We describe an alternative procedure for obtaining
approximate Brueckner orbitals in *ab initio*
electronic structure theory. Whereas approximate Brueckner
orbitals have traditionally been obtained by mixing the
orbitals until the coefficients of singly substituted
determinants in the many-electron wavefunction become zero,
we remove singly substituted determinants at the outset and
obtain orbitals which minimize the total electronic energy.
Such orbitals may be described as variational Brueckner
orbitals. These two procedures yield the same set of exact
Brueckner orbitals in the full configuration interaction
limit but differ for truncated wavefunctions. We consider
the simplest variant of this approach in the context of
coupled-cluster theory, optimizing orbitals for the
coupled-cluster doubles (CCD) model. An efficient new
method is presented for solving the coupled equations
defining the energy, doubles amplitudes, and orbital mixing
parameters. Results for several small molecules indicate
nearly identical performance between the traditional
Brueckner CCD method and the variational Brueckner orbital
CCD approach. However, variational Brueckner orbitals offer
certain advantages: they simplify analytic gradients by
removing the need to solve the coupled-perturbed Brueckner
coupled-cluster equations for the orbital response, and
their straightforward extensions for inactive orbitals
suggests possible uses in size-extensive models of
nondynamical electron correlation. Application to
O_{4}^{+} demonstrates the utility of
variational Brueckner orbitals in symmetry breaking cases.