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Exhibit (a)(1)(iv)​
Offer by
TORTOISE ENERGY INFRASTRUCTURE
CORPORATION
To Purchase for Cash
up to 5% of the Fund’s Outstanding Shares of
Common Stock
THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M.,
NEW YORK CITY TIME, ON NOVEMBER 1, 2022 UNLESS THE OFFER TO PURCHASE
IS EXTENDED
THIS OFFER TO PURCHASE IS NOT CONDITIONED ON ANY MINIMUM NUMBER OF SHARES BEING TENDERED, BUT IS SUBJECT TO OTHER CONDITIONS AS OUTLINED IN THE OFFER TO PURCHASE AND IN THE LETTER OF TRANSMITTAL.
October 3, 2022​
To Our Clients:
Enclosed for your consideration is the Offer to Purchase, dated October 3, 2022, of Tortoise Energy Infrastructure Corporation, a Maryland corporation registered under the Investment Company Act of 1940, as amended, as a closed-end, non-diversified management investment company (the “Fund”), and a related Letter of Transmittal (which together constitute the “Offer”), pursuant to which the Fund is offering to repurchase up to 5% of the Fund’s outstanding shares of Common Stock, par value $0.001 per share (the “Shares”), upon the terms and conditions set forth in the Offer.
Tortoise Capital Advisors, L.L.C. (“Tortoise”) serves as the Fund’s Investment Manager. Tortoise is a limited liability company organized under the laws of Delaware on October 4, 2002 and a registered investment adviser under the Investment Advisers Act of 1940. The principal business address of Tortoise is 6363 College Boulevard, Suite 100A, Overland Park, KS 66211.
The Offer to Purchase and the Letter of Transmittal are being forwarded to you for your information only and cannot be used by you to tender Shares held by us for your account. We are the holder of record of Shares held for your account. A tender of such Shares can be made only by us as the holder of record and only pursuant to your instructions.
Your attention is called to the following:
(1) The purchase price to be paid for the Shares is an amount per Share equal to 98% of the net asset value per Share as determined by the Fund at the close of regular trading on the New York Stock Exchange on November 1, 2022 or such later date to which the Offer is extended (the “Expiration Date”). The Fund’s Shares have at times traded at a premium to the Fund’s net asset value per Share. It may not be in a Stockholder’s interest to tender Shares in connection with the Offer if the Shares are trading at a premium. The market price of the Shares can and does fluctuate. Accordingly, on the Expiration Date, the market price of the Shares may be above or below the Fund’s net asset value per Share. The Fund’s net asset value and the market price of the Fund’s Common Stock, can be obtained on our website at https://cef.tortoiseecofin.com/​ or from Georgeson LLC, the Fund’s Information Agent, by calling toll free at 1-877-278-9672.
(2) The Offer is not conditioned upon any minimum number of Shares being tendered.
(3) If the Offer is not suspended or postponed, the Fund will purchase all Shares validly tendered prior to 5:00 p.m., New York City time, on the Expiration Date, provided that the number of Shares tendered by all stockholders does not exceed 5% of the Fund’s outstanding Shares. In the event that more than 5% of the Fund’s outstanding Shares are tendered, the Fund will purchase 5% of the Fund’s outstanding Shares on a pro rata basis.

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(4) Tendering Stockholders will not be obligated to pay brokerage commissions or, subject to Instruction 7, “Stock Transfer Taxes,” of the Letter of Transmittal, stock transfer taxes on the purchase of Shares by the Fund pursuant to the Offer.
(5) Your instructions to us should be forwarded in ample time before the Expiration Date to permit us to submit a tender on your behalf. Instructions received after this date will not be honored.
If you wish to have us tender any or all of your Shares, please so instruct us by completing, executing and returning to us the instruction form set forth below. An envelope to return your instructions to us is enclosed. If you authorize tender of your Shares, all such Shares will be tendered unless otherwise specified below. YOUR INSTRUCTIONS TO US SHOULD BE FOR- WARDED AS PROMPTLY AS POSSIBLE IN ORDER TO PERMIT US TO SUBMIT A TENDER ON YOUR BEHALF IN ACCORDANCE WITH THE TERMS AND CONDITIONS OF THE OFFER.
The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any jurisdiction in which the making or acceptance of the Repurchase Offer would not be in compliance with the applicable law.
Neither the Fund, its Board of Directors nor the Investment Manager to the Fund is making any recommendation to any Stockholder whether to tender or refrain from tendering Shares in the Offer. Each Stockholder is urged to read and evaluate the Offer and accompanying materials carefully.

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INSTRUCTIONS
The undersigned acknowledge(s) receipt of your letter, and the enclosed Offer to Purchase, dated October 3, 2022 relating to Tortoise Energy Infrastructure Corporation (the “Fund”) to purchase up to 5% of the Fund’s outstanding shares of Common Stock, par value $0.001 per share (the “Shares”).
This will instruct you to tender to the Fund the number of Shares indicated below (which are held by you for the account of the undersigned), upon the terms and subject to the conditions set forth in the Offer to Purchase that you have furnished to the undersigned.

​ | ​ | AGGREGATE NUMBER OF SHARES TO BE TENDERED: | ​ | ​
​ | ​ | Shares | ​ | ​
​ | ​ | Enter number of Shares to be tendered. | ​ | ​