examples - description of functions of conditionally negative type on a group

Recall that a kernel conditionaly of negative type on a set $X$ is a map $psi:Xtimes Xrightarrowmathbb{R}$ with the following properties:

1) $psi(x,x)=0$

2) $psi(y,x)=psi(x,y)$

3) for any elements $x_1,...x_n$ and all real numbers $c_1,...,c_n$, with $c_1+...+c_n=0$, the following inequality holds:
$$
sum_{i=1}^{n}sum_{j=1}^{n}
c_ic_jpsi(x_i,x_j)leq 0.
$$

Let $G$ be a discrete group.
Recall that a function $Grightarrow mathbb{R}$ is conditionally of
negative type if the kernel $psi$, defined by $psi(g,h)= psi(h^{−1}g)$ is conditionaly of negative type.

Does there exist class of discrete groups which admit an explicit description of functions which are conditionaly of negative type?