The latter follows approximately the steepest descent direction, behaving like the gradient method.

His most important contribution is the introduction of the gradient method in quantum chemistry.

For non-differentiable functions, gradient methods are ill-defined.

They offer alternatives to the use of numerical derivatives in the Gauss-Newton method and gradient methods.

The basic idea of gradient methods is to move atoms according to the total net forces acting on them.

An analytical formula of the gradient of potential energy is preferentially required by the gradient methods.

In this case, the Powell's direction set method or the downhill simplex method can generally be more efficient than the gradient methods.

Figure 2 shows a highly simplified comparison between the conjugate and the simple gradient methods on a 1D energy curve.

In 2009, the topological gradient method has been applied to tomographic reconstruction.

Evaluating derivative couplings with analytic gradient methods has the advantage of high accuracy and very low cost, usually much cheaper than one single point calculation.