diff --git a/CHANGELOG.md b/CHANGELOG.md
index e5ba49e..f46ded0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,10 +7,15 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ## [Unreleased]
 ### Changed
 - vdW radii scaling parameter can now be adjusted via `mindlessgen.toml` or CLI
+- better type hints for `Callables`
 
 ### Fixed
 - Unit conversion for (currenly unused) vdW radii from the original Fortran project
-- minor print output issues (no new line breaks...)
+- minor print output issues (no new line breaks, more consistent verbosity differentiation, ...)
+- bug in `postprocess_mol` which led to an unassigned return variable in the single-point case
+
+### Added
+- Support for the novel "g-xTB" method (working title: GP3-xTB)
 
 ## [0.4.0] - 2024-09-19
 ### Changed
diff --git a/src/mindlessgen/generator/main.py b/src/mindlessgen/generator/main.py
index e8d4c13..237d1ec 100644
--- a/src/mindlessgen/generator/main.py
+++ b/src/mindlessgen/generator/main.py
@@ -4,12 +4,13 @@
 
 from __future__ import annotations
 
+from collections.abc import Callable
 from pathlib import Path
 import multiprocessing as mp
 import warnings
 
 from ..molecules import generate_random_molecule, Molecule
-from ..qm import XTB, get_xtb_path, QMMethod, ORCA, get_orca_path
+from ..qm import XTB, get_xtb_path, QMMethod, ORCA, get_orca_path, GP3, get_gp3_path
 from ..molecules import iterative_optimization, postprocess_mol
 from ..prog import ConfigManager
 
@@ -41,12 +42,15 @@ def generator(config: ConfigManager) -> tuple[list[Molecule] | None, int]:
 
     # Import and set up required engines
     refine_engine: QMMethod = setup_engines(
-        config.refine.engine, config, get_xtb_path, get_orca_path
+        config.refine.engine,
+        config,
+        get_xtb_path,
+        get_orca_path,  # GP3 cannot be used anyway
     )
 
     if config.general.postprocess:
         postprocess_engine: QMMethod | None = setup_engines(
-            config.postprocess.engine, config, get_xtb_path, get_orca_path
+            config.postprocess.engine, config, get_xtb_path, get_orca_path, get_gp3_path
         )
     else:
         postprocess_engine = None
@@ -273,8 +277,9 @@ def header(version: str) -> str:
 def setup_engines(
     engine_type: str,
     cfg: ConfigManager,
-    xtb_path_func,
-    orca_path_func,
+    xtb_path_func: Callable,
+    orca_path_func: Callable,
+    gp3_path_func: Callable | None = None,
 ):
     """
     Set up the required engine.
@@ -295,5 +300,12 @@ def setup_engines(
         except ImportError as e:
             raise ImportError("orca not found.") from e
         return ORCA(path, cfg.orca)
+    elif engine_type == "gp3":
+        if gp3_path_func is None:
+            raise ImportError("No callable function for determining the gp3 path.")
+        path = gp3_path_func()
+        if not path:
+            raise ImportError("'gp3' binary could not be found.")
+        return GP3(path)
     else:
         raise NotImplementedError("Engine not implemented.")
diff --git a/src/mindlessgen/molecules/postprocess.py b/src/mindlessgen/molecules/postprocess.py
index 543285d..17f6ae4 100644
--- a/src/mindlessgen/molecules/postprocess.py
+++ b/src/mindlessgen/molecules/postprocess.py
@@ -34,6 +34,7 @@ def postprocess_mol(
     else:
         try:
             engine.singlepoint(mol, verbosity=verbosity)
+            postprocmol = mol
         except RuntimeError as e:
             raise RuntimeError(
                 "Single point calculation in postprocessing failed."
diff --git a/src/mindlessgen/molecules/refinement.py b/src/mindlessgen/molecules/refinement.py
index 638df9b..291c1a9 100644
--- a/src/mindlessgen/molecules/refinement.py
+++ b/src/mindlessgen/molecules/refinement.py
@@ -68,7 +68,7 @@ def iterative_optimization(
                     )
                 break  # Stop if the atom counts are the same as in the previous cycle
         if len(fragmols) == 1:
-            if verbosity > 0:
+            if verbosity > 1:
                 print(
                     f"Only one fragment detected in cycle {cycle + 1}. "
                     + f"Stopping at cycle {cycle + 1}."
diff --git a/src/mindlessgen/prog/config.py b/src/mindlessgen/prog/config.py
index 6562729..491b4b7 100644
--- a/src/mindlessgen/prog/config.py
+++ b/src/mindlessgen/prog/config.py
@@ -497,7 +497,7 @@ def engine(self, engine: str):
         """
         if not isinstance(engine, str):
             raise TypeError("Postprocess engine should be a string.")
-        if engine not in ["xtb", "orca"]:
+        if engine not in ["xtb", "orca", "gp3"]:
             raise ValueError("Postprocess engine can only be xtb or orca.")
         self._engine = engine
 
diff --git a/src/mindlessgen/qm/__init__.py b/src/mindlessgen/qm/__init__.py
index 18cc01a..a5e8e3a 100644
--- a/src/mindlessgen/qm/__init__.py
+++ b/src/mindlessgen/qm/__init__.py
@@ -5,5 +5,14 @@
 from .base import QMMethod
 from .xtb import XTB, get_xtb_path
 from .orca import ORCA, get_orca_path
+from .gp3 import GP3, get_gp3_path
 
-__all__ = ["XTB", "get_xtb_path", "QMMethod", "ORCA", "get_orca_path"]
+__all__ = [
+    "XTB",
+    "get_xtb_path",
+    "QMMethod",
+    "ORCA",
+    "get_orca_path",
+    "GP3",
+    "get_gp3_path",
+]
diff --git a/src/mindlessgen/qm/gp3.py b/src/mindlessgen/qm/gp3.py
new file mode 100644
index 0000000..0ca4d40
--- /dev/null
+++ b/src/mindlessgen/qm/gp3.py
@@ -0,0 +1,180 @@
+"""
+This module contains all interactions with the GP3-xTB binary
+for next-gen tight-binding calculations.
+"""
+
+import subprocess as sp
+import shutil
+from pathlib import Path
+from tempfile import TemporaryDirectory
+
+from ..molecules import Molecule
+from .base import QMMethod
+
+
+class GP3(QMMethod):
+    """
+    This class handles all interaction with the GP3 external dependency.
+    """
+
+    def __init__(self, path: str | Path) -> None:
+        """
+        Initialize the GP3 class.
+        """
+        if isinstance(path, str):
+            self.path: Path = Path(path).resolve()
+        elif isinstance(path, Path):
+            self.path = path
+        else:
+            raise TypeError("gp3_path should be a string or a Path object.")
+
+    def singlepoint(self, molecule: Molecule, verbosity: int = 1) -> str:
+        """
+        Perform a single-point calculation using GP3-xTB.
+        """
+
+        # Create a unique temporary directory using TemporaryDirectory context manager
+        with TemporaryDirectory(prefix="gp3_") as temp_dir:
+            temp_path = Path(temp_dir).resolve()
+            # write the molecule to a temporary file
+            molecule.write_xyz_to_file(str(temp_path / "molecule.xyz"))
+
+            # run gp3
+            arguments = [
+                "-c",
+                "molecule.xyz",
+            ]
+            # dump molecule.charge and molecule.uhf to a file
+            if molecule.charge != 0:
+                with open(temp_path / ".CHRG", "w", encoding="utf-8") as f:
+                    f.write(str(molecule.charge))
+            if molecule.uhf != 0:
+                with open(temp_path / ".UHF", "w", encoding="utf-8") as f:
+                    f.write(str(molecule.uhf))
+
+            if verbosity > 2:
+                print(f"Running command: gp3 {' '.join(arguments)}")
+
+            gp3_log_out, gp3_log_err, return_code = self._run(
+                temp_path=temp_path, arguments=arguments
+            )
+            if verbosity > 2:
+                print(gp3_log_out)
+            if return_code != 0:
+                raise RuntimeError(
+                    f"GP3-xTB failed with return code {return_code}:\n{gp3_log_err}"
+                )
+
+            return gp3_log_out
+
+    def check_gap(
+        self, molecule: Molecule, threshold: float = 0.5, verbosity: int = 1
+    ) -> bool:
+        """
+        Check if the HL gap is larger than a given threshold.
+
+        Arguments:
+        molecule (Molecule): Molecule to check
+        threshold (float): Threshold for the gap
+
+        Returns:
+        bool: True if the gap is larger than the threshold, False otherwise
+        """
+
+        # Perform a single point calculation
+        try:
+            gp3_out = self.singlepoint(molecule)
+        except RuntimeError as e:
+            raise RuntimeError("Single point calculation failed.") from e
+
+        # Parse the output to get the gap
+        hlgap = None
+        for line in gp3_out.split("\n"):
+            if "gap (eV)" in line and "dE" not in line:
+                # check if "alpha->alpha" is present in the same line
+                # then, the line looks as follows:
+                # gap (eV)  alpha->alpha  :        7.02263204
+                if "alpha->alpha" in line:
+                    hlgap = float(line.split()[4])
+                    break
+                # otherwise, the line looks as follows:
+                # gap (eV)                :        9.06694119
+                hlgap = float(line.split()[3])
+                break
+        if hlgap is None:
+            raise ValueError("GP3-xTB gap not determined.")
+
+        if verbosity > 1:
+            print(f"GP3-xTB HOMO-LUMO gap: {hlgap:5f}")
+
+        return hlgap > threshold
+
+    def optimize(
+        self, molecule: Molecule, max_cycles: int | None = None, verbosity: int = 1
+    ) -> Molecule:
+        """
+        Optimize a molecule using GP3-xTB.
+        """
+        raise NotImplementedError("Optimization is not yet implemented for GP3-xTB.")
+
+    def _run(self, temp_path: Path, arguments: list[str]) -> tuple[str, str, int]:
+        """
+        Run GP3-xTB with the given arguments.
+
+        Arguments:
+        arguments (list[str]): The arguments to pass to GP3-xTB.
+
+        Returns:
+        tuple[str, str, int]: The output of the GP3-xTB calculation (stdout and stderr)
+                              and the return code
+        """
+        try:
+            gp3_out = sp.run(
+                [str(self.path)] + arguments,
+                cwd=temp_path,
+                capture_output=True,
+                check=True,
+            )
+            # get the output of the GP3-xTB calculation (of both stdout and stderr)
+            gp3_log_out = gp3_out.stdout.decode("utf8")
+            gp3_log_err = gp3_out.stderr.decode("utf8")
+            if (
+                "no SCF convergence" in gp3_log_out
+                or "nuclear repulsion" not in gp3_log_out
+            ):
+                raise sp.CalledProcessError(
+                    1,
+                    str(self.path),
+                    gp3_log_out.encode("utf8"),
+                    gp3_log_err.encode("utf8"),
+                )
+            return gp3_log_out, gp3_log_err, 0
+        except sp.CalledProcessError as e:
+            gp3_log_out = e.stdout.decode("utf8")
+            gp3_log_err = e.stderr.decode("utf8")
+            return gp3_log_out, gp3_log_err, e.returncode
+
+
+# TODO: 1. Convert this to a @staticmethod of Class GP3
+#       2. Rename to `get_method` or similar to enable an abstract interface
+#       3. Add the renamed method to the ABC `QMMethod`
+#       4. In `main.py`: Remove the passing of the path finder functions as arguments
+#          and remove the boiler plate code to make it more general.
+def get_gp3_path(binary_name: str | Path | None = None) -> Path:
+    """
+    Get the path to the GP3 binary based on different possible names
+    that are searched for in the PATH.
+    """
+    default_gp3_names: list[str | Path] = ["gp3", "gp3_dev"]
+    # put binary name at the beginning of the lixt to prioritize it
+    if binary_name is not None:
+        binary_names = [binary_name] + default_gp3_names
+    else:
+        binary_names = default_gp3_names
+    # Get gp3 path from 'which gp3' command
+    for binpath in binary_names:
+        which_gp3 = shutil.which(binpath)
+        if which_gp3:
+            gp3_path = Path(which_gp3).resolve()
+            return gp3_path
+    raise ImportError("'gp3' binary could not be found.")
diff --git a/src/mindlessgen/qm/xtb.py b/src/mindlessgen/qm/xtb.py
index 163b936..60d3afd 100644
--- a/src/mindlessgen/qm/xtb.py
+++ b/src/mindlessgen/qm/xtb.py
@@ -76,7 +76,7 @@ def optimize(
 
     def singlepoint(self, molecule: Molecule, verbosity: int = 1) -> str:
         """
-        Optimize a molecule using xtb.
+        Perform a single-point calculation using xtb.
         """
 
         # Create a unique temporary directory using TemporaryDirectory context manager
@@ -97,7 +97,7 @@ def singlepoint(self, molecule: Molecule, verbosity: int = 1) -> str:
                 arguments += ["--uhf", str(molecule.uhf)]
 
             if verbosity > 2:
-                print(f"Running command: {' '.join(arguments)}")
+                print(f"Running command: xtb {' '.join(arguments)}")
 
             xtb_log_out, xtb_log_err, return_code = self._run(
                 temp_path=temp_path, arguments=arguments
@@ -141,7 +141,7 @@ def check_gap(
         if hlgap is None:
             raise ValueError("HOMO-LUMO gap not determined.")
         if verbosity > 1:
-            print(f"HOMO-LUMO gap: {hlgap:5f}")
+            print(f"xTB HOMO-LUMO gap: {hlgap:5f}")
 
         if hlgap > threshold:
             return True