Quantum Chemistry 5.1 - Harmonic Oscillator Model

[@inventaunmanana4860]

Thank you sir for making all these videos. They are super clear and accurate.

[@nkyu3035]

suddenly i have a doubt why, at equilibrium, V(r) is local minimum(at r=r_0). if V(r_0) is negative like this, 2 atoms would get closer until V(r) becomes 0 (say, r=r_1). - isn't it when molecule reaches equilibrium? - If not, is it because equilibrium is has to do with Force rather than Energy? does molecule not move in a condition of negative V and zero Force? what keeps the molecule from getting closer in the presence of negative V? on the other hand, if V(r_1)=0, there'd be no attraction between atoms, thus no bond. as you can tell, these're all mixed up o_o;; hope you can guide me onto the right path.

[@TMPChem]

You're confusing force and potential. Potential energy is the energy that objects possess due to their position in space. Objects at high altitude have a high potential energy due to Earth's gravity. Force is a vector field which causes objects to accelerate in a given direction. All objects on Earth's surface feel approximately the same gravitational force (per unit mass) pulling them in the direction of Earth's center. Potential energy is a scalar value which is defined at every point in space. Force is the negative first derivative of potential energy with respect to position. When the derivative of the potential is zero, the force is zero, and the object is not accelerating in any direction. If a harmonic oscillator is at r = ro and v = 0, then it will remain and ro with a velocity of zero. If it is displaced from equilibrium (ro), it will feel a force which accelerates it back towards the equilibrium point. The magnitude of the force is proportional to the distance from equilibrium, thus the force is linear and the potential is quadratic.

[@nkyu3035]

this is what i wanted! so, the reason zero V(r) didn't mean no movement is that we didn't set V(r) in that way yet, right?

[@TMPChem]

V(r) doesn't tell you anything about movement. -dV(r)/dr tells you the force acting on the particle. In classical mechanics, F = ma, and a = dx^2/dt^2. In order to determine the particle's trajectory [x(t)], you need to specify an initial position x(0) and initial velocity v(0) = dx(0)/dt. Potential energy tells you force. Force tells you acceleration. Acceleration tells you the change in velocity. Velocity tells you the change in position.

[@solsticetwo3476]

TMP Chem - I think he knew all these from the beginning. He is just bothering you. You should ignore all his question from here on