Hemoglobin including iron atom, vitamin B12 containing cobalt atom and ruthenium- based dye molecules are examples of organic molecules. We explore whether electron correlations arising from transition-metal atoms have any special role in the functioning of organic molecules using the effective multi-orbital Anderson model. We choose deoxy and oxy-heme molecules which are examples of hemoglobin derivatives because they have many experimental and theoretical studies. The experimental magnetic susceptibility measurements find that deoxy and oxy-heme molecules exhibit a high-spin to low-spin transition. We use four different computational methods: density functional theory (DFT), DFT+U, DFT+mean-field approximation (DFT+MFA) and DFT+quantum Monte Carlo (DFT+QMC) to study this transition. In this thesis, we compare the results of these methods with each other and the experimental results. DFT and DFT+U methods do not yield the high-spin state for deoxy-heme. DFT method correctly does not find the location of impurity bound state (IBS) known as correlated new electronic states. These methods obtain low-spin for oxy-heme, but they find that magnetic correlations are very small. DFT+MFA works well for high-spin, but this technique does not obtain low-spin because it does not find the location of IBS correctly. DFT+QMC gives the high(low)- spin state for deoxy-heme (oxy-heme) and finds IBS and magnetic correlations. We obtain that DFT+QMC works better among these methods for deoxy and oxy-heme molecules. Moreover, we investigate whether we can observe the IBS and magnetic correlations for vitamin B12, dye molecules and single-atom catalysts by using these computational approaches.