.21 kcal/mol) than the single-point value associated with the starting structure. Calculations carried out on systems having the equivalent starting geometry but inhabiting the ²B₁ and ²B₂ electronic states yielded final energies that were considerably higher (0.17 and 0.31 hartree, resp.) than the energy obtained in the ²A₁ optimization.

3. Discussion

We have presented here a series of studies on X + YCH₄ (X = Cu, Zn, Cd, Ga, Al, Au, Hg, and Y = C, Si, Ge) reactions, attempting to identify possible general patterns. The very first study presented, the Cu + CH₄ reaction was simultaneously being studied experimentally at Toronto University in Canada [32, 33, 101–104], allowing us to make a very close comparison and correlation between their cryogenic experiments and our quantum mechanical calculations. This was due to the fact that Jaime Garcia-Prieto (a member of our group in Mexico) was working with Professor Geoffrey Ozin at Lash Miller Lab. in Toronto on the photochemical activation of Cu in methane matrices at near-absolute zero conditions. Originally Ozin expected the open shell Cu: ²D excited state to be responsible for methane activation, but our calculations proved that the higher lying ²P was the real culprit, albeit through a series of avoided crossings a fact which was finally acknowledged in the experimental and theoretical papers [32, 60]. Since then our group, mainly through the late Sidonio Castillo and his collaborators, studied a series of transition metals. We have presented here an overview of this line of research although we evidently must accept that the list of metals studied to date is far from exhaustive. This notwithstanding, we provide here enough examples of the mechanism first advanced in our explanation of the Lash Miller Lab experiments of the activation of methane by copper [60, 82]. In short we have advanced a daring hypothesis avoided crossings and transition probabilities for curves of the same symmetry play a systematic and clear-cut role in the activation of methane, silane, and germane. Indeed, we show the evidence that in general, the most stable intermediate has a rather weak binding, thus leading to the products. The potential energy surfaces lead from the reactants climbing to this transition state which requires moderate energies, normally derived from photoactivation processes and finally yielding the final products (XH + YH₃ or H + XYH₃). To document this, we report the configurations and bond distances as they evolve in each specific case. We kindly refer our readers to access our original papers for details. In any case, our reported energies are compatible with the spectra of reactants, intermediates, and products. For instance, the probabilities for the Ga + CH₄ reaction agree quite well with experimental results [83, 96], whereas those obtained for other systems reported here were widely discussed in the original papers [82–88].

The potential energy surfaces for the coinage metals Cu and Au with silane are rather similar. The main difference lies in the energies of their respective second excited states, making their potential energy wells differ from their respective intermediate complexes onward to the final products. To wit, in the Au + SiH₄ reaction, the minimum at 120 degrees has only a depth of 3.34 kcal/mol, while for Cu + SiH₄ the minimum lies at 100 degrees and is 5.58 kcal/mol deep. These results would make the study of the Ag + SiH₄ reaction all the more desirable, a valid proposition for several other metals. We explicitly state here that our work on these systems is far from complete. Take for instance our results involving Hg which are rather different from the other metals, thus, naturally deserving closer scrutiny. Perhaps we may tentatively relate this peculiarity of mercury to its particularly stable ground state ¹S₀ (with its closed 5d¹⁰ 6s² valence shell), from which stem the unique dense metal liquid character of mercury, in dire contrast with its solid metal neighbors with stable electronic arrangements. In effect we dare propose that this line of research is both valid and promising and needs much more work and attention, especially so with a close collaboration with cryogenic experiments, as we hope to establish.

Difference of PES of coinage metals interacting with silane is due to the second excited state leading to the reported well depths for the potentials for the ground state. Analogously, the PES of pseudotransition metals interacting with silane is very similar, and the main difference is the ¹P singlet energy of the pseudotransition metals at the second excited state. This causes the depth wells of potential (11.5 kcal mol⁻¹, 180°) for Zn + SiH₄, while for Cd + SiH₄ it is (20.7 kcal mol⁻¹, 180°), and for Hg it is (28 kcal mol⁻¹, 180°), since the initial formation of the intermediate until the product formation.

The methane complexes with Zn and Cd in the second excited state ¹P at has energies ~141 and 125.6 kcal mol⁻¹, respectively. The germane complexes with Cd and Hg in the second excited state ¹P at have energies 128.5 and 157.6 kcal mol⁻¹, respectively. The initial excitation energy of the pseudotransition metals yields the depth wells of potential, which is ~25 kcal mol⁻¹ for Zn + CH₄ and 31.9 kcal mol⁻¹ Cd + CH₄. The initial excitation energy of the pseudotransition metals yields the depth wells of potential, which is 13.6 and 21.0 kcal mol⁻¹ for Cd + GeH₄ and Hg + GeH₄, respectively.

Finally, PES of metals Al ²D doublet and Ga ²P doublet in the second excited state interacting with methane for has energies 93.9 and 93.7 kcal mol⁻¹, respectively. The initial energy of the metals yields the depth wells of potential, of 6.5 and 6.1 kcal mol⁻¹ for Al + CH₄ and Ga + CH₄, respectively, and 6.21 taken from reference [100] and 6.1 kcal mol⁻¹ for Al + SiH₄ and Ga + SiH₄, respectively. While the latter result is as expected, in the previous one there is a very small deviation. This is due to the very small energy difference at 2nd excited state between Al and Ga, and to the approximation error carried out by the numerical solutions of the system. In defense of this argumentation, it is the fact that the dissociation energy of the ionic Al⁺−CH₄ complex has been experimentally reported to be 2120 ± 105 cm‒1 (6.06 ± 0.3 kcal mol⁻¹) [99]. Somewhat coincidentally we have obtained the value of 6.5 kcal mol⁻¹ for the dissociation energy of Al + CH₄ complex. It is quite remarkable that the dissociation energies for Al⁺−CH₄ and Al + CH₄ are quite close, and that the experimental value for this ionic Al⁺–CH₄ reaction is the expected value for the dissociation energy of Al–CH₄.

A very important issue is to get the most stable intermediate with the lowest energy on which the breaking of the intermediate is achieved. The products of the reaction emerge at the end from the X A′ state, calculated using the parameter values obtained at this minimum.

The intermediate has a much lower energy than the final products due to the endergonic nature of these reactions. Initially, the metal needs a photoexcitation for taking it to an excited state for being inserted in a Y–H bond of the gas molecule, in order to surpass the activation barrier of the ground state for the reaction. After the avoided crossings, the deformed metastable intermediate arrives to the most stable arrangement, having the lowest energy with the optimal geometry. At this low energy arrangement, its internal bond orientation produces a still strong electrostatic repulsion due to the energy gained by the photoexcitation of the metal, greater than the energy of the intermediate. The metal atom also shares its energy with the carbon and hydrogens. Thus, the new energies of the products cannot be greater than the initial excitation of the metal or lower than the energy of the reactants in their ground state.

The resulting probabilities for the case of Ga + CH₄ are in agreement with previous experimental results [83], whereas those obtained for the other cases are only theoretical predictions.

4. Conclusions

From the theory of transition probabilities at avoided crossings between curves of the same symmetry, we can deduce that the character of the wave function is the same at the beginning of the highest state path than at the minimum of the ground state path after all avoided crossings.

The energy value of the initial state of the metal which eventually leads to the intermediate, as well as the character of the wavefunction is crucial for the product formation. This character corresponds to the dominant excited state of the metal inserting in the gas molecule and is independent of the gas in consideration (methane, silane, or germane).

As expected the wells’ potential depth is dependent on the energy level of the metal excited state in consideration, and the pathway is reflected in the character of the wavefunction revealing the electronic configuration of the corresponding excited state. This means that the higher the energy of the metal atom excited state, the deeper the potential energy well at the ground state minimum.

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