CH-481 Chemistry and Computers

Transcription

1 CH-481 Chemistry and Computers B. L. Tembe Rm 365, Chemistry Dept We will use the IITB moodle site for out of class interaction Course material can be found in /courses/ch481

2 Course Overview Computers are tools like spectrometers or calorimeters, which are tools for chemists Can compute reasonable information on molecular and macroscopic (bulk) systems Old statement chemistry is an experimental science Computational chemistry is now an accepted branch of chemistry

3 Today s lecture About Computers to the unexposed Hardware and software Algorithms and Programs Programming languages Operatining systems Login/Passwords Files Chemical Applications of computers

4 Your Working Area on the computer Login/password Directories Files- program files, data files, video files executable files, booting files, music files For creating and saving you need an editor We will use vi or pico in linux. Pico is easier for beginners. Type pico filename to create/edit a file named filename

5 Operating systems Windows (Proprietary Software) Linux (Public Domain/Free) Installation of the software Upgradation You may register and take the linux short term courses available in the Institute from time to time

6 Programming Languages C, C++,.. Java Visual Basic, Fortran Pascal SQL

7 Fortran: Formula Translation y = x ½ y = sqrt (x) y = x cubed y = x ** x or x* x * x cos (x) tan (x) alog (x), alog10 (x) y = (x**3)**4 y = asin (x)

8 5 important rules in fortran Start program statement from 7 th column and do not use tabs Line numbers in columns 1 to 5 Continuation character in column 6 c in first column implies a comment (not part of the program s executable statement variables starting with i,j,k,l,m,n are integers

9 algorithms Unambigous sequence of steps/statements for carrying out any task A good algorithm a prerequsite for a program Eg: direction to go to your house in your home-town a) go to CSTM station b) take a train to Darjeeling c) reach 33, Tensing St, Dargeeling

10 A sample program c my first program (this is a comment card/line) program myprogm (this is an optional line) c input an integer read(*,*) n c sum integers from 1 to n msum = 0 do 10 i = 1,n ( this is a do or for loop, for repeated operations) msum = msum + i 10 continue Write (*,*) n, msum stop end c use all small case letters for convenience

11 Summary Introduction to computers Algorithms and programs Operating systems A sample program NOT DONE Compiling a programme: f77 prog.f Executing a program./a.out Two lab batches: 2 to 4 pm, 4 to 6 pm

12 Review of Last Lecture Introduction to computers Algorithms and programs Operating systems A sample program What was not done DONE: Compiling a programme: f77 prog.f Executing a program./a.out

13 Types of Files Fortran Files: prog.f, qchem.f, stats.f. C program files: prog.c, nmr.c,. Data files: kinetics.dat, mydata1, Executable files:./a.out prog.exe How to compile programs f77 prog.f This creates a file./a.out gcc prog.c,,,, To run a program, just type./a.out

14 Algorithms, Flow Charts and Programs For our purpose, these are three representations of the problem that we need to solve, the last one, being the most useful Unambigous sequence of steps/statements for carrying out any task A flow chart outlines or presents the algorithm in such a way that the flow of control of execution (recall traffic signals and police men) is clearly visible.

15 Example of a flow chart Conversion of energy into different units Input the value of energy in kcal/mol, = x In how many other units do you want energy to be calculated? none Ej = x * 4.18/(1000* * 10**(23) ) Eev= x/23.06 Eau = Eev/27.2

16 A program for the precious task C read the value of energy in kcal/mol read (*,*) x eev = x / eau = eev/27.06 ej = x * 4.18 / (1000 * * 10 **23) write (*,*) energy in kcal/mol, ev, au, j) write (*,*) x, eev, eau, ej stop end

17 Elementary functions in Fortran y = x + z / c + a * b p = sin (theta) + alog (conc) q = exp (-energy/(boltz*temp)) r = d ** f t = sqrt (23.0) a = a + b z = acos (y)

18 Summary of second lecture Reviewed the first lecture Types of files, compilation and execution Algorithms, flowcharts and program Next Lecture Algorithm for the sine function Calculation of the sine function Main ingredients of programs Convergence and iterations

19 An Algorithm for calculation of the sine function Sin (x) = x x 3 /3! + x 5 /5! x 7 /7! + x 9 /9! How to construct an algorithm for the series? Observe the trends in the terms 1) as n (no of terms) increases, terms become small; i.e, the series may converge 2) Each successive term can be obtained from the previous term by multiplying by x 2 and dividing by (n+1) x (n + 2), ie, we can iterate

20 Algorithm for sin (x) Get the value x in radians Initialize the value of sum (of terms) Calculate successive terms Add successive terms to the sum If the value of the sum does not change by more than say, 10 ** (-10) by adding a new term, stop the addition of successive terms Print the value of the sum and the no. of terms

21 Programme to calculate sin (x) C program sinex write(*,*) input the value of theta in deg x = theta * / sum = 0.0 term = x denom = 1.0 nterm = 1 10 sum = sum + term denom = denom term = -term * x * x / (denom * (denom-1)) nterm = nterm + 1 if ( (abs (term).gt. 10**(-10) ) go to 10 write(*,*) nterm, sum, fortran sine fn ftsnfu = sin (x) write(*,*) nterm, sum,ftsnfn stop end

22 Steps in the algorithm/flowchart sum = x, denom = 1, term = x, nterms = 1 denom = denom + 2 term = - term * x * x /(denom * (denom -1) ) sum = sum + term nterms = nterms + 1 Is term < 10 ** (-10) Write sum, nterms stop

23 Elementary Principles or ingredients of Computer Programming Input Output Declaration statements Execution statements Iterative statements or loops Control of transfer ( if or while statements) Functions, subprograms or Procedures End of lines, functions or subroutines

24 Calculation of the value of sin (x) at 101 equispaced points c calculate the value of sin (x) at 101 equispaced points between 0 and 2pi (including the end points). twopi = 2.0 * do 10 i =1, 101 x = real (i-1) * 0.01 * twopi y = sin (x) write (*, *) x and sin (x) =, x, y c the above statement can be improved) 10 continue end

25 What you are expected to learn in this course Run elementary programs for calculating Fibonacci series, the sine function, energy conversion factors, arrranging numbers is ascending order, solve a quadratic eq., elementary interpolation and integration, matrix multiplication, reading and writing to files, and Using scilabto diagonalize matrices, plot elementary wavefunctions, and solve differential equations.

26 do 10 i =1, 100, 1 the last part 1 indicates that i is incremented by 1 every time. If we want to increment the variable i in steps of 2, we use do 10 i =1, 100, 2 executable statements 10 continue There are other alternatives to the do statement such as sum = 0.0 do i=1, 100,2 sum = sum +(real (i))**3 end do Computer treats real numbers and integers very differently

27 Observe the graph

28 We need to write a program which gives the value of f (x) as per the above formula. This is given below. read (*, *) x if (x.lt.0.0) then funct = 0.0 else if (0.0.le. x.and. x.lt. 5.0) then funct = 5.0 else if (5.0.le. x.and. x.lt. 10.0) then funct = 10.0 else funct = x endif write (*,*) x, funct= ', x, funct end c the above program illustrates the use of the if statement

29 Solution of a quadratic equation The general form of the quadratic equation is a x * x + bx + c The roots of this equation are [ - b + (b * b 4.0 * a * c) **(-1/2) ] / ( 2*a) [ - b - (b * b 4.0 * a * c) **(-1/2) ] / ( 2*a)

30 program quadratic c program quadratic write (*, *) 'input the values of a, b and c:' read (*, *) a, b, c if ((a.eq. 0.0).and. (b.ne. 0.0)) then x = -c/b twoa=2.0*a write (*, *) 'the solution of linear equation x=', x go to 100 else if ((a.eq. 0.0).and. (b.eq. 0.0)) then write (*, *) 'both coefficients a and b are zero' go to 100 endif

31 ww = b * b * a * c if (ww.lt. 0.0) then go to 50 else rtofww = sqrt (ww) root1 =( -b + rtofww) / twoa root2 =( -b - rtofww) / twoa write (*, *) 'real roots 1 and 2 are', root1, root2 go to 100 endif 50 continue c the roots are complex b**2-4 * a * c is -ve ww = 4.0 * a * c - b * b rtofww = sqrt (ww) realpt = -b / twoa ximpt = rtofww / twoa write (*, *) 'complex roots' write (*, *) 'root1', 'real part=', realpt, 'imaginary part=', ximpt ximpt2 = -ximpt write (*, *) 'root2', 'real part=', realpt, 'imaginary part=', ximpt2 100 continue end

32 Summary: The main ingredients of a program 1) an instructionto carry out a mathematical operation (such as evaluating a formula for a given value of a variable), 2) repeatinga calculation until a conditionis satisfied, 3) allocation of storagespace for calculated quantities such as matrices 4) reading inputsfrom files and writing the output to files as well as the computer screen, 5) terminatingthe program either on completion or giving messages if something has gone wrong with the execution of the program.

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