Because explicitly computing this quantity is computationally costly, the program Gaussian uses the Berny algorithm to approximate it using energies along the optimization pathway. For 10 points each:
[10h] Name this quantity. When using methods like synchronous transit, the final optimized geometry is only valid if this quantity has exactly one negative eigenvalue.
ANSWER: Hessian matrix
[10e] Hessian matrices are used to find transition states since transition states are this type of point on the potential energy surface. These points are a local minimum in one direction and a local maximum in an orthogonal direction.
ANSWER: saddle points
[10m] When optimizing transition state geometries, it's often more convenient to represent the internal coordinates with matrices named for this letter. The expression “P V divided by nRT” gives a quantity denoted by this letter that represents real gas behavior.
ANSWER: Z [accept Z-matrices] (The second sentence refers to the compressibility factor.)
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