Blog Entry © Wednesday, September 3, 2025, by James Pate Williams, Jr. Solution of Exercise 1.11 in Modern Quantum Chemistry an Introduction to Advanced Electronic Structure Theory © 1996 by Attila Szabo and Neil S. Ostlund

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// EigenVV2x2.cpp (c) Wednesday, September 3, 2025
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Solution to Exercise 1.11 in "Quantum Chemistry
// an Introduction to Advanced Electronic Structure
// Theory (c) 1996 by Attila Szabo and Neil S. Ostlund 

#include "pch.h"
#include "framework.h"
#include "EigenVV2x2.h"

#define MAX_LOADSTRING 100

// Global Variables:
HINSTANCE hInst;                                // current instance
WCHAR szTitle[MAX_LOADSTRING];                  // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING];            // the main window class name
std::wstring text;                              // output wide string

// Forward declarations of functions included in this code module:
ATOM                MyRegisterClass(HINSTANCE hInstance);
BOOL                InitInstance(HINSTANCE, int);
LRESULT CALLBACK    WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    About(HWND, UINT, WPARAM, LPARAM);

int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
                     _In_opt_ HINSTANCE hPrevInstance,
                     _In_ LPWSTR    lpCmdLine,
                     _In_ int       nCmdShow)
{
    UNREFERENCED_PARAMETER(hPrevInstance);
    UNREFERENCED_PARAMETER(lpCmdLine);

    // TODO: Place code here.

    // Initialize global strings
    LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
    LoadStringW(hInstance, IDC_EIGENVV2X2, szWindowClass, MAX_LOADSTRING);
    MyRegisterClass(hInstance);

    // Perform application initialization:
    if (!InitInstance (hInstance, nCmdShow))
    {
        return FALSE;
    }

    HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_EIGENVV2X2));

    MSG msg;

    // Main message loop:
    while (GetMessage(&msg, nullptr, 0, 0))
    {
        if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
        {
            TranslateMessage(&msg);
            DispatchMessage(&msg);
        }
    }

    return (int) msg.wParam;
}

//
//  FUNCTION: MyRegisterClass()
//
//  PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
    WNDCLASSEXW wcex;

    wcex.cbSize = sizeof(WNDCLASSEX);

    wcex.style          = CS_HREDRAW | CS_VREDRAW;
    wcex.lpfnWndProc    = WndProc;
    wcex.cbClsExtra     = 0;
    wcex.cbWndExtra     = 0;
    wcex.hInstance      = hInstance;
    wcex.hIcon          = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_EIGENVV2X2));
    wcex.hCursor        = LoadCursor(nullptr, IDC_ARROW);
    wcex.hbrBackground  = (HBRUSH)(COLOR_WINDOW+1);
    wcex.lpszMenuName   = MAKEINTRESOURCEW(IDC_EIGENVV2X2);
    wcex.lpszClassName  = szWindowClass;
    wcex.hIconSm        = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

    return RegisterClassExW(&wcex);
}

//
//   FUNCTION: InitInstance(HINSTANCE, int)
//
//   PURPOSE: Saves instance handle and creates main window
//
//   COMMENTS:
//
//        In this function, we save the instance handle in a global variable and
//        create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
   hInst = hInstance; // Store instance handle in our global variable

   HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);

   if (!hWnd)
   {
      return FALSE;
   }

   ShowWindow(hWnd, nCmdShow);
   UpdateWindow(hWnd);

   return TRUE;
}

#define IDC_STATIC1         1000
#define IDC_STATIC2         1010
#define IDC_STATIC3         1020
#define IDC_STATIC4         1030

#define IDC_EDIT_A11        2000
#define IDC_EDIT_A12        2010
#define IDC_EDIT_A21        2020
#define IDC_EDIT_A22        2030
#define IDC_EDIT_MULTILINE  3000

#define IDC_BUTTON_COMPUTE  4000
#define IDC_BUTTON_CANCEL   4010

//
//  FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
//  PURPOSE: Processes messages for the main window.
//
//  WM_COMMAND  - process the application menu
//  WM_PAINT    - Paint the main window
//  WM_DESTROY  - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    static HFONT hFont = { };
    static HWND hEditMultiline = { };
    static HWND hEditA11 = { };
    static HWND hEditA12 = { };
    static HWND hEditA21 = { };
    static HWND hEditA22 = { };

    switch (message)
    {
    case WM_CREATE:
    {
        hFont = CreateFont(16, 0, 0, 0, FW_NORMAL, FALSE, FALSE, FALSE,
            ANSI_CHARSET, OUT_DEFAULT_PRECIS, CLIP_DEFAULT_PRECIS,
            DEFAULT_QUALITY, DEFAULT_PITCH | FF_SWISS, L"Courier New Bold");

        CreateWindowEx(0, L"STATIC", L"A[1][1]:", WS_CHILD | WS_VISIBLE,
            10, 10, 80, 20, hWnd, (HMENU)IDC_STATIC1, hInst, NULL);
        CreateWindowEx(0, L"STATIC", L"A[1][2]:", WS_CHILD | WS_VISIBLE,
            10, 40, 80, 20, hWnd, (HMENU)IDC_STATIC2, hInst, NULL);
        CreateWindowEx(0, L"STATIC", L"A[2][1]:", WS_CHILD | WS_VISIBLE,
            10, 70, 80, 20, hWnd, (HMENU)IDC_STATIC3, hInst, NULL);
        CreateWindowEx(0, L"STATIC", L"A[2][2]:", WS_CHILD | WS_VISIBLE,
            10, 100, 80, 20, hWnd, (HMENU)IDC_STATIC4, hInst, NULL);

        hEditA11 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
            100, 10, 200, 20, hWnd, (HMENU)IDC_EDIT_A11, hInst, NULL);
        hEditA12 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
            100, 40, 200, 20, hWnd, (HMENU)IDC_EDIT_A12, hInst, NULL);
        hEditA21 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
            100, 70, 200, 20, hWnd, (HMENU)IDC_EDIT_A21, hInst, NULL);
        hEditA22 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
            100, 100, 200, 20, hWnd, (HMENU)IDC_EDIT_A22, hInst, NULL);

        hEditMultiline = CreateWindowEx(
            WS_EX_CLIENTEDGE,                       // Extended style for sunken border
            TEXT("EDIT"),                           // Class name
            TEXT(""),                               // Initial text (can be blank)
            WS_CHILD | WS_VISIBLE | WS_VSCROLL | ES_AUTOHSCROLL |
            ES_LEFT | ES_MULTILINE | ES_AUTOVSCROLL | WS_HSCROLL | WS_VSCROLL,
            310, 10, 300, 300,                      // Position and size
            hWnd,                                   // Parent window handle
            (HMENU)IDC_EDIT_MULTILINE,              // Unique control ID
            hInst,                                  // Application instance
            NULL                                    // Extra parameter
        );

        CreateWindowEx(0, L"BUTTON", L"Compute", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
            10, 130, 80, 30, hWnd, (HMENU)IDC_BUTTON_COMPUTE, hInst, NULL);
        CreateWindowEx(0, L"BUTTON", L"Cancel", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
            220, 130, 80, 30, hWnd, (HMENU)IDC_BUTTON_CANCEL, hInst, NULL);

        SendMessage(hEditMultiline, WM_SETFONT, (WPARAM)hFont, TRUE);
        SetDlgItemText(hWnd, IDC_EDIT_A11, L"3");
        SetDlgItemText(hWnd, IDC_EDIT_A12, L"1");
        SetDlgItemText(hWnd, IDC_EDIT_A21, L"1");
        SetDlgItemText(hWnd, IDC_EDIT_A22, L"3");
    }
    break;
    case WM_COMMAND:
        {
            int wmId = LOWORD(wParam);
            // Parse the menu selections:
            switch (wmId)
            {
            case IDM_ABOUT:
                DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
                break;
            case IDC_BUTTON_COMPUTE:
            {
                WCHAR line[128] = L"";

                text = L"";

                // eigenvalues
                std::vector<double> omega(3);
                // matrix
                std::vector<std::vector<double>> A(3,
                    std::vector<double>(3));
                std::vector<std::vector<double>> B(3,
                    std::vector<double>(3));
                // eigenvectors
                std::vector<std::vector<double>> c(3,
                    std::vector<double>(3));

                GetWindowText(hEditA11, line, 128);
                std::wstring A11Str(line);
                A[1][1] = std::stod(A11Str);
                GetWindowText(hEditA12, line, 128);
                std::wstring A12Str(line);
                A[1][2] = std::stod(A12Str);
                GetWindowText(hEditA21, line, 128);
                std::wstring A21Str(line);
                A[2][1] = std::stod(A21Str);
                GetWindowText(hEditA22, line, 128);
                std::wstring A22Str(line);
                A[2][2] = std::stod(A22Str);
                
                double term1 = A[1][1] + A[2][2];
                double term2 = pow(A[2][2] - A[1][1], 2.0);
                double term3 = 4.0 * A[1][2] * A[2][1];

                // compute eigenvalues

                omega[1] = 0.5 * (term1 - sqrt(term2 + term3));
                omega[2] = 0.5 * (term1 + sqrt(term2 + term3));

                swprintf_s(line, L"Eigenvalues:\r\n\r\n");
                text += std::wstring(line);
                swprintf_s(line, L"omega 1 = %13.10lf\r\n", omega[1]);
                text += std::wstring(line);
                swprintf_s(line, L"omega 2 = %13.10lf\r\n\r\n", omega[2]);
                text += std::wstring(line);

                // compute eigenvalues using a unitary transformation 
                // matrix A must be symmetric

                double theta0 = 0.0;

                if (A[1][1] == A[2][2])
                {
                    theta0 = 0.5 * acos(0.0);
                }

                else
                {
                    theta0 = 0.5 * atan(2.0 * A[1][2] /
                        (A[1][1] - A[2][2]));
                }

                // compute the eigenvalues
                
                omega[1] = A[1][1] * pow(cos(theta0), 2.0) +
                    A[2][2] * pow(sin(theta0), 2.0) +
                    A[1][2] * sin(2.0 * theta0);
                omega[2] = A[1][1] * pow(cos(theta0), 2.0) +
                    A[2][2] * pow(sin(theta0), 2.0) -
                    A[1][2] * sin(2.0 * theta0);
                
                swprintf_s(line, L"Eigenvalues:\r\n\r\n");
                text += std::wstring(line);
                swprintf_s(line, L"omega 1 = %13.10lf\r\n", omega[1]);
                text += std::wstring(line);
                swprintf_s(line, L"omega 2 = %13.10lf\r\n\r\n", omega[2]);
                text += std::wstring(line);

                // compute eigenvectors

                c[1][1] = cos(theta0);
                c[1][2] = sin(theta0);
                c[2][1] = sin(theta0);
                c[2][2] = -cos(theta0);

                swprintf_s(line, L"Eigenvectors:\r\n\r\n");
                text += std::wstring(line);
                swprintf_s(line, L"c 11 = %13.10lf\r\n", c[1][1]);
                text += std::wstring(line);
                swprintf_s(line, L"c 12 = %13.10lf\r\n", c[1][2]);
                text += std::wstring(line);
                swprintf_s(line, L"c 21 = %13.10lf\r\n", c[2][1]);
                text += std::wstring(line);
                swprintf_s(line, L"c 22 = %13.10lf\r\n", c[2][2]);
                text += std::wstring(line);
                SetWindowText(hEditMultiline, text.c_str());
                break;
            }
            case IDC_BUTTON_CANCEL:
            {
                PostQuitMessage(0);
                break;
            }
            break;
            case IDM_EXIT:
                DestroyWindow(hWnd);
                break;
            default:
                return DefWindowProc(hWnd, message, wParam, lParam);
            }
        }
        break;
    case WM_PAINT:
        {
            PAINTSTRUCT ps;
            HDC hdc = BeginPaint(hWnd, &ps);
            // TODO: Add any drawing code that uses hdc here...
            EndPaint(hWnd, &ps);
        }
        break;
    case WM_DESTROY:
        PostQuitMessage(0);
        break;
    default:
        return DefWindowProc(hWnd, message, wParam, lParam);
    }
    return 0;
}

// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    switch (message)
    {
    case WM_INITDIALOG:
        return (INT_PTR)TRUE;

    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    }
    return (INT_PTR)FALSE;
}

Author: jamespatewilliamsjr

Blog Entry © Wednesday, September 3, 2025, by James Pate Williams, Jr. Solution of Exercise 1.11 in Modern Quantum Chemistry an Introduction to Advanced Electronic Structure Theory © 1996 by Attila Szabo and Neil S. Ostlund

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Blog Entry © Sunday, August 24, 2025, by James Pate Williams, Jr. Corrections to New Quantum Chemical Total Molecular Ground-State Energies for the Helium Hydride Cation (a Hetero Nuclear molecule) and the Hydrogen Molecule (a Homo Nuclear Molecule)

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