dp da change in the equilibrium geometry. Assuming the equilibrium geometry, can be expressed as (5) The first term on the right-hand side represents the gradient in the iso-geometric chemical space and contains the elements of . The second term takes into account the displacement of the equilibrium geometry. in the second term has the elements of . is the Hessian matrix of energy with respect to the nuclear coordinates. contains the elements of . While quantum alchemy can efficiently compute these derivatives as described later, the computational costs of and are still high. When p is the energy-related functionality, Eq. ( ) becomes , and their evaluations are avoided. For the other functionalities, must be evaluated. That is, the computational cost of MDM becomes significantly higher when targeting general properties. Therefore, in our previous study, MDM was only applied for optimizing energetic functionalities. For the design of general properties, the present MDM avoids This procedure is repeated until the variation in a becomes sufficiently small (Figure (b)). The full optimization problem is solved under that condition since the equilibrium geometry change is