Task: Fix basis order issue in molden.load (issue #1961) (pyscf/pyscf#1963)

org: pyscf
repo: pyscf
pr_number: 1963
issue_title: Fix basis order issue in molden.load (issue #1961)
resolved_issues: number: 1961
title: Re-ordering basis functions introduces mismatch
body: #1620 introduced ordering basis functions if they are not ordered correctly. When using `molden.load` to load molecules from molden files, the MO coefficients are not ordered accordingly, which leads to a mismatch and therefore wrong results. 
One example would be the minimally augmented basis sets (like ma-def2-SVP) from ORCA, which have some s-type AOs appended after the p-type AOs from the standard def2-SVP.

The code has changed significantly since #1620, which makes fixing the problem a bit harder.

Reference solution:
fix_patch: diff --git a/pyscf/gto/mole.py b/pyscf/gto/mole.py
index c8e460afef..b515875dee 100644
--- a/pyscf/gto/mole.py
+++ b/pyscf/gto/mole.py
@@ -419,7 +419,7 @@ def str2atm(line):
     return list(zip(z, c.tolist()))
 
 #TODO: sort exponents
-def format_basis(basis_tab):
+def format_basis(basis_tab, sort_basis=True):
     '''Convert the input :attr:`Mole.basis` to the internal data format.
 
     ``{ atom: [(l, ((-exp, c_1, c_2, ..),
@@ -457,10 +457,16 @@ def format_basis(basis_tab):
     fmt_basis = {}
     for atom, atom_basis in basis_tab.items():
         symb = _atom_symbol(atom)
-        fmt_basis[symb] = basis_converter(symb, atom_basis)
-
-        if len(fmt_basis[symb]) == 0:
+        _basis = basis_converter(symb, atom_basis)
+        if len(_basis) == 0:
             raise BasisNotFoundError('Basis not found for  %s' % symb)
+
+        # Sort basis accroding to angular momentum. This is important for method
+        # decontract_basis, which assumes that basis functions with the same
+        # angular momentum are grouped together. Related to issue #1620 #1770
+        if sort_basis:
+            _basis = sorted([b for b in _basis if b], key=lambda b: b[0])
+        fmt_basis[symb] = _basis
     return fmt_basis
 
 def _generate_basis_converter():
@@ -503,11 +509,6 @@ def converter(symb, raw_basis):
                     _basis.extend(nparray_to_list(rawb))
         else:
             _basis = nparray_to_list(raw_basis)
-
-        # Sort basis accroding to angular momentum. This is important for method
-        # decontract_basis, which assumes that basis functions with the same
-        # angular momentum are grouped together. Related to issue #1620 #1770
-        _basis = sorted([b for b in _basis if b], key=lambda b: b[0])
         return _basis
     return converter
 
@@ -654,6 +655,8 @@ def _to_full_contraction(mol, bas_idx):
             bas_idx = ib0 + numpy.where(mol._bas[ib0:ib1,ANG_OF] == l)[0]
             if len(bas_idx) == 0:
                 continue
+            if bas_idx[0] + len(bas_idx) != bas_idx[-1] + 1:
+                raise NotImplementedError('Discontinuous bases of same angular momentum')
 
             mol_exps, b_coeff = _to_full_contraction(mol, bas_idx)
             nprim, nc = b_coeff.shape
@@ -2523,11 +2526,13 @@ def build(self, dump_input=True, parse_arg=ARGPARSE,
         if self.verbose >= logger.WARN:
             self.check_sanity()
 
-        self._atom = self.format_atom(self.atom, unit=self.unit)
+        if self.atom:
+            self._atom = self.format_atom(self.atom, unit=self.unit)
         uniq_atoms = {a[0] for a in self._atom}
 
-        _basis = _parse_default_basis(self.basis, uniq_atoms)
-        self._basis = self.format_basis(_basis)
+        if self.basis:
+            _basis = _parse_default_basis(self.basis, uniq_atoms)
+            self._basis = self.format_basis(_basis)
         env = self._env[:PTR_ENV_START]
         self._atm, self._bas, self._env = \
                 self.make_env(self._atom, self._basis, env, self.nucmod,
@@ -2643,30 +2648,12 @@ def _build_symmetry(self, *args, **kwargs):
                            for ir in self.irrep_id]
         return self
 
-    @lib.with_doc(format_atom.__doc__)
-    def format_atom(self, atom, origin=0, axes=None, unit='Ang'):
-        return format_atom(atom, origin, axes, unit)
-
-    @lib.with_doc(format_basis.__doc__)
-    def format_basis(self, basis_tab):
-        return format_basis(basis_tab)
-
-    @lib.with_doc(format_pseudo.__doc__)
-    def format_pseudo(self, pseudo_tab):
-        return format_pseudo(pseudo_tab)
-
-    @lib.with_doc(format_ecp.__doc__)
-    def format_ecp(self, ecp_tab):
-        return format_ecp(ecp_tab)
-
-    @lib.with_doc(expand_etb.__doc__)
-    def expand_etb(self, l, n, alpha, beta):
-        return expand_etb(l, n, alpha, beta)
-
-    @lib.with_doc(expand_etbs.__doc__)
-    def expand_etbs(self, etbs):
-        return expand_etbs(etbs)
-    etbs = expand_etbs
+    format_atom = staticmethod(format_atom)
+    format_basis = staticmethod(format_basis)
+    format_pseudo = staticmethod(format_pseudo)
+    format_ecp = staticmethod(format_ecp)
+    expand_etb = staticmethod(expand_etb)
+    expand_etbs = etbs = staticmethod(expand_etbs)
 
     @lib.with_doc(make_env.__doc__)
     def make_env(self, atoms, basis, pre_env=[], nucmod={}, nucprop=None):
diff --git a/pyscf/tools/molden.py b/pyscf/tools/molden.py
index 8d0ac4e48f..07862101be 100644
--- a/pyscf/tools/molden.py
+++ b/pyscf/tools/molden.py
@@ -239,8 +239,16 @@ def read_one_bas(lsym, nb, fac=1):
         elif dat[0].upper() in 'SPDFGHIJ':
             basis[symb].append(read_one_bas(*dat))
 
-    mol.basis = envs['basis'] = basis
     mol.atom = [atoms[i] for i in atom_seq]
+    uniq_atoms = {a[0] for a in mol.atom}
+
+    # To avoid the mol.build() sort the basis, disable mol.basis and set the
+    # internal data _basis directly. It is a workaround to solve issue #1961.
+    # Mole.decontract_basis function should be rewritten to support
+    # discontinuous bases that have the same angular momentum.
+    mol.basis = {}
+    _basis = gto.mole._parse_default_basis(basis, uniq_atoms)
+    mol._basis = envs['basis'] = gto.format_basis(_basis, sort_basis=False)
     return mol
 
 def _parse_mo(lines, envs):
@@ -353,6 +361,8 @@ def load(moldenfile, verbose=0):
             else:
                 sys.stderr.write('Unknown section %s\n' % sec_title)
 
+    mo_energy, mo_coeff, mo_occ, irrep_labels, spins = None, None, None, None, None
+
     for sec_kind in _SEC_ORDER:
         if sec_kind == 'MO' and 'MO' in sec_kinds:
             if len(sec_kinds['MO']) == 1:
@@ -392,6 +402,8 @@ def load(moldenfile, verbose=0):
     if isinstance(mo_occ, tuple):
         mol.spin = int(mo_occ[0].sum() - mo_occ[1].sum())
 
+    if not mol._built:
+        mol.build(0, 0)
     return mol, mo_energy, mo_coeff, mo_occ, irrep_labels, spins
 
 parse = read = load
@@ -503,8 +515,9 @@ def remove_high_l(mol, mo_coeff=None):
     '''
     pmol = mol.copy()
     pmol.basis = {}
+    pmol._basis = {}
     for symb, bas in mol._basis.items():
-        pmol.basis[symb] = [b for b in bas if b[0] <= 4]
+        pmol._basis[symb] = [b for b in bas if b[0] <= 4]
     pmol.build(0, 0)
     if mo_coeff is None:
         return pmol, None