Thermodynamic definition of mean temperature

The notion of mean temperature is crucial for a number of fields, including climate science, fluid dynamics, and biophysics. However, so far its correct thermodynamic foundation is lacking or even believed to be impossible. A physically correct definition should not be based on mathematical notions of the means (e.g., the mean geometric or mean arithmetic), because they are not unique, and they ignore the fact that temperature is an ordinal level variable. We offer a thermodynamic definition of the mean temperature that is based upon the following two assumptions. First, the correct definition should necessarily involve equilibration processes in the initially nonequilibrium system. Among such processes, reversible equilibration and fully irreversible equilibration are the two extreme cases. Second, within the thermodynamic approach we assume that the mean temperature is determined mostly by energy and entropy. Together with the dimensional analysis, the two assumptions lead to a definition of the mean temperature that is determined up to a weight factor that can be fixed to 1/2 due to the maximum ignorance principle. The mean temperature for ideal and (van der Waals) nonideal gases with temperature-independent heat capacity is given by a general and compact formula that (besides the initial temperatures) only depends on the heat capacities and concentration of gases. Our method works for any nonequilibrium initial state, not only two-temperature states.

Photodissociation of 1,3,5-Triazine: An Ab Initio and RRKM Study

The ab initio/Rice-Ramsperger-Kassel-Marcus (RRKM) approach has been applied to investigate the photodissociation mechanism of 1,3,5-triazine at different wavelengths of the absorbed photon. Reaction pathways leading to various decomposition products have been mapped out at the G3(MP2,CC)//B3LYP level, and then the RRKM and microcanonical variational transition state theories have been applied to compute rate constants for individual reaction steps. Relative product yields (branching ratios) for the dissociation products have been calculated using the steady-state approach. The results show that, after being excited by 275, 248, or 193 nm photons, the triazine molecule isomerizes to an opened-ring structure on the first singlet excited-state potential energy surface (PES), which is followed by relaxation into the ground electronic state via internal conversion. On the contrary, excitation by 285 and 295 nm photons cannot initiate the ring-opening reaction on the excited-state PES, and the molecule relaxes into the energized ring isomer in the ground electronic state. The dissociation reaction starting from the ring isomer is calculated to have branching ratios of various reaction channels significantly different from those for the reaction initiating from the opened-ring structure. The existence of two distinct mechanisms of 1,3,5-triazine photodissociation can explain the inconsistency in the translational energy distributions of HCN moieties at different wavelengths observed experimentally.

Ab initio and RRKM study of photodissociation of azulene cation

The ab initio/Rice-Ramsperger-Kassel-Marcus (RRKM) approach has been applied to investigate the photodissociation mechanism of the azulene cation at different values of the photon energy. Reaction pathways leading to various decomposition products have been mapped out at the G3(MP2,CC)//B3LYP level and then the RRKM and microcanonical variational transition state theories have been applied to compute rate constants for individual reaction steps. Relative product yields (branching ratios) for the dissociation products have been calculated using the steady-state approach. The results show that a photoexcited azulene cation can readily isomerize to a naphthalene cation. The major dissociation channels are elimination of atomic hydrogen, an H2 molecule, and acetylene. The branching ratio of the H elimination channel decreases with an increase of the photon energy. The branching ratio of the acetylene elimination as well as that of the H2 elimination rise as the photon energy increases. The main C8H6+ fragment at all photon energies considered is a pentalene cation, and its yield decreases slightly with increasing excitation energy, whereas the branching ratios of the other C8H6+ fragments, phenylacetylene and benzocyclobutadiene cations, grow.

Photodissociation of azulene at 193 nm: ab initio and RRKM study

The ab initio/Rice-Ramsperger-Kassel-Marcus (RRKM) approach has been applied to investigate the photodissociation mechanism of azulene at 6.4 eV (the laser wavelength of 193 nm) upon absorption of one UV photon followed by internal conversion into the ground electronic state. Reaction pathways leading to various decomposition products have been mapped out at the G3(MP2,CC)//B3LYP level and then the RRKM and microcanonical variational transition state theories have been applied to compute rate constants for individual reaction steps. Relative product yields (branching ratios) for the dissociation products have been calculated using the steady-state approach. The results show that photoexcited azulene can readily isomerize to naphthalene and the major dissociation channel is elimination of an H-atom from naphthalene. The branching ratio of this channel decreases with an increase of the photon energy. Acetylene elimination is the second probable reaction channel and its branching ratio rises as the photon energy increases. The main C8H6 fragments at 193 nm are phenylacetylene and pentalene and the yield of the latter grows fast with the increasing excitation energy.

Theoretical study of isomerization and dissociation of acetylene dication in the ground and excited electronic states

Ab initio calculations employing the configuration interaction method including Davidson's corrections for quadruple excitations have been carried out to unravel the dissociation mechanism of acetylene dication in various electronic states and to elucidate ultrafast acetylene-vinylidene isomerization recently observed experimentally. Both in the ground triplet and the lowest singlet electronic states of C2H2(2+) the proton migration barrier is shown to remain high, in the range of 50 kcal/mol. On the other hand, the barrier in the excited 2 3A" and 1 3A' states decreases to about 15 and 34 kcal/mol, respectively, indicating that the ultrafast proton migration is possible in these states, especially, in 2 3A", even at relatively low available vibrational energies. Rice-Ramsperger-Kassel-Marcus calculations of individual reaction-rate constants and product branching ratios indicate that if C2H(2)2+ dissociates from the ground triplet state, the major reaction products should be CCH+(3Sigma-)+H+ followed by CH+(3Pi)+CH+(1Sigma+) and with a minor contribution (approximately 1%) of C2H+(2A1)+C+(2P). In the lowest singlet state, C2H+(2A1)+C+(2P) are the major dissociation products at low available energies when the other channels are closed, whereas at Eint>5 eV, the CCH+(1A')+H+ products have the largest branching ratio, up to 70% and higher, that of CH+(1Sigma+)+CH+(1Sigma+) is in the range of 25%-27%, and the yield of C2H++C+ is only 2%-3%. The calculated product branching ratios at Eint approximately 17 eV are in qualitative agreement with the available experimental data. The appearance thresholds calculated for the CCH++H+, CH++CH+, and C2H++C+ products are 34.25, 35.12, and 34.55 eV. The results of calculations in the presence of strong electric field show that the field can make the vinylidene isomer unstable and the proton elimination spontaneous, but is unlikely to significantly reduce the barrier for the acetylene-vinylidene isomerization and to render the acetylene configuration unstable or metastable with respect to proton migration.