BLW-ED:

A Program for Inter-Molecular Interaction

Energy Decomposition Analysis

 

 

Version 1.0

 

Yirong Mo and Jiali Gao

 

Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, U.S.A.

 

 

 

 

 

 

 

Date of this version of module: July 29, 2000

Date of most recent manual update: July 29, 2000

 

Copyright 2000

BLW-ED abstract

BLW-ED is a program for computing energy components of intermolecular interactions.  In this analysis, the total interaction energy of a system is decomposed into electrostatic, exchange, polarization and charge transfer energy terms at the Hartree-Fock level.  The key of this BLW-ED scheme is the definition and the full optimization of the diabatic state wavefunction, where the charge transfer among interacting molecules is deactivated.  An improved feature of the BLW-ED method over other approaches is its stability as the size of basis functions increase.  The BLW program is currently implemented with the use of Gaussian94 checkpoint and integral files, where the electronic primitive integrals are stored.  At the present, only conventional (non direct) SCF procedure is permitted in the computation, and thus, it is limited by a maximum of 255 basis functions (maximum for raffinetti integral format).  The output includes a Gaussian initial guess format, which can be used to generate the electron density cube file and derive various properties (like dipole moment and populations) for the BLW using Gaussian.

 

 

Referencing for BLW-ED

A) J. Chem. Phys. format:

The energy decomposition analysis is carried out using the BLW-ED program.1-2

1.  Y. Mo, J. Gao, S. D. Peyerimhoff, J. Chem. Phys. 112, 5530 (2000).

 

2.  Y. Mo, and J. Gao, BLW-ED version 1.0, University of Minnesota, Minneapolis, M.N., 2000. 

 

B) American Chemical Society format:

The energy decomposition analysis is carried out using the BLW-ED program.1-2

1.      Mo, Y.; Gao, J.; Peyerimhoff, S. D. J. Chem. Phys. 2000, 112, 5530.

2.    Mo, Y.; Gao, J. BLW-ED version 1.0, University of Minnesota, Minneapolis, M.N., 2000.

Availability of BLW-ED

BLW-ED version 1.0 is available upon request from the authors at the University of Minnesota (ymo@chem.umn.edu, or gao@chem.umn.edu).  In the present implementation of the method described in Y. Mo, J. Gao, S. D. Peyerimhoff, J. Chem. Phys. 112, 5530 (2000), BLW-ED makes use of Gaussian94 temporary files, including checkpoint and integral files.  A utility file, g94int, that converts Gaussian94 files into a format for BLW-ED is also distributed .  Although the BLW-ED program is not directly interfaced with Gaussian94, it uses the information and integral files generated by Gaussian94. Thus, users of BLW-ED should have access to Gaussian94 and should obtain a valid license for Gaussian94 from Gaussian, Inc.  


Contents

Title page                                                                                                                               1

BLW-ED abstract                                                                                                                  2

Referencing for BLW-ED                                                                                                       3

Availability of BLW-ED                                                                                                          4

Contents                                                                                                                                 5

1. INTRODUCTION                                                                                                            6

 

2. THEORETICAL BACKGROUND                                                                                   6

2.A.  The block-localized wave function (BLW) method

2.B.   The BLW energy decomposition (BLW-ED) method

3. PROGRAM STRUCTURE                                                                                              12

3.A.  Overall design

4. INSTALLATION OF BLW AND ITS USE                                                                     13

4.A.  Program distribution

4.B.   Installation

5. DESCRIPTION OF INPUT                                                                                            14

6. TEST RUN                                                                                                                      15

1. INTRODUCTION

BLW-ED is a program for analysis of energy components in intermolecular interactions.  Energy decomposition analysis can lead to deeper understanding of intermolecular interactions, and the quantitative results may be used to guide development of empirical, yet computationally fast force fields for biomolecular simulation and modeling. For example, state-of-the-art molecular mechanics force fields for liquid and biopolymer simulations make use of pairwise potentials and fixed partial charges on atoms. There is need to improve these force fields by incorporating explicit many-body polarization terms into the potential energy function.  Furthermore, recent studies using semiempirical divide-and-conquer quantum mechanical methods suggest that charge transfer interactions could be significant in aqueous solvation of biological systems such as proteins. Since these findings have important implications in force field development, an accurate estimate of the polarization and charge transfer interaction as well as the electrostatic component is warranted.  The BLW-ED method analyzes these effects using a block-localized wave function (BLW) technique. 

Although several energy decomposition schemes have been proposed, including the widely used Morokuma scheme, the common difficulty in these approaches is a lack of well-defined diabatic state necessary for computing charge transfer energies.  The diabatic state represents a charge-localized system, corresponding to one of the most stable resonance structures in valence bond theory.   In many cases, computational results on the charge transfer and polarization term are very sensitive to the basis functions used in the computation, often leading to unrealistic predictions if large basis functions are used. In the present BLW-ED method, we define specific diabatic states using a block-localized wave function method.  As a result, the computational results converges with large basis sets.  Similar to the Morokuma scheme, the BLW-ED method separates the total intermolecular interaction energy into electrostatic, exchange, polarization and charge transfer interactions.

 

2. THEORETICAL BACKGROUND

2.A. The block-localized wave function method

            The block-localized wave function (BLW) method is developed to circumvent the delocalized nature of molecular orbitals in Hatree-Fock (HF) theory to study properties of localized, or valence bond-like, electronic structures. Although ab initio valence bond (VB) method can be used to study resonance effect and to define electronic localized states, its computational costs can quickly become intractable and thus prevent applications to large molecular systems.  The BLW method provides a convenient approach to define valence bond-like resonance configurations at the computational cost comparable to HF molecular orbital calculations.

            The method has been described in the following references.

Y. Mo, S. D. Peyerimhoff, J. Chem. Phys. 1998, 109, 1687.

Y. Mo, Y. Zhang, J. Gao, J. Am. Chem. Soc. 1999, 121, 5737.

Y. Mo, J. Gao, J. Phys. Chem. A,  2000, 104, 3012.

 

2.B. The BLW energy decomposition (BLW-ED) method

 

Here, we briefly describe the BLW-ED method.  The interaction energy with the counterpoise correction for the BSSE between two molecules A and B is expressed as

                                                  (1)

where YAB is the overall optimized wave function for the supermolecule AB composed of monomers A and B, whose wave functions are represented by YA0 and YB0 respectively.

            We start from the two monomers YA0 and YB0 and make them approach to the geometry of the dimer AB, by freezing their respective electron densities and suppressing the electron-exchange between the monomers A and B.  At this point the whole system is therefore represented by the Hartree product of YA0 and YB0 as

                                                                                                    (2)

The expectation energy of YABH compared to the sum of the individual energies of monomers A and B is defined as the electrostatic energy DEes

                                                         (3)

The antisymmetry requirement changes YABH to YABBLW0

                                                                                          (4)

which is the initial diabatic state wavefunction for the dimer AB.  The permission for the electron exchange between A and B results in the exchange energy term DEex

                                                                  (5)

which is also called Pauli-exchange repulsion and always positive.  It should be noted that in many cases people use the sum of (4) and (5) in discussions.

            Clearly, the approaching of monomers will perturb their respective electron densities and evolve the initial localized wave function  YABBLW0 to the final localized wave function  YABBLW, and the stabilization energy is ascribed to the polarization effect

                                                                         (6)

In YABBLW the charge-transfer effect between A and B is deactivated and each molecular orbital is expanded in either A or B spaces, as we have discussed in the pretext.  The lift of this restriction allows electrons to move around the whole dimer and correspondingly each molecular orbital will be extend to the both A and B spaces, resulting in the fully delocalized state YAB.  This step is a charge-transfer step.  Since the charge transfer occurs between the occupied localized MOs in A (or B) and the virtual localized MOs in B (or A), the mixing of the localized MOs results in the wavefunction YAB for the dimer, and in this process, the BSSE will be introduced if the adopted basis set is not complete.  Thus, in the BLW-ED scheme, the charge transfer stabilization energy DECT is defined as

                                                                    (7)

 

NOTE:  In the BLW-ED version 1.0, the BSSE is not automatically computed.  Thus, users should carry out this computation separately.           

 

.
3. PROGRAM STRUCTURE

3.A. Overall design

The BLW-ED program makes use of electronic integrals computed by Gaussian94 and carries out BLW-SCF electronic structure calculations.  There is no direct interface between the BLW-ED program and Gaussian94, although it uses the Gaussian utility program formchk and another utility program g94int that translates the Gaussian94 format into that of the BLW-ED format.  These utility programs are used primarily for convenience in other applications.

 

4. INSTALLATION OF BLW AND ITS USE

4.A. Program distribution

     BLW-ED, version 1.0, is distributed by the authors at the University of Minnesota, along with g94int (gao@chem.umn.edu or ymo@chem.umn.edu).  To successfully execute BLW-ED, the user must have access of Gaussian94 and its accompanying utility programs.  Gaussian94 is a licensed program by Gaussian, Inc.

 

4.B. Installation

The user should carry out the following steps:

1.      Obtain the BLW-ED and the g94int utility program (gao@chem.umn.edu or ymo@chem.umn.edu).  Compile blw-ed.f using your FORTRAN compiler, e.g., "f77 –o blw-ed -[optimization options] blw-ed.f"

2.      Obtain the Gaussian programs.  The formchk utility program should have been automatically generated if Gaussian94 has been successfully compiled.

3.      To generate the g94int utility program, first, define the path for the Gaussian94 util.a library in makefile.  Then, run the make file: "make -f makefile". 

 

 

5. DESCRIPTION OF INPUT

Overview

BLW-ED is run using a single script file which (1) execute the Gaussian calculations and generate the necessary integrals, (2) reformat the Gaussian files, and (3) run BLW-ED calculations. Three Gaussian input files are needed for dimer AB, monomers A and B, respectively.  No particular input for the BLW-ED calculations anymore, which will get the information from the checkpoint files of monomers.  Examples are provided in the test jobs.

 

6. TEST RUNS

This section describes one test job. It includes a full input file, initial coordinates that has been previously optimized, and an output file that can be checked against the user's output so that he or she will be confident that the code has performed correctly on his or her machine.

 

 

6.1 Test Job 1 – H3N-BH3 complex

 

            This test job (1) performs a single-point HF/6-31G* calculation for the dimer, (2) reformat the Gaussian integrals for BLW-ED, (3) performs a single-point HF/6-31G* calculation for the monomers, and (4) performs BLW-ED calculation.  It takes roughly 50 seconds on an SGI computer (180 MHz).

 

            6.1A.  Input files

 

            The job file contains the script commands for executing the entire test job calculations.  It generates a number of temporary scratch files and removes them after the job is completed. The Gaussian outputs are written into dimer.out for the H3N-BH3 dimer, monomer_A.out and monomer_B.dat for H3N and BH3, respectively, and BLW-ED output into dimer-blw.out.

 

A very important point is that the geometries (and basis sets) in dimer.out, monomer_A.dat and monomer_B.dat should be consistent. 

 

            The main output of interest in dimer-blw.out reads like

 

     ***************BLW-ED RESULTS***************

 

     Electrostatic Energy Term     =     -90.48                              (kcal/mol)

     Exchange                 Energy Term     =     101.70                              (kcal/mol)

     Polarization  Energy Term     =     -19.43                              (kcal/mol)

     Charge-Transfer      Energy Term     =     -29.51 + BSSE term         (kcal/mol)

 

     Total Interaction      Energy Term     =     -37.72 + BSSE term         (kcal/mol)

 

     ***************BLW-ED RESULTS***************

 

where the BSSE term should be computed separately.  After the “C Matrix” which prints out the block-localized MO’s, there are re-orthogonalized MO’s, which are in GAUSSIAN’s initial guess format (3E20.10).  The latter can be used to generate the cube electron density file and make population analysis using GAUSSIAN.