The development of a highly efficient and environmentally friendly process for the hydrolysis of cellulose into reducing sugars could be one of the key technologies for large-scale use of cellulosic biomass in the future. In order to pursue this goal, an ionic liquid (IL)-grafting biochar sulfonic acid catalyst (BC-SO₃H-IL) was proposed and conveniently prepared with bamboo powder as a carbon resource and 1-(trimethoxy propyl silane)-3-methyl imidazolium chloride as the IL. Its catalytic performance for the heterogeneous hydrolysis of cellulose and bamboo was checked under microwave irradiation. The designed BC-SO₃H-IL catalyst was found to show much higher turnover number (TON, 3.22–6.23 for cellulose and 0.26–2.53 for bamboo) and excellent repeatability for this hydrolysis compared to the corresponding biochar sulfonic acid (BC-SO₃H, TON, 1.51–1.81 for cellulose and 0.14–1.33 for bamboo). This is likely to be because the IL groups flexibly joined to biochar sulfonic acid, like cellulose binding domain (CBD) of cellulase, efficiently breaks in the hydrogen bonding network of cellulose molecules. On the other hand, they probably play a harmonious role in the SO₃H groups (as a catalysis domain (CD) of cellulase) catalyzing cleavage of the β-1,4 glycosidic bonds of cellulose, as supported by TGA characterization and catalytic reaction results.

New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S₀ and S₁ states follow the ‘biradical’ torsion model, but the double bond is stiffer in the S₀ state; by contrast, the S₂ state follows the ‘zwitterionic’ torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated –CH₂ methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.

The eigenvectors of the electronic stress tensor can be used to identify where new bond paths form in a chemical reaction. In cases where the eigenvectors of the stress tensor are not available, the gradient-expansion-approximation suggests using the eigenvalues of the second derivative tensor of the electron density instead; this approximation can be made quantitatively accurate by scaling and shifting the second-derivative tensor, but it has a weaker physical basis and less predictive power for chemical reactivity than the stress tensor. These tools provide an extension of the quantum theory of atoms and molecules from the characterization of molecular electronic structure to the prediction of chemical reactivity.