(* Linear H3-Molecule, identical to p.27-29 of Gertrude F. Neumark,
PhD thesis Columbia University, New York, 1951  
parametrized with 6-31G(d,p): E = -1.6018, d = 0.932 *)
c = {kinf -> 1.255, eefact -> 0.7686};
T = kinf*1.125/P^2+kinf*2.25/Q^2
Vne = -3/(2*P)-(3-(R+Q)^2/P^2)/P-2/(R+2*Q)-(3-R^2/Q^2)/Q-2/Q
Vnn = 2/(R+Q)+1/(2*(R+Q))
Vee = eefact*2*(1-(3/20)*(P/Q)^2+(1/32)*(P/Q)^3)/Q+1/(2*Q)
func = T+Vne+Vnn+Vee /. c;

N[t = FindMinimum[func,{P,1.9},{Q,1.5},{R,0.2}],20]
u = t[[2]];
N[ (Vnn+Vne+Vee)/T /. c /. u ]
N[ (Q+R)*0.529177 /. u ]
plot1=Graphics[{
Circle[{0,0},P],Circle[{-Q,0},Q],
Circle[{Q,0},Q],Disk[{Q+R,0},0.08],
Disk[{-Q-R,0},0.08],Disk[{0,0},0.08],
Line[{{-Q-R,0},{Q+R,0}}]}] /. u

Show[plot1,{AspectRatio->Automatic}]