Gaussian software relaxed potential energy scan

It is equal and opposite to the force acting on the other nucleus, and it is also equal to the mass times the acceleration Р В Р вЂ Р Р†Р вЂљРЎв„ўР вЂ™Р’В¬x by NewtonР В Р вЂ Р В РІР‚С™Р Р†РІР‚С›РЎС›s second law (see section on the harmonic oscillator in Chapter 4). The force on one nucleus due to stretching or compressing the bond is equal to the force constant of the bond k times the distance between the nuclei Р В РІР‚СљР вЂ™Р’В°x 2 x 1Р В РІР‚СљР РЋРІР‚С”. The whole molecule can undergo motion (translation), and it can vibrate.

Although there is only one space coordinate, there are two degrees of freedom. Here we shall consider a homonuclear diatomic molecule restricted to a onedimensional x-space (Starzak, 1989) (Fig. The new coordinates are found by rotation of the old ones in the x-y plane such that they lie along the principal axes of the ellipse. If, instead of making an arbitrary choice of the coordinate system, we choose more wisely, the ellipse can be expressed more simply, without cross terms There we found that an arbitrary elliptical orbit can be described with an arbitrarily oriented pair of coordinates (for two degrees of freedom) but that we must expect cross terms like 8xy in Eq. We shall concentrate on the potential energy term of the nuclear Hamiltonian and adopt a strategy similar to the one used in simplifying the equation of an ellipse in Chapter 2. Separation of the Hamiltonian is not feasible because of the cross terms it contains, but expressed in terms of its normal coordinates, the Hamiltonian can be separated. Like any other Hamiltonian, the nuclear Hamiltonian can, in principle, be separated into a sum of partial Hamiltonians leading to a sum of energies and a product of wave functions. It governs motions of the nuclei, in particular, vibrational motion. The Р В Р вЂ Р В РІР‚С™Р вЂ™Р’ВР В Р вЂ Р В РІР‚С™Р вЂ™Р’ВneglectedР В Р вЂ Р В РІР‚С™Р Р†РІР‚С›РЎС›Р В Р вЂ Р В РІР‚С™Р Р†РІР‚С›РЎС› part of the molecular Schroedinger equation, after making the BornР В Р вЂ Р В РІР‚С™Р Р†Р вЂљРЎС™Oppenheimer separation in the Р В РЎвЂ”Р вЂ™Р’В¬Р В РЎвЂњrst section of this chapter, is What is the speed of a nitrogen atom as it passes through the point r Р В РІР‚в„ўР РЋР’В 1:106? What is the maximum speed of the nitrogen atoms as they move toward andР В РІР‚СњР В Р вЂ№0. How long does it take for each N atom to get from its minimum speed to its maximum speed?Р В РІР‚СњР вЂ™Р’В©. (h) The frequency of oscillation in cm 1.Р В РІР‚СњР В Р С“. (g) The period of oscillation in seconds. (f) The frequency of oscillation in hertz. (e) The force on the virtual oscillator of mass m at excursion r max. (d) The force constant k in newtons per meter. (c) The maximum potential energy per N 2 molecule e in joules. (a) The maximum excursion r max r 0 in meters. What is the maximum kinetic energy of the N N system as deР В РЎвЂ”Р вЂ™Р’В¬Р В РЎвЂњned? What is the maximum potential energy of the N N system as deР В РЎвЂ”Р вЂ™Р’В¬Р В РЎвЂњned?Р В РІР‚СњР вЂ™Р’В¦. Can the two-mass N N system be regarded as a one-mass system having a reduced mass m? If so, what is m?Р В РІР‚СњР СћРЎвЂ™. What is the interatomic separation at the minimum potential energy? For convenience, deР В РЎвЂ”Р вЂ™Р’В¬Р В РЎвЂњne the minimum potential energy of the system as zero at the minimum of the potential well.Р В РІР‚СњР вЂ™Р’В¤. Where in their excursion is the maximum atomic speed attained?Р В РІР‚СњР В РІвЂљВ¬. What is the minimum atomic speed? Where in their excursion do the atoms reach their minimum speed?Р В РІР‚СњР РЋРЎвЂє. Suppose that we agree to regard the N N molecule as a classical (nonquantum) harmonic oscillator and we stipulate that each N atom makes a maximum excursionР В РІР‚СњР В РІР‚С›way from its equilibrium bond length of 0.006 A during each vibration.Р В РІР‚СњР В Р вЂ№. SEMIEMPIRICAL CALCULATIONS ON LARGER MOLECULES

Gaussian software relaxed potential energy scan