.. tip:: All input files can be downloaded: :download:`Files `. nosi ====== .. contents:: :local: This option defines the implementation details of nonothorgonal state interaction (NOSI) calculations for excited and diabaitc states. .. option:: offdiag_correlation .. list-table:: :stub-columns: 1 :widths: 5 20 * - Value - ``overlap_weighted`` Will use overlap weighted method * - - ``energy_weighted`` Will use energy weighted method * - - ``correlation_potential`` Will use correlation functional method, given by the ``xc_functional`` option * - Default - ``overlap_weighted`` Define the off-diagonal correlation method. .. option:: xc_functional .. list-table:: :stub-columns: 1 :widths: 5 20 * - Value - A valid exchange-correlation functional name * - Default - None When ``offdiag_correlation`` is set to ``correlation_potential``, this option is required to specify the exchange-correlation functional to be used. All valid functional names are available in :doc:`scf`. .. option:: zero_threshold .. list-table:: :stub-columns: 1 :widths: 5 20 * - Value - A real number * - Default - ``1.E-6`` When the overlap of two orbitals is smaller than this value, they will be treated as zero .. warning:: Do not set a too large value (like ``1.E-4``). It may leads to wrong results. .. option:: files .. list-table:: :stub-columns: 1 :widths: 5 20 * - Value - One or more file names * - Default - None List the mwfn file names of the determinants to be read. .. option:: spin_filp .. list-table:: :stub-columns: 1 :widths: 5 20 * - Value - One or more file names * - Default - None List of determinants to perform spin flip (alpha to beta and beta to alpha). .. warning:: Only supported when the numbers of alpha electrons and beta electrons number equal. For example, in the following input: .. code-block:: bash :linenos: nosi files det1.mwfn det2.mwfn det3.mwfn spin_filp det2.mwfn det3.mwfn end In this case, **5** determinants will be used for NOSI calculations: - det1.mwfn - det2.mwfn - det3.mwfn - det2.mwfn (spin flipped) - det3.mwfn (spin flipped) Theoretical Background ------------------------- XXXXXX Input Examples -------------------- Example: Excited States of (E)-Dimethyldiazene (Manually) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this example, we will calculate the ground state and 2 singlet excited states of (E)-Dimethyldiazene with TSO-DFT methods. Then, we will calculate the NOSI for these 3 states. We will use B3LYP/cc-pVTZ level of theory. .. tip:: Acutally, in Qbics, the calculation of excited states using TSO+NOSI can be automatically done by a keyword ``msdft``, see :doc:`msdft` for details. In the following examples, we will calculate the ground and excited states of (E)-Dimethyldiazene using TSO-DFT methods, details of which can be found in :doc:`../tutorials/tso1` and :doc:`./scfguess`. - dma-s0.inp: Ground state; - dma-s1.inp: S\ :sub:`1` state, corresponding to HOMO (16) → LUMO (17) transition; - dma-s2.inp: S\ :sub:`2` state, corresponding to HOMO-1 (15) → LUMO (17) transition. .. tabs:: .. tab:: dma-s0.inp .. code-block:: bash :linenos: :caption: dma-s0.inp basis cc-pvtz end scf charge 0 spin2p1 1 type U # For TSO-DFT, unrestricted SCF is preferred. end mol N -0.11855722 0.06367877 -0.00010027 N 1.11855814 -0.06366086 -0.00010026 C 1.81864333 1.22402113 0.00009549 H 1.12816980 2.07452976 0.00011126 H 2.46787129 1.25512096 0.88302715 H 2.46820089 1.25538193 -0.88260363 C -0.81864582 -1.22402070 0.00009559 H -0.12816015 -2.07453667 0.00011125 H -1.46787530 -1.25512668 0.88303320 H -1.46820496 -1.25538766 -0.88260977 end task energy b3lyp end .. tab:: dma-s1.inp .. code-block:: bash :linenos: :caption: dma-s1.inp basis cc-pvtz end scf charge 0 spin2p1 1 type U no_scf TSO end # 16->17 scfguess type mwfn file dma-s0.mwfn orb 32 1 1-15 17-204 : 1-203 orb 0 1 16 : 204 end mol N -0.11855722 0.06367877 -0.00010027 N 1.11855814 -0.06366086 -0.00010026 C 1.81864333 1.22402113 0.00009549 H 1.12816980 2.07452976 0.00011126 H 2.46787129 1.25512096 0.88302715 H 2.46820089 1.25538193 -0.88260363 C -0.81864582 -1.22402070 0.00009559 H -0.12816015 -2.07453667 0.00011125 H -1.46787530 -1.25512668 0.88303320 H -1.46820496 -1.25538766 -0.88260977 end task energy b3lyp end .. tab:: dma-s2.inp .. code-block:: bash :linenos: :caption: dma-s2.inp basis cc-pvtz end scf charge 0 spin2p1 1 type U no_scf TSO end # 15->17 scfguess type mwfn file dma-s0.mwfn orb 32 1 1-14 16-204 : 1-203 orb 0 1 15 : 204 end mol N -0.11855722 0.06367877 -0.00010027 N 1.11855814 -0.06366086 -0.00010026 C 1.81864333 1.22402113 0.00009549 H 1.12816980 2.07452976 0.00011126 H 2.46787129 1.25512096 0.88302715 H 2.46820089 1.25538193 -0.88260363 C -0.81864582 -1.22402070 0.00009559 H -0.12816015 -2.07453667 0.00011125 H -1.46787530 -1.25512668 0.88303320 H -1.46820496 -1.25538766 -0.88260977 end task energy b3lyp end After calculation, we can collect the results: .. list-table:: * - State - Energy (Hartree) - Excited Energy (eV) * - S\ :sub:`0` - -189.34737058 - 0 * - S\ :sub:`1` - -189.24112513 - 2.89 * - S\ :sub:`2` - -189.11479416 - 6.33 Since TSO-DFT is a **single-determinant method,** S\ :sub:`1` and S\ :sub:`2` are NOT spin eigenfunctions. To be more accurate, we will use NOSI to get more accurate resutls, using the following 3 input files. They only differ in the ``offdiag_correlation`` option. .. tabs:: .. tab:: nosi-1a.inp .. code-block:: bash :linenos: :caption: nosi-1a.inp basis cc-pvtz end mol N -0.11855722 0.06367877 -0.00010027 N 1.11855814 -0.06366086 -0.00010026 C 1.81864333 1.22402113 0.00009549 H 1.12816980 2.07452976 0.00011126 H 2.46787129 1.25512096 0.88302715 H 2.46820089 1.25538193 -0.88260363 C -0.81864582 -1.22402070 0.00009559 H -0.12816015 -2.07453667 0.00011125 H -1.46787530 -1.25512668 0.88303320 H -1.46820496 -1.25538766 -0.88260977 end nosi offdiag_correlation overlap_weighted files dma-s0.mwfn dma-s1.mwfn dma-s2.mwfn spin_flip dma-s1.mwfn dma-s2.mwfn end task energy nosi end .. tab:: nosi-1b.inp .. code-block:: bash :linenos: :caption: nosi-1b.inp basis cc-pvtz end mol N -0.11855722 0.06367877 -0.00010027 N 1.11855814 -0.06366086 -0.00010026 C 1.81864333 1.22402113 0.00009549 H 1.12816980 2.07452976 0.00011126 H 2.46787129 1.25512096 0.88302715 H 2.46820089 1.25538193 -0.88260363 C -0.81864582 -1.22402070 0.00009559 H -0.12816015 -2.07453667 0.00011125 H -1.46787530 -1.25512668 0.88303320 H -1.46820496 -1.25538766 -0.88260977 end nosi offdiag_correlation energy_weighted files dma-s0.mwfn dma-s1.mwfn dma-s2.mwfn spin_flip dma-s1.mwfn dma-s2.mwfn end task energy nosi end .. tab:: nosi-1c.inp .. code-block:: bash :linenos: :caption: nosi-1c.inp basis cc-pvtz end mol N -0.11855722 0.06367877 -0.00010027 N 1.11855814 -0.06366086 -0.00010026 C 1.81864333 1.22402113 0.00009549 H 1.12816980 2.07452976 0.00011126 H 2.46787129 1.25512096 0.88302715 H 2.46820089 1.25538193 -0.88260363 C -0.81864582 -1.22402070 0.00009559 H -0.12816015 -2.07453667 0.00011125 H -1.46787530 -1.25512668 0.88303320 H -1.46820496 -1.25538766 -0.88260977 end nosi offdiag_correlation correlation_potential xc_functional b3lyp files dma-s0.mwfn dma-s1.mwfn dma-s2.mwfn spin_flip dma-s1.mwfn dma-s2.mwfn end task energy nosi end You should pay attention to the following points: - The basis sets and molecular structure should be the same as the ones used for TSO-DFT calculations. (You can copy the input files from the TSO-DFT calculations.) - If ``offdiag_correlation`` is set to ``correlation_potential``, the ``xc_functional`` option should be set as the same as the ones used for TSO-DFT calculations. In ``files`` option, you should list the mwfn file names of the determinants to be read. In ``spin_flip`` option, you should list the mwfn file names of the determinants that will be used for spin flip. For example, in the above input, ``dma-s1.mwfn`` and ``dma-s2.mwfn`` will be used for spin flip. In this case, the NOSI calculation will be performed for the following 5 determinants: - dma-s0.mwfn - dma-s1.mwfn - dma-s1.mwfn (spin flipped) - dma-s2.mwfn - dma-s2.mwfn (spin flipped) After calculation, we can collect the results. Let's see ``nosi-1a.out`` first: .. code-block:: bash :linenos: :caption: nosi-1a.out Read non-orthogonal determinants: 0 dma-s0.mwfn 1 dma-s1.mwfn Spin flipped: dma-s1.mwfn 2 dma-s2.mwfn Spin flipped: dma-s2.mwfn ... ---- NOSI Overlap Matrix ---- ============================= 0 1 2 3 4 0 1.00000000 0.00000000 -0.00001375 0.00000000 0.00004606 1 0.00000000 1.00000000 0.00000000 0.00000000 -0.00000000 2 -0.00001375 0.00000000 1.00000000 -0.00000000 0.00000000 3 0.00000000 0.00000000 -0.00000000 1.00000000 0.00000000 4 0.00004606 -0.00000000 0.00000000 0.00000000 1.00000000 ---- NO Hamiltonian Matrix Functional ---- ========================================== 0 1 2 3 4 0 -189.34737100 0.00000058 0.00260277 -0.00000192 -0.00871858 1 0.00000058 -189.24112500 0.02084657 0.00000885 0.00001057 2 0.00260277 0.02084657 -189.24112500 0.00001057 0.00000885 3 -0.00000192 0.00000885 0.00001057 -189.11479400 0.09206962 4 -0.00871858 0.00001057 0.00000885 0.09206962 -189.11479400 ---- NOSI Coefficients Matrix (column vectors are eigenvectors) ---- ==================================================================== 0 1 2 3 4 0 -1.00000000 0.00000101 -0.00001030 -0.00001197 0.00003201 1 0.00000657 -0.70710678 -0.70710678 0.00002152 -0.00006937 2 -0.00000575 0.70710678 -0.70710678 -0.00002152 -0.00006937 3 -0.00001417 -0.00002152 0.00006937 -0.70710678 -0.70710678 4 0.00001496 0.00002152 0.00006937 0.70710678 -0.70710678 ---- NOSI Results ---- ====================== State NOSI Energies Excited Energy Osc. Str. DX DY DZ (Hartree) (eV) (a.u.) (a.u.) (a.u.) 0 -189.34737100 0.00000000 0.00000000 42.82332 0.00029 0.00187 1 -189.26197158 2.32371833 0.00000000 0.00003 -0.00001 0.00001 2 -189.22027843 3.45818894 0.00000000 -0.00001 -0.00008 0.00000 3 -189.20686368 3.82320418 0.00000000 0.00000 0.00000 -0.00000 4 -189.02272432 8.83363623 0.93845302 2.85145 0.75310 -0.00001 In ``Read non-orthogonal determinants:``, the determinants are shown: - :math:`\phi_0` dma-s0.mwfn - :math:`\phi_1` dma-s1.mwfn - :math:`\phi_2` dma-s1.mwfn (spin flipped) - :math:`\phi_3` dma-s2.mwfn - :math:`\phi_4` dma-s2.mwfn (spin flipped) In ``NOSI Overlap Matrix``, the matrix elements :math:`\left\langle\phi_i\middle|\phi_j\right\rangle` are calculated. In ``NO Hamiltonian Matrix Functional``, the matrix elements :math:`\left\langle\phi_i\left|\hat{H}\right|\phi_j\right\rangle` are calculated. In ``NOSI Coefficients Matrix``, the column vectors are eigenvectors of the NOSI Hamiltonian matrix. For example, in column ``1``, we have: .. math:: \left|\psi_1\right\rangle = 0.00000101 \left|\phi_0\right\rangle -0.70710678 \left|\phi_1\right\rangle +0.70710678 \left|\phi_2\right\rangle - 0.00002152\left|\phi_3\right\rangle + 0.00002152 \left|\phi_4\right\rangle When a determinant and its spin flipped counterpart are combined with out-of-phases (``-0.70710678`` and ``-0.70710678``), this is a **triplet** state. When a determinant and its spin flipped counterpart are combined with in-phases (``0.70710678`` and ``0.70710678``), this is a **singlet** state. The excited energies are shown in ``NOSI Results``. Now, we can collect resutls from ``nosi-1a.out``, ``nosi-1b.out`` and ``nosi-1c.out`` together to get the final results: .. list-table:: * - State - TSO - Overlap Weighted - Energy Weighted - Correlation Potential * - - Excited Energy (eV) - NOSI Excited Energy (eV) - NOSI Excited Energy (eV) - NOSI Excited Energy (eV) * - S\ :sub:`0` - 0 - 0 - 0 - 0 * - T\ :sub:`1` - N/A - 2.32 - 2.32 - 2.35 * - S\ :sub:`1` - 2.89 - 3.46 - 3.46 - 3.43 * - T\ :sub:`2` - N/A - 3.82 - 3.80 - 5.25 * - S\ :sub:`2` - 6.33 - 8.83 - 8.85 - 7.40 We can see that, the NOSI results are generally improved upon TSO results. The results from overlap- and energy-weighted methods are very close to each other, while the results from correlation potential method are slightly different for high-lying states. For every calculation, a CI coefficient file and a spectrum file are generated. For example, ``nosi-1a-ci.txt`` and ``nosi-1a-spectrum.txt``. Example: Diabatic States of a Transition State ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In :doc:`./opt`, we have calculated the transition state of a S\ :sub:`N`\ 2 reaction. In the following examples, we will calculate the diabatic states of Cl-CH\ :sub:`3`-Cl using TSO-DFT methods, details of which can be found in :doc:`../tutorials/tso2` and :doc:`./scfguess`. - ``diab-1.inp``: Diabatic state of Cl···CH\ :sub:`3`-Cl (reactant complex); - ``diab-2.inp``: Diabatic state of Cl-CH\ :sub:`3`···Cl (product complex); .. tabs:: .. tab:: diab-1.inp .. code-block:: bash :linenos: :caption: diab-1.inp basis def2-svp end scf charge -1 spin2p1 1 type U no_scf tso end scfguess type fragden frag 0 1 1-5 frag -1 1 6 end mol C -2.28626983 4.81332375 -0.81110844 H -1.77793692 3.91128195 -1.11951067 H -1.75817077 5.56455137 -0.24234234 H -3.32378354 4.96301934 -1.07305839 Cl -1.62247473 5.87896571 -2.80504772 Cl -2.93223857 3.76141614 1.19669198 end task energy b3lyp end .. tab:: diab-2.inp .. code-block:: bash :linenos: :caption: diab-2.inp basis def2-svp end scf charge -1 spin2p1 1 type U no_scf tso end scfguess type fragden frag 0 1 1-4 6 frag -1 1 5 end mol C -2.28626983 4.81332375 -0.81110844 H -1.77793692 3.91128195 -1.11951067 H -1.75817077 5.56455137 -0.24234234 H -3.32378354 4.96301934 -1.07305839 Cl -1.62247473 5.87896571 -2.80504772 Cl -2.93223857 3.76141614 1.19669198 end task energy b3lyp end After calculation, we will obtain the reactant and product diabatic states: ``diab-1.mwfn`` and ``diab-2.mwfn``. Now, using NOSI, we can combine them to obtain 2 adiabatic states: .. code-block:: bash :linenos: :caption: nosi-2.inp basis def2-svp end mol C -2.28626983 4.81332375 -0.81110844 H -1.77793692 3.91128195 -1.11951067 H -1.75817077 5.56455137 -0.24234234 H -3.32378354 4.96301934 -1.07305839 Cl -1.62247473 5.87896571 -2.80504772 Cl -2.93223857 3.76141614 1.19669198 end nosi files diab-1.mwfn diab-2.mwfn end task energy nosi end In this case, we do not need assign ``spin_flip`` option since the reactant and product diabatic states are closed shell. In ``nosi...end``, there is no ``offdiag_correlation`` option. This means that the off-diagonal correlation will be calculated using the (default) overlap weighted method. After calculation, we will obtain the adiabatic states: ``nosi-2.out``: .. code-block:: bash :linenos: :caption: nosi-2.out ---- NOSI Overlap Matrix ---- ============================= 0 1 0 1.00000000 0.76098229 1 0.76098229 1.00000000 ---- NO Hamiltonian Matrix Functional ---- ========================================== 0 1 0 -959.99564600 -730.60245583 1 -730.60245583 -959.99557700 ---- NOSI Coefficients Matrix (column vectors are eigenvectors) ---- ==================================================================== 0 1 0 -0.53311086 1.44624356 1 -0.53259535 -1.44643349 ---- Singlet and Triplet Excitation Energies ---- ================================================= Eigenstate 0: -960.03127186 Hartree; Excitation energy: 0.00000000 eV Eigenstate 1: -959.73288097 Hartree; Excitation energy: 8.11963379 eV ---- Singlet State Weights ---- =============================== 0 1 0 0.50027469 0.49972531 1 0.49972531 0.50027469 ---- NOSI Results ---- ====================== State NOSI Energies Excited Energy Osc. Str. DX DY DZ (Hartree) (eV) (a.u.) (a.u.) (a.u.) 0 -960.03127186 0.00000000 0.00000000 -268.39724 567.48539 -94.86319 1 -959.73288097 8.11921604 1.46991870 1.07003 1.72943 -3.26904 We can see that, unlike the excited states, the diabatic states are highly overlapping (In ``NOSI Overlap Matrix``, :math:`S_{01} = 0.76098229`). In ``NOSI Coefficients Matrix``, the column vectors are the **adiabatic states**, indicating that the reactant and product diabatic states are mixed in a 1:1 ratio in both the ground and excited states. The adiabatic state energies are shown here (A standard DFT calculation is also given in ``adiab.inp``): .. list-table:: * - NOSI Adiabatic State 0 - NOSI Adiabatic State 1 - DFT Adiabatic * - -960.03127186 Hartree - -959.73288097 Hartree - -960.05738745 Hartree