Atri Mukhopadhyay

Correlation problem in open-shell atoms and molecules. A non-perturbative linked cluster formulation

In this paper we present a non-perturbative approach to the calculation of correlation energies of open-shell systems. The formulation utilizes an Ursell-type expansion about a multi-determinant starting wavefunction. We have proved a theorem which enables us to derive an effective hamiltonian for the system consisting entirely of linked terms. In the symmetry-degenerate case this effective hamiltonian acts within the subspace of a set of symmetry-degenerate functions, and generates the energy eigenvalues of the system. The present theory has been cast in a diagrammatic language which facilitates the analysis of the correlation problem. The workability of the theory has been tested on a 4 π electron problem, transbutadiene, for which we have calculated the lowest π-π* singlet and triplet energies. The agreement between the results of the present theory and that found from a full CI calculation is excellent. The desirable feature of the theory is that the effective hamiltonian is energy-independent. We hav...

Applications of a non-perturbative many-body formalism to general open-shell atomic and molecular problems: calculation of the ground and the lowest π-π* singlet and triplet energies and the first ionization potential of trans-butadiene

In this paper we explore the feasibility of widening the scope of the non-perturbative open-shell many-body formalism recently developed by us [1], which utilizes an Ursell type of cluster expansion about certain starting wavefunctions spanning a model space. We show that, by generalizing the definition of the cluster expansion operator, we can incorporate into the model space (a) determinants differing widely in energy and (b) determinants differing in their number of electrons. This flexibility is useful for the calculation of difference energies of interest, like transition energies and ionization potentials of atomic and molecular systems. The generalized scheme has been tested on the 4π-electron problem trans-butadiene for which, by choosing a very general model space, we have calculated the energies of the ground, the lowest π-π* singlet and triplet and the first ionization potential by choosing a single composite cluster expansion operator for all states. Results for some more restricted choice of ...

A non-perturbative open-shell theory for atomic and molecular systems: application to transbutadiene

A non-perturbative theory is proposed in this article in which an energy independent effective Hamiltonian is obtained for open-shell systems. We have given a diagrammatic version of theory to facilitate the analysis of the problem. The theory has been applied to a model 4-π electron problem, for calculating the lowestπ-π* singlet and triplet energy levels of transbutadiene. Comparison with full Cl calculation indicates the excellent workability of the theory.

Professor Sisir Kumar Mitra (1890–1963)

Sisir Kumar Mitra was born in Konnagar, Hooghly, near Calcutta, on 24 October 1890. He was the third son of Joykrishna Mitra and Saratkumari Mitra. His father was a school teacher and a learned man. He was also a close associate of Pandit Ishwar Chandra Vidyasagar, Pandit Shiv Nath Sastry, Bipin Chandra Pal and other progressive thinkers. Mitra’s mother, Saratkumari, completed her medical training from Campbell Medical School, Calcutta in 1892, and got a job at Lady Dufferin Hospital, at Bhagalpur, Bihar. Consequently, the family shifted, and Joykrishna Mitra started working at the Bhagalpur Municipality.

Sir Asutosh Mookerjee (1864–1924)

Sir Asutosh Mookerjee (1864–1924) is well-known as a great educationist, a legal luminary, a peerless vice-chancellor and, above all, a builder of institutions. He transformed the University of Calcutta from a provincial affiliating and examination centre to an outstanding seat of teaching and research in Asia. This is a story of a man of indomitable courage, his abiding perseverance and dynamic dreaming.

Professor Satyendra Nath Bose (1894–1974)

Satyendra Nath Bose (Fig. 5.1), popularly known as Satyen Bose, was born the eldest and the only son of Surendranath and Amodini, in Calcutta, on 1 January 1894. Bose had six younger sisters. His father was a trained accountant in the Executive Engineering Department of the East Indian Railways and mother Amodini was a housewife.

Professor Meghnad Saha (1893–1956)

Meghnad Saha was born on 6 October 1893, to a poor family in Sheoratali, a village 30 miles north of Dhaka in the Dhaka District of the then undivided Bengal of India.

Sir Kariamanickam Srinivasa Krishnan (1898–1961)

K.S. Krishnan was born on 4 December 1898 in the village of Vizhupanoor, close to the temple town of Srivilliputtur, in the present-day Tamil Nadu. Krishnan’s father, Srinivasa Iyengar, was a Brahmin farmer-scholar of the old school, deeply knowledgeable in Tamil and Sanskrit religious literature. Krishnan’s mother, Nachiyar Ammal, was a lady of strong character and took care of the family’s social and domestic duties and looked after the agricultural lands and property. The family had a strong religious and scholastic tradition. From his father, Krishnan had inherited an abiding love for religion, philosophy and had a thorough knowledge of Tamil and Sanskrit literature and language. After the early demise of his father, Krishnan’s mother took the responsibility of bringing up the children and educating her sons.

Professor Debendra Mohan Bose (1885–1975)

Debendra Mohan Bose was born on 26 November 1885 in an educated, cultured Brahmo family in Calcutta. His father Dr. Mohini Mohan Bose was a homoeopathic doctor trained in the USA. His mother Subarnaprova Bose was inclined towards social service and child welfare. One of his paternal uncles, Ananda Mohan Bose, was the first Indian Wrangler in the Mathematical Tripos of Cambridge University. His maternal uncle was the pioneer Indian scientist Acharya Jagadis Chandra Bose (J.C. Bose), whose discoveries in Physics and Botany are world-renowned. Since Debendra Mohan and his brother Sudhanshu Mohan lost their father at an early age, his maternal uncle Acharya Jagadish Chandra Bose (J.C. Bose) closely monitored their academic upbringing.

Sir Chandrasekhara Venkata Raman (1888–1970)

Chandrasekhara Venkata Raman (C.V. Raman) was born on 7 November 1888, in a village called Tiruvanaikkaval in the present state of Tamil Nadu. His father Chandrasekhara Iyer came from an agrarian Brahmin family but had the courage and determination to break away from the age-old family tradition. He received Western education and became a teacher. Raman’s father had studied Science and Mathematics.