It has been noted in several sources (e.g. J. Romero *et al.* Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. [arXiv:1701.02691](https://arxiv.org/abs/1701.02691) **[quant-ph]**) that one of the disadvantages of the Coupled Cluster method for the description of electron correlation is that, since $e^T$ in 
$$E_\mathrm{CC} = \langle0|e^{-T}He^T|0\rangle$$ isn't unitary, the method isn't variational (the energy obtained by solving CC equations isn't a rigorous upper bound to the exact energy). 

Could someone please explain to me the connection between non-unitarity of $e^T$ and the method not being variational.