Add an entirely complex but hermitian splitting by Suzuki

Prog/splittings.f90

@@ -428,23 +428,21 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(34)%Vcoeffs(5) = splits(34)%Vcoeffs(3)
     splits(34)%Vcoeffs(6) = splits(34)%Vcoeffs(2)
 
-    ! A hermitian method as given in Suzuki 1990
-    call createsplit(splits(35), 6, 6)
+    ! A hermitian fourth order method as given in Suzuki 1990
+    call createsplit(splits(35), 5, 5)
     alpha = CMPLX(1.D0/2.D0, Sqrt(3.D0)/6.D0, kind=kind(0.D0))
     beta =  CMPLX(1.D0/2.D0, 0.2071067811865, dp)
-    splits(35)%Tcoeffs(1) = 
-    splits(35)%Tcoeffs(2) = 
-    splits(35)%Tcoeffs(3) = 
-    splits(35)%Tcoeffs(4) = 
-    splits(35)%Tcoeffs(5) = 
-    splits(35)%Tcoeffs(6) = 
+    splits(35)%Tcoeffs(1) = Conjg(alpha*beta)/2.D0
+    splits(35)%Tcoeffs(2) = conjg(beta)/2.D0
+    splits(35)%Tcoeffs(3) = (beta*conjg(alpha) +  Conjg(beta)*alpha)/2
+    splits(35)%Tcoeffs(4) = beta/2.0
+    splits(35)%Tcoeffs(5) = beta*alpha/2.D0
 
     splits(35)%Vcoeffs(1) = 0.D0
-    splits(35)%Vcoeffs(2) = 
-    splits(35)%Vcoeffs(3) = 
-    splits(35)%Vcoeffs(4) = 
-    splits(35)%Vcoeffs(5) = 
-    splits(35)%Vcoeffs(6) = 
+    splits(35)%Vcoeffs(2) = Conjg(alpha*beta)
+    splits(35)%Vcoeffs(3) = Conjg(beta)*alpha
+    splits(35)%Vcoeffs(4) = beta*conjg(alpha)
+    splits(35)%Vcoeffs(5) = beta*alpha
 
 end subroutine
 end module splittings