Using a Spreadsheet To Solve the Schrödinger Equations for the Energies of the Ground Electronic State and the Two Lowest Excited States of H2

We have designed an exercise suitable for a lab or project in an undergraduate physical chemistry course that creates a Microsoft Excel spreadsheet to calculate the energy of the S0 ground electronic state and the S1 and T1 excited states of H2. The spreadsheet calculations circumvent the construction and diagonalization of the Fock matrix and thus can be accomplished by any undergraduate chemistry student with basic calculus skills. The wave functions of the S0, S1, and T1 states of H2 are constructed from the symmetry-adapted bonding and antibonding molecular orbitals (MO). All quantum mechanical integrals are estimated using the Monte Carlo integration method. Due to the stochastic nature of the spreadsheet calculations, 25 runs were carried out to obtain the mean energy of the S0, S1, and T1 electronic states of H2. The accuracy of the spreadsheet calculations is comparable to that of the HF/STO-3G calculations. The atomic and molecular orbitals and the energy components can be easily calculated and plotted for better visualization and understanding of essential quantum chemical concepts. This spreadsheet can also be adapted to tackle a wider range of quantum chemistry problems with different levels of complexity

Gene expression patterns in the hippocampus and amygdala of endogenous depression and chronic stress models

The etiology of depression is still poorly understood, but two major causative hypotheses have been put forth: the monoamine deficiency and the stress hypotheses of depression. We evaluate these hypotheses using animal models of endogenous depression and chronic stress. The endogenously depressed rat and its control strain were developed by bidirectional selective breeding from the Wistar–Kyoto (WKY) rat, an accepted model of major depressive disorder (MDD). The WKY More Immobile (WMI) substrain shows high immobility/despair-like behavior in the forced swim test (FST), while the control substrain, WKY Less Immobile (WLI), shows no depressive behavior in the FST. Chronic stress responses were investigated by using Brown Norway, Fischer 344, Lewis and WKY, genetically and behaviorally distinct strains of rats. Animals were either not stressed (NS) or exposed to chronic restraint stress (CRS). Genome-wide microarray analyses identified differentially expressed genes in hippocampi and amygdalae of the endogenous depression and the chronic stress models. No significant difference was observed in the expression of monoaminergic transmission-related genes in either model. Furthermore, very few genes showed overlapping changes in the WMI vs WLI and CRS vs NS comparisons, strongly suggesting divergence between endogenous depressive behavior- and chronic stress-related molecular mechanisms. Taken together, these results posit that although chronic stress may induce depressive behavior, its molecular underpinnings differ from those of endogenous depression in animals and possibly in humans, suggesting the need for different treatments. The identification of novel endogenous depression-related and chronic stress response genes suggests that unexplored molecular mechanisms could be targeted for the development of novel therapeutic agents

Using a Spreadsheet To Solve the Schrödinger Equations for the Energies of the Ground Electronic State and the Two Lowest Excited States of H₂

We have designed an exercise suitable for a lab or project in an undergraduate physical chemistry course that creates a Microsoft Excel spreadsheet to calculate the energy of the S₀ ground electronic state and the S₁ and T₁ excited states of H₂. The spreadsheet calculations circumvent the construction and diagonalization of the Fock matrix and thus can be accomplished by any undergraduate chemistry student with basic calculus skills. The wave functions of the S₀, S₁, and T₁ states of H₂ are constructed from the symmetry-adapted bonding and antibonding molecular orbitals (MO). All quantum mechanical integrals are estimated using the Monte Carlo integration method. Due to the stochastic nature of the spreadsheet calculations, 25 runs were carried out to obtain the mean energy of the S₀, S₁, and T₁ electronic states of H₂. The accuracy of the spreadsheet calculations is comparable to that of the HF/STO-3G calculations. The atomic and molecular orbitals and the energy components can be easily calculated and plotted for better visualization and understanding of essential quantum chemical concepts. This spreadsheet can also be adapted to tackle a wider range of quantum chemistry problems with different levels of complexity

Using a Spreadsheet To Solve the Schrödinger Equations for the Energies of the Ground Electronic State and the Two Lowest Excited States of H₂

We have designed an exercise suitable for a lab or project in an undergraduate physical chemistry course that creates a Microsoft Excel spreadsheet to calculate the energy of the S₀ ground electronic state and the S₁ and T₁ excited states of H₂. The spreadsheet calculations circumvent the construction and diagonalization of the Fock matrix and thus can be accomplished by any undergraduate chemistry student with basic calculus skills. The wave functions of the S₀, S₁, and T₁ states of H₂ are constructed from the symmetry-adapted bonding and antibonding molecular orbitals (MO). All quantum mechanical integrals are estimated using the Monte Carlo integration method. Due to the stochastic nature of the spreadsheet calculations, 25 runs were carried out to obtain the mean energy of the S₀, S₁, and T₁ electronic states of H₂. The accuracy of the spreadsheet calculations is comparable to that of the HF/STO-3G calculations. The atomic and molecular orbitals and the energy components can be easily calculated and plotted for better visualization and understanding of essential quantum chemical concepts. This spreadsheet can also be adapted to tackle a wider range of quantum chemistry problems with different levels of complexity