Consider the algebraic subset \({\mathcal L}\subset\bigwedge^{2}\mathfrak{g}^\ast\otimes\mathfrak{g}= \mathbb{R}^{(n^3-n^2)/2}\) of all Lie brackets on a fixed real \(n\)-dimensional vector space \(\mathfrak{g}\). Each \(\mu\in{\mathcal L}\) defines a connected and simply connected Lie group \(G_\mu\) endowed with the left invariant Riemannian metric induced by a fixed inner product \(\) on \(\mathfrak{g}\). The set of all left invariant Riemannian metrics on \(G_\mu\) is identified with the orbit \({\mathcal O}_\mu=\text{Gl}(n,\mathbb{R}).\mu\). By degeneration \(\mu\rightarrow\lambda\) of one Lie algebra \(\mu\in{\mathcal L}\) to another Lie algebra \(\lambda\in{\mathcal L}\) is meant that \(\lambda\) belongs to the closure of \({{\mathcal O}_\mu}\) in \(\mathbb{R}^{(n^3-n^2)/2}\). On \({\mathcal L}\) a functional \(F\) is defined by \(\mu\rightarrow F(\mu)=\text{tr} \mathbf{R}_\mu^2\), where \(\mathbf{R}_\mu\) is a symmetric transformation defined in terms of the Ricci curvature operator of \(\mu\). Then, the limits of the flow lines of the gradient flow of \(F\) are degenerations of their starting points. This property of \(F\) is used to obtain interesting relations between the space of all left invariant metrics on \(n\)-dimensional connected and simply connected Lie groups and critical points of \(F:\) (1) \(G_\mu\) has only one left invariant Riemannian metric up to isometry and scaling if and only if the only possible degeneration of \(\mu\) is \(0\). (2) If \(\mu\) degenerates to \(\lambda\) and \(G_\lambda\) admits a left invariant Riemannian metric satisfying a pinched curvature condition then the same holds for \(G_\mu\). (3) The orbit \(\text{Sl}(n,\mathbb{R}).\mu\) is closed if and only if \(G_\mu\) has left invariant Riemannian metric such that its curvature tensor is a multiple of the identity. The closed \(\text{Sl}(n,\mathbb{R})\)-orbits of \({\mathcal L}\) are classified. Explicit 1-parameter families of mutually non-isometric Einstein solvmanifolds of dimensions 10 and 11 respectively are derived from curves of closed orbits of a representation of \(\bigwedge^2\text{Sl}(m,\mathbb{R})\otimes\text{Sl}(n,\mathbb{R})\).