A brief review of relativistic quantum chemistry is given here. Relativistic effects and their importance in chemistry are discussed. An outline of different theoretical aspects is presented. Aspects of variation techniques relevant to relativistic calculations are discussed in detail. These involve the derivation of min-max theorems for Dirac, Dirac-Hartree-Fock and Dirac-Coulomb calculations. The consequence of relativistic Hamiltonians being unbounded are also discussed for other lines of investigation. The upper bounds derived are physically interpreted. Sample Dirac-Hartree-Fock results for the Be atom, calculated using both STO and GTO bases for the nonrelativistic orbitals and the upper components of the relativistic orbitals, are given. The inadequacy of the so-called kinetically balanced basis set is discussed and illustrated with these results. The importance of the variational or dynamical balance and hence the merit of the LCAS-MS scheme is pointed out. The possibility of calculating quantum electrodynamical pair energy from relativistic configuration interaction calculations on a two-electron atom is discussed and exemplified. The present status of relativistic molecular calculations is briefly reviewed. Conclusions on the aspects of variational analysis and molecular calculations are enclosed.

The retarded interaction between an electron and a spin-0 nucleus, that has been derived from electro-dynamical perturbation theory is discussed here. A brief account of the derivation is given. The retarded form is correct through order $v^2/c^2$. Use of the relative coordinates leads to an effective oneelectron operator that can be used through all orders of perturbation theory. A few unitary transformations give rise to the interaction that is valid in the non-relativistic limit.

A temperature-dependent integrated kinetics for the overall process of photosynthesis in green plants is discussed. The C₄ plants are chosen and in these plants, the rate of photosynthesis does not depend on the partial pressure of O₂. Using some basic concepts like chemical equilibrium or steady state approximation, a simplified scheme is developed for both light and dark reactions. The light reaction rate per reaction center ($R'_1$) in thylakoid membrane is related to the rate of exciton transfer between chlorophyll neighbours and an expression is formulated for the light reaction rate $R'_1$. A relation between $R'_1$ and the NADPH formation rate is established. The relation takes care of the survival probability of the membrane. The CO₂ saturation probability in bundle sheath is also taken into consideration. The photochemical efficiency (𝜙) is expressed in terms of these probabilities. The rate of glucose production is given by $R_{\text{glucose}} = (8/3)(R'_1v_L)\phi(T)g(T)$ ([G3P]/[$P_i$]$^2_{\text{leaf}}$)$_{SS}$Q$_{\text{G3P} \rightarrow \text{glucose}}$ where 𝑔 is the activity quotient of the involved enzymes, and G3P represent glycealdehyde-3-phosphate in steady state. A Gaussian distribution for temperaturedependence and a sigmoid function for de-activation are incorporated through the quotient 𝑔. In general, the probabilities are given by sigmoid curves. The corresponding parameters can be easily determined. The theoretically determined temperature-dependence of photochemical efficiency and glucose production rate agree well with the experimental ones, thereby validating the formalism.

We give a detailed description of the use of explicit as well as implicit solvation treatments to compute the reduction potentials of biomolecules in a medium. The explicit solvent method involves quantum mechanical/molecular mechanics (QM/MM) treatment of the solvated moiety followed by a Monte-Carlo (MC) simulation of the primary solvent layer. The QM task for considerably large biomolecules is normally carried out by density functional treatment (DFT) along with the MM-assisted evaluation of the most stable configuration for the primary layer and biomolecule complex. The MC simulation accounts for the dynamics of the associated solvent molecules. Contributions of the solvent molecules of the bulk towards the absolute free energy change of the reductive process are incorporated in terms of the Born energy of ion-dielectric interaction, the Onsager energy of dipole-dielectric interaction and the Debye-Hückel energy of ion-ionic cloud interaction. In the implicit solvent treatment, one employs the polarizable continuum model (PCM). Thus the contribution of all the solvent molecules towards the free energy change are incorporated by considering the whole solvent as a dielectric continuum.

As an example, the QM(DFT)/MM/MC-Born/Onsager/Debye-Hückel corrections yielded the oneelectron reduction potential of Pheophytin-a in the solvent DMF as $−0.92 \pm 0.27$ V and the two-electron reduction potential as $−1.34 \pm 0.25$ V at 298.15 K while the DFT-DPCM method yielded the corresponding values as $−1.03 \pm 0.17$ V and $−1.30 \pm 0.17$ V, respectively. The calculated values more or less agree with the observed mid-point potentials of −0.90 V and −1.25 V, respectively. Moreover, a numerical finite difference Poisson-Boltzmann solution along with the DFT-DPCM methodology was employed to calculate the reduction potential of Pheophytin-a within the thylakoid membrane. The calculated reduction potential value of −0.58 V is in agreement with the reported value of −0.61 V that appears in the socalled 𝑍-scheme and is considerably different from the value in vitro.

The rate of glucose equivalent production in C₄ green plants is investigated as a function of the intercellular partial pressure of CO₂, so as to find the precise physical chemistry of photosynthesis. Expressions are first formulated for the dependence of photochemical efficiency and of rubisco activation on pressure. Then a pressure-dependent rate law is derived. The latter is successfully tested for two specific C₄ plants, namely, Panicum antidotale and Panicum coloratum.

Both implicit solvation method (dielectric polarizable continuum model, DPCM) and hybrid solvation method (cluster-continuum model) were adopted to calculate the $pK_a$ of mono-protonated form of $13^2$-(demethoxycarbonyl) pheophytin 𝑎 (Pheo) in methanol. In the cluster-continuum model calculations, we considered only 1 solvent molecule attached explicitly and others treated implicitly whereas in the DPCM calculations all the solvent molecules were treated implicitly. DPCM calculations were carried out on Pheo, PheoH+, Pheo-CH₃OH and PheoH⁺-CH₃OH in methanol solution. The aim of these calculations was to determine the free energy changes involved in the deprotonation of PheoH⁺ ($\Delta G_{\text{sol}}$) and finally to obtain the corresponding $pK_a$ value. DPCM calculations were carried out employing the restricted open-shell density functional treatment (ROB3LYP) using the 6-31G(𝑑) basis set to determine the free energy of solvation of bare Pheo and PheoH+ and of the clusters, Pheo-CH₃OH and PheoH⁺-CH₃OH in methanol. In-vacuo geometries of all the species were obtained by performing optimizations at ROB3LYP level using the 6-31G(𝑑) basis. Electronic energies of all the species were then obtained by carrying out single point DFT calculations using 6-311+G(2𝑑, 2𝑝) basis set on the respective optimized geometries. Differences in thermal energy and molecular entropy were calculated by carrying out frequency calculations at ROB3LYP/STO-3G level on the optimized geometries of the truncated models. The optimized geometries of the clusters display intermolecular hydrogen bonding interactions. The $pK_a$ values of PheoH⁺ calculated by DFT-DPCM and cluster-continuum methods are 6.12 and 4.70 respectively while the observed value is 4.14. The hydrogen bonding interaction between the solute and the solvent can be attributed for the good performance of the cluster-continuum model over pure continuum model.

This work aims to verify the experimental thermochemistry of the reactions involved in Calvin cycle that produces glucose equivalent by using products from the light-activated reactions in chloroplast. The molecular geometry of each involved species in water has been optimized by density functional theory using SCRF-PCM methodology at M06-2X/6-311++G(3df,3pd) level. The thermal correction to Gibbs free energy of each solute has been calculated at the same level of theory. An explicit accounting of the intramolecular and intermolecular hydrogen bonding has been made for each solute molecule by using theoretically determined values from different sources. These data have been added together to obtain the standard Gibbs free energy 𝐺^∅ for each molecule in solution. Finally, the free energy change 𝛥𝐺 of each involved reaction has been determined using the experimental concentrations under physiological conditions. The calculated 𝛥𝐺 values are generally in good agreement with the experimentally found free energy changes, with only a few relatively large deviations. Five regulating steps with moderately large and negative 𝛥𝐺 have been identified, whereas only three of them were clearly identified from experiment. We particularly show that the steps involving the formation of G3P from 3-PG and the regeneration of RuBP from Ru5P are thermodynamically strongly favored, and therefore, they take part in driving the metabolic process. We have illustrated Calvin cycle by vividly distinguishing the controlling steps from the potentially reversible reactions.