Non-holonomic constraints

In this next test the effective nuclear charges were determined for the non-holonomic constraint method using the Virial theorem. ... 

The success of these preliminary results was deemed sufficient to continue the project. In fact, some of these simple approximations may be adequate for certain commercial applications. These results frequently show too much binding, particularly for the non-holonomic constraint method. Normally, because traditional work is based on a variational principle, there is too little binding, but these models are over constrained and may loose some of the kinetic energy, or some of the electron-electron interaction potential. 

Attempts to base the Ml theory on a kinetic energy term associated with the separation parameter generally fail. Only in the non-holonomic constraint method has any success been achieved with a dynamic interpretation of the separation parameter, and it falls apart with the one-electron atomic system. 

Temperature constraining aims at fixing the instantaneous temperature T to the reference heat-bath value To without allowing for any fluctuations. In this sense, temperature constraining represents a hard boundary condition, in constrast to the soft boundary conditions employed by all other thermostats mentioned in this article. Note that constraining the temperature, i.e., enforcing the relation T(t) = To (or T(t) = 0) represents a non-holonomic constraint. Holonomic constraints are those... 

I fall vertically downwards. Constraints are often categorised as holonomic or non-mic. Holonomic constraints can be expressed in the form... 

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