In the most general case, CC can be understood simply as a prescription for a trial wave function (ansatz) that uses the exponential excitation operators. This ansatz can be then optimized variationally, and this is variational CC.^[1] It is much more expensive than the common CC that uses another approximation (besides the ansatz), which linearizes the CC amplitude equations in a certain way. In most cases, this is a good approximation.

"Variational" means that a method has some ansatz for the wave function which is optimized (varied) to get the minimal energy. This is then guaranteed to be greater or equal to the true energy by the variational principle. In this sense, the common CCSD is not variational even for two-electron systems: there is no energy that would be optimized in the procedure.

Perhaps you could understand "variational" as a method that is in some way guaranteed to always give an energy greater or equal to the true energy. In general, the non-variational CC is not such a method. But for two-electron systems, CCSD is exact, so technically, it is variational in this other derived sense. But as it is exact, which is a stronger statement, I see little sense in stressing the "variational" aspect. Also, I know of no method that would be variational in this second sense, but not in the first sense.

Reference

1. Troy Van Voorhis and Martin Head-Gordon. J. Chem. Phys. 2000, 113, 8873.

In the most general case, CC can be understood simply as a prescription for a trial wave function (ansatz) that uses the exponential excitation operators. This ansatz can be then optimized variationally, and this is variational CC.^[1] It is much more expensive than the common CC that uses another approximation (besides the ansatz), which linearizes the CC amplitude equations in a certain way. In most cases, this is a good approximation.

"Variational" means that a method has some ansatz for the wave function which is optimized (varied) to get the minimal energy. This is then guaranteed to be greater or equal to the true energy by the variational principle. In this sense, the common CCSD is not variational even for two-electron systems: there is no energy that would be optimized in the procedure.

Perhaps you could understand "variational" as a method that is in some way guaranteed to always give an energy greater or equal to the true energy. In general, the non-variational CC is not such a method. But for two-electron systems, the CCSD energy is exact, so technically, it is variational in this other derived sense. But as it is exact, which is a stronger statement, I see little sense in stressing the "variational" aspect. Also, I know of no method that would be variational in this second sense, but not in the first sense.

Reference

1. Troy Van Voorhis and Martin Head-Gordon. J. Chem. Phys. 2000, 113, 8873.

In the most general case, CC can be understood simply as a prescription for a trial wave function (ansatz) that uses the exponential excitation operators. This ansatz can be then optimized variationally, and this is variational CC. It is much more expensive than the common CC that uses another approximation (besides the ansatz), which linearizes the CC amplitude equations in a certain way. In most cases, this is a good approximation.

"Variational" means that a method has some ansatz for the wave function which is optimized (varied) to get the minimal energy. This is then guaranteed to be greater or equal to the true energy by the variational principle. In this sense, the common CCSD is not variational even for two-electron systems: there is no energy that would be optimized in the procedure.

Perhaps you could understand "variational" as a method that is in some way guaranteed to always give an energy greater or equal to the true energy. In general, the non-variational CC is not such a method. But for two-electron systems, CCSD is exact, so technically, it is variational in this other derived sense. But as it is exact, which is a stronger statement, I see little sense in stressing the "variational" aspect. Also, I know of no method that would be variational in this second sense, but not in the first sense.

In the most general case, CC can be understood simply as a prescription for a trial wave function (ansatz) that uses the exponential excitation operators. This ansatz can be then optimized variationally, and this is variational CC.^[1] It is much more expensive than the common CC that uses another approximation (besides the ansatz), which linearizes the CC amplitude equations in a certain way. In most cases, this is a good approximation.

"Variational" means that a method has some ansatz for the wave function which is optimized (varied) to get the minimal energy. This is then guaranteed to be greater or equal to the true energy by the variational principle. In this sense, the common CCSD is not variational even for two-electron systems: there is no energy that would be optimized in the procedure.

Perhaps you could understand "variational" as a method that is in some way guaranteed to always give an energy greater or equal to the true energy. In general, the non-variational CC is not such a method. But for two-electron systems, CCSD is exact, so technically, it is variational in this other derived sense. But as it is exact, which is a stronger statement, I see little sense in stressing the "variational" aspect. Also, I know of no method that would be variational in this second sense, but not in the first sense.

Reference

1. Troy Van Voorhis and Martin Head-Gordon. J. Chem. Phys. 2000, 113, 8873.